Identifier
-
Mp00107:
Semistandard tableaux
—catabolism⟶
Semistandard tableaux
St000737: Semistandard tableaux ⟶ ℤ
Values
=>
Cc0019;cc-rep-0
Cc0019;cc-rep
[[1,2]]=>[[1,2]]=>1
[[2,2]]=>[[2,2]]=>2
[[1],[2]]=>[[1,2]]=>1
[[1,3]]=>[[1,3]]=>1
[[2,3]]=>[[2,3]]=>2
[[3,3]]=>[[3,3]]=>3
[[1],[3]]=>[[1,3]]=>1
[[2],[3]]=>[[2,3]]=>2
[[1,1,2]]=>[[1,1,2]]=>1
[[1,2,2]]=>[[1,2,2]]=>1
[[2,2,2]]=>[[2,2,2]]=>2
[[1,1],[2]]=>[[1,1,2]]=>1
[[1,2],[2]]=>[[1,2,2]]=>1
[[1,4]]=>[[1,4]]=>1
[[2,4]]=>[[2,4]]=>2
[[3,4]]=>[[3,4]]=>3
[[4,4]]=>[[4,4]]=>4
[[1],[4]]=>[[1,4]]=>1
[[2],[4]]=>[[2,4]]=>2
[[3],[4]]=>[[3,4]]=>3
[[1,1,3]]=>[[1,1,3]]=>1
[[1,2,3]]=>[[1,2,3]]=>1
[[1,3,3]]=>[[1,3,3]]=>1
[[2,2,3]]=>[[2,2,3]]=>2
[[2,3,3]]=>[[2,3,3]]=>2
[[3,3,3]]=>[[3,3,3]]=>3
[[1,1],[3]]=>[[1,1,3]]=>1
[[1,2],[3]]=>[[1,2,3]]=>1
[[1,3],[2]]=>[[1,2],[3]]=>1
[[1,3],[3]]=>[[1,3,3]]=>1
[[2,2],[3]]=>[[2,2,3]]=>2
[[2,3],[3]]=>[[2,3,3]]=>2
[[1],[2],[3]]=>[[1,2],[3]]=>1
[[1,1,1,2]]=>[[1,1,1,2]]=>1
[[1,1,2,2]]=>[[1,1,2,2]]=>1
[[1,2,2,2]]=>[[1,2,2,2]]=>1
[[2,2,2,2]]=>[[2,2,2,2]]=>2
[[1,1,1],[2]]=>[[1,1,1,2]]=>1
[[1,1,2],[2]]=>[[1,1,2,2]]=>1
[[1,2,2],[2]]=>[[1,2,2,2]]=>1
[[1,1],[2,2]]=>[[1,1,2,2]]=>1
[[1,5]]=>[[1,5]]=>1
[[2,5]]=>[[2,5]]=>2
[[3,5]]=>[[3,5]]=>3
[[4,5]]=>[[4,5]]=>4
[[5,5]]=>[[5,5]]=>5
[[1],[5]]=>[[1,5]]=>1
[[2],[5]]=>[[2,5]]=>2
[[3],[5]]=>[[3,5]]=>3
[[4],[5]]=>[[4,5]]=>4
[[1,1,4]]=>[[1,1,4]]=>1
[[1,2,4]]=>[[1,2,4]]=>1
[[1,3,4]]=>[[1,3,4]]=>1
[[1,4,4]]=>[[1,4,4]]=>1
[[2,2,4]]=>[[2,2,4]]=>2
[[2,3,4]]=>[[2,3,4]]=>2
[[2,4,4]]=>[[2,4,4]]=>2
[[3,3,4]]=>[[3,3,4]]=>3
[[3,4,4]]=>[[3,4,4]]=>3
[[4,4,4]]=>[[4,4,4]]=>4
[[1,1],[4]]=>[[1,1,4]]=>1
[[1,2],[4]]=>[[1,2,4]]=>1
[[1,4],[2]]=>[[1,2],[4]]=>1
[[1,3],[4]]=>[[1,3,4]]=>1
[[1,4],[3]]=>[[1,3],[4]]=>1
[[1,4],[4]]=>[[1,4,4]]=>1
[[2,2],[4]]=>[[2,2,4]]=>2
[[2,3],[4]]=>[[2,3,4]]=>2
[[2,4],[3]]=>[[2,3],[4]]=>2
[[2,4],[4]]=>[[2,4,4]]=>2
[[3,3],[4]]=>[[3,3,4]]=>3
[[3,4],[4]]=>[[3,4,4]]=>3
[[1],[2],[4]]=>[[1,2],[4]]=>1
[[1],[3],[4]]=>[[1,3],[4]]=>1
[[2],[3],[4]]=>[[2,3],[4]]=>2
[[1,1,1,3]]=>[[1,1,1,3]]=>1
[[1,1,2,3]]=>[[1,1,2,3]]=>1
[[1,1,3,3]]=>[[1,1,3,3]]=>1
[[1,2,2,3]]=>[[1,2,2,3]]=>1
[[1,2,3,3]]=>[[1,2,3,3]]=>1
[[1,3,3,3]]=>[[1,3,3,3]]=>1
[[2,2,2,3]]=>[[2,2,2,3]]=>2
[[2,2,3,3]]=>[[2,2,3,3]]=>2
[[2,3,3,3]]=>[[2,3,3,3]]=>2
[[3,3,3,3]]=>[[3,3,3,3]]=>3
[[1,1,1],[3]]=>[[1,1,1,3]]=>1
[[1,1,2],[3]]=>[[1,1,2,3]]=>1
[[1,1,3],[2]]=>[[1,1,2],[3]]=>1
[[1,1,3],[3]]=>[[1,1,3,3]]=>1
[[1,2,2],[3]]=>[[1,2,2,3]]=>1
[[1,2,3],[2]]=>[[1,2,2],[3]]=>1
[[1,2,3],[3]]=>[[1,2,3,3]]=>1
[[1,3,3],[2]]=>[[1,2,3],[3]]=>1
[[1,3,3],[3]]=>[[1,3,3,3]]=>1
[[2,2,2],[3]]=>[[2,2,2,3]]=>2
[[2,2,3],[3]]=>[[2,2,3,3]]=>2
[[2,3,3],[3]]=>[[2,3,3,3]]=>2
[[1,1],[2,3]]=>[[1,1,2,3]]=>1
[[1,1],[3,3]]=>[[1,1,3,3]]=>1
[[1,2],[2,3]]=>[[1,2,2,3]]=>1
[[1,2],[3,3]]=>[[1,2,3,3]]=>1
[[2,2],[3,3]]=>[[2,2,3,3]]=>2
[[1,1],[2],[3]]=>[[1,1,2],[3]]=>1
[[1,2],[2],[3]]=>[[1,2,2],[3]]=>1
[[1,3],[2],[3]]=>[[1,2,3],[3]]=>1
[[1,1,1,1,2]]=>[[1,1,1,1,2]]=>1
[[1,1,1,2,2]]=>[[1,1,1,2,2]]=>1
[[1,1,2,2,2]]=>[[1,1,2,2,2]]=>1
[[1,2,2,2,2]]=>[[1,2,2,2,2]]=>1
[[2,2,2,2,2]]=>[[2,2,2,2,2]]=>2
[[1,1,1,1],[2]]=>[[1,1,1,1,2]]=>1
[[1,1,1,2],[2]]=>[[1,1,1,2,2]]=>1
[[1,1,2,2],[2]]=>[[1,1,2,2,2]]=>1
[[1,2,2,2],[2]]=>[[1,2,2,2,2]]=>1
[[1,1,1],[2,2]]=>[[1,1,1,2,2]]=>1
[[1,1,2],[2,2]]=>[[1,1,2,2,2]]=>1
[[1,6]]=>[[1,6]]=>1
[[2,6]]=>[[2,6]]=>2
[[3,6]]=>[[3,6]]=>3
[[4,6]]=>[[4,6]]=>4
[[5,6]]=>[[5,6]]=>5
[[6,6]]=>[[6,6]]=>6
[[1],[6]]=>[[1,6]]=>1
[[2],[6]]=>[[2,6]]=>2
[[3],[6]]=>[[3,6]]=>3
[[4],[6]]=>[[4,6]]=>4
[[5],[6]]=>[[5,6]]=>5
[[1,1,5]]=>[[1,1,5]]=>1
[[1,2,5]]=>[[1,2,5]]=>1
[[1,3,5]]=>[[1,3,5]]=>1
[[1,4,5]]=>[[1,4,5]]=>1
[[1,5,5]]=>[[1,5,5]]=>1
[[2,2,5]]=>[[2,2,5]]=>2
[[2,3,5]]=>[[2,3,5]]=>2
[[2,4,5]]=>[[2,4,5]]=>2
[[2,5,5]]=>[[2,5,5]]=>2
[[3,3,5]]=>[[3,3,5]]=>3
[[3,4,5]]=>[[3,4,5]]=>3
[[3,5,5]]=>[[3,5,5]]=>3
[[4,4,5]]=>[[4,4,5]]=>4
[[4,5,5]]=>[[4,5,5]]=>4
[[5,5,5]]=>[[5,5,5]]=>5
[[1,1],[5]]=>[[1,1,5]]=>1
[[1,2],[5]]=>[[1,2,5]]=>1
[[1,5],[2]]=>[[1,2],[5]]=>1
[[1,3],[5]]=>[[1,3,5]]=>1
[[1,5],[3]]=>[[1,3],[5]]=>1
[[1,4],[5]]=>[[1,4,5]]=>1
[[1,5],[4]]=>[[1,4],[5]]=>1
[[1,5],[5]]=>[[1,5,5]]=>1
[[2,2],[5]]=>[[2,2,5]]=>2
[[2,3],[5]]=>[[2,3,5]]=>2
[[2,5],[3]]=>[[2,3],[5]]=>2
[[2,4],[5]]=>[[2,4,5]]=>2
[[2,5],[4]]=>[[2,4],[5]]=>2
[[2,5],[5]]=>[[2,5,5]]=>2
[[3,3],[5]]=>[[3,3,5]]=>3
[[3,4],[5]]=>[[3,4,5]]=>3
[[3,5],[4]]=>[[3,4],[5]]=>3
[[3,5],[5]]=>[[3,5,5]]=>3
[[4,4],[5]]=>[[4,4,5]]=>4
[[4,5],[5]]=>[[4,5,5]]=>4
[[1],[2],[5]]=>[[1,2],[5]]=>1
[[1],[3],[5]]=>[[1,3],[5]]=>1
[[1],[4],[5]]=>[[1,4],[5]]=>1
[[2],[3],[5]]=>[[2,3],[5]]=>2
[[2],[4],[5]]=>[[2,4],[5]]=>2
[[3],[4],[5]]=>[[3,4],[5]]=>3
[[1,1,1,4]]=>[[1,1,1,4]]=>1
[[1,1,2,4]]=>[[1,1,2,4]]=>1
[[1,1,3,4]]=>[[1,1,3,4]]=>1
[[1,1,4,4]]=>[[1,1,4,4]]=>1
[[1,2,2,4]]=>[[1,2,2,4]]=>1
[[1,2,3,4]]=>[[1,2,3,4]]=>1
[[1,2,4,4]]=>[[1,2,4,4]]=>1
[[1,3,3,4]]=>[[1,3,3,4]]=>1
[[1,3,4,4]]=>[[1,3,4,4]]=>1
[[1,4,4,4]]=>[[1,4,4,4]]=>1
[[2,2,2,4]]=>[[2,2,2,4]]=>2
[[2,2,3,4]]=>[[2,2,3,4]]=>2
[[2,2,4,4]]=>[[2,2,4,4]]=>2
[[2,3,3,4]]=>[[2,3,3,4]]=>2
[[2,3,4,4]]=>[[2,3,4,4]]=>2
[[2,4,4,4]]=>[[2,4,4,4]]=>2
[[3,3,3,4]]=>[[3,3,3,4]]=>3
[[3,3,4,4]]=>[[3,3,4,4]]=>3
[[3,4,4,4]]=>[[3,4,4,4]]=>3
[[4,4,4,4]]=>[[4,4,4,4]]=>4
[[1,1,1],[4]]=>[[1,1,1,4]]=>1
[[1,1,2],[4]]=>[[1,1,2,4]]=>1
[[1,1,4],[2]]=>[[1,1,2],[4]]=>1
[[1,1,3],[4]]=>[[1,1,3,4]]=>1
[[1,1,4],[3]]=>[[1,1,3],[4]]=>1
[[1,1,4],[4]]=>[[1,1,4,4]]=>1
[[1,2,2],[4]]=>[[1,2,2,4]]=>1
[[1,2,4],[2]]=>[[1,2,2],[4]]=>1
[[1,2,3],[4]]=>[[1,2,3,4]]=>1
[[1,2,4],[3]]=>[[1,2,3],[4]]=>1
[[1,3,4],[2]]=>[[1,2,4],[3]]=>1
[[1,2,4],[4]]=>[[1,2,4,4]]=>1
[[1,4,4],[2]]=>[[1,2,4],[4]]=>1
[[1,3,3],[4]]=>[[1,3,3,4]]=>1
[[1,3,4],[3]]=>[[1,3,3],[4]]=>1
[[1,3,4],[4]]=>[[1,3,4,4]]=>1
[[1,4,4],[3]]=>[[1,3,4],[4]]=>1
[[1,4,4],[4]]=>[[1,4,4,4]]=>1
[[2,2,2],[4]]=>[[2,2,2,4]]=>2
[[2,2,3],[4]]=>[[2,2,3,4]]=>2
[[2,2,4],[3]]=>[[2,2,3],[4]]=>2
[[2,2,4],[4]]=>[[2,2,4,4]]=>2
[[2,3,3],[4]]=>[[2,3,3,4]]=>2
[[2,3,4],[3]]=>[[2,3,3],[4]]=>2
[[2,3,4],[4]]=>[[2,3,4,4]]=>2
[[2,4,4],[3]]=>[[2,3,4],[4]]=>2
[[2,4,4],[4]]=>[[2,4,4,4]]=>2
[[3,3,3],[4]]=>[[3,3,3,4]]=>3
[[3,3,4],[4]]=>[[3,3,4,4]]=>3
[[3,4,4],[4]]=>[[3,4,4,4]]=>3
[[1,1],[2,4]]=>[[1,1,2,4]]=>1
[[1,1],[3,4]]=>[[1,1,3,4]]=>1
[[1,1],[4,4]]=>[[1,1,4,4]]=>1
[[1,2],[2,4]]=>[[1,2,2,4]]=>1
[[1,2],[3,4]]=>[[1,2,3,4]]=>1
[[1,3],[2,4]]=>[[1,2,4],[3]]=>1
[[1,2],[4,4]]=>[[1,2,4,4]]=>1
[[1,3],[3,4]]=>[[1,3,3,4]]=>1
[[1,3],[4,4]]=>[[1,3,4,4]]=>1
[[2,2],[3,4]]=>[[2,2,3,4]]=>2
[[2,2],[4,4]]=>[[2,2,4,4]]=>2
[[2,3],[3,4]]=>[[2,3,3,4]]=>2
[[2,3],[4,4]]=>[[2,3,4,4]]=>2
[[3,3],[4,4]]=>[[3,3,4,4]]=>3
[[1,1],[2],[4]]=>[[1,1,2],[4]]=>1
[[1,1],[3],[4]]=>[[1,1,3],[4]]=>1
[[1,2],[2],[4]]=>[[1,2,2],[4]]=>1
[[1,2],[3],[4]]=>[[1,2,3],[4]]=>1
[[1,3],[2],[4]]=>[[1,2,4],[3]]=>1
[[1,4],[2],[3]]=>[[1,2],[3],[4]]=>1
[[1,4],[2],[4]]=>[[1,2,4],[4]]=>1
[[1,3],[3],[4]]=>[[1,3,3],[4]]=>1
[[1,4],[3],[4]]=>[[1,3,4],[4]]=>1
[[2,2],[3],[4]]=>[[2,2,3],[4]]=>2
[[2,3],[3],[4]]=>[[2,3,3],[4]]=>2
[[2,4],[3],[4]]=>[[2,3,4],[4]]=>2
[[1],[2],[3],[4]]=>[[1,2],[3],[4]]=>1
[[1,1,1,1,3]]=>[[1,1,1,1,3]]=>1
[[1,1,1,2,3]]=>[[1,1,1,2,3]]=>1
[[1,1,1,3,3]]=>[[1,1,1,3,3]]=>1
[[1,1,2,2,3]]=>[[1,1,2,2,3]]=>1
[[1,1,2,3,3]]=>[[1,1,2,3,3]]=>1
[[1,1,3,3,3]]=>[[1,1,3,3,3]]=>1
[[1,2,2,2,3]]=>[[1,2,2,2,3]]=>1
[[1,2,2,3,3]]=>[[1,2,2,3,3]]=>1
[[1,2,3,3,3]]=>[[1,2,3,3,3]]=>1
[[1,3,3,3,3]]=>[[1,3,3,3,3]]=>1
[[2,2,2,2,3]]=>[[2,2,2,2,3]]=>2
[[2,2,2,3,3]]=>[[2,2,2,3,3]]=>2
[[2,2,3,3,3]]=>[[2,2,3,3,3]]=>2
[[2,3,3,3,3]]=>[[2,3,3,3,3]]=>2
[[3,3,3,3,3]]=>[[3,3,3,3,3]]=>3
[[1,1,1,1],[3]]=>[[1,1,1,1,3]]=>1
[[1,1,1,2],[3]]=>[[1,1,1,2,3]]=>1
[[1,1,1,3],[2]]=>[[1,1,1,2],[3]]=>1
[[1,1,1,3],[3]]=>[[1,1,1,3,3]]=>1
[[1,1,2,2],[3]]=>[[1,1,2,2,3]]=>1
[[1,1,2,3],[2]]=>[[1,1,2,2],[3]]=>1
[[1,1,2,3],[3]]=>[[1,1,2,3,3]]=>1
[[1,1,3,3],[2]]=>[[1,1,2,3],[3]]=>1
[[1,1,3,3],[3]]=>[[1,1,3,3,3]]=>1
[[1,2,2,2],[3]]=>[[1,2,2,2,3]]=>1
[[1,2,2,3],[2]]=>[[1,2,2,2],[3]]=>1
[[1,2,2,3],[3]]=>[[1,2,2,3,3]]=>1
[[1,2,3,3],[2]]=>[[1,2,2,3],[3]]=>1
[[1,2,3,3],[3]]=>[[1,2,3,3,3]]=>1
[[1,3,3,3],[2]]=>[[1,2,3,3],[3]]=>1
[[1,3,3,3],[3]]=>[[1,3,3,3,3]]=>1
[[2,2,2,2],[3]]=>[[2,2,2,2,3]]=>2
[[2,2,2,3],[3]]=>[[2,2,2,3,3]]=>2
[[2,2,3,3],[3]]=>[[2,2,3,3,3]]=>2
[[2,3,3,3],[3]]=>[[2,3,3,3,3]]=>2
[[1,1,1],[2,3]]=>[[1,1,1,2,3]]=>1
[[1,1,1],[3,3]]=>[[1,1,1,3,3]]=>1
[[1,1,2],[2,3]]=>[[1,1,2,2,3]]=>1
[[1,1,3],[2,2]]=>[[1,1,2,2],[3]]=>1
[[1,1,2],[3,3]]=>[[1,1,2,3,3]]=>1
[[1,1,3],[2,3]]=>[[1,1,2,3],[3]]=>1
[[1,1,3],[3,3]]=>[[1,1,3,3,3]]=>1
[[1,2,2],[2,3]]=>[[1,2,2,2,3]]=>1
[[1,2,2],[3,3]]=>[[1,2,2,3,3]]=>1
[[1,2,3],[2,3]]=>[[1,2,2,3],[3]]=>1
[[1,2,3],[3,3]]=>[[1,2,3,3,3]]=>1
[[2,2,2],[3,3]]=>[[2,2,2,3,3]]=>2
[[2,2,3],[3,3]]=>[[2,2,3,3,3]]=>2
[[1,1,1],[2],[3]]=>[[1,1,1,2],[3]]=>1
[[1,1,2],[2],[3]]=>[[1,1,2,2],[3]]=>1
[[1,1,3],[2],[3]]=>[[1,1,2,3],[3]]=>1
[[1,2,2],[2],[3]]=>[[1,2,2,2],[3]]=>1
[[1,2,3],[2],[3]]=>[[1,2,2,3],[3]]=>1
[[1,3,3],[2],[3]]=>[[1,2,3,3],[3]]=>1
[[1,1],[2,2],[3]]=>[[1,1,2,2],[3]]=>1
[[1,1],[2,3],[3]]=>[[1,1,2,3],[3]]=>1
[[1,2],[2,3],[3]]=>[[1,2,2,3],[3]]=>1
[[1,1,1,1,1,2]]=>[[1,1,1,1,1,2]]=>1
[[1,1,1,1,2,2]]=>[[1,1,1,1,2,2]]=>1
[[1,1,1,2,2,2]]=>[[1,1,1,2,2,2]]=>1
[[1,1,2,2,2,2]]=>[[1,1,2,2,2,2]]=>1
[[1,2,2,2,2,2]]=>[[1,2,2,2,2,2]]=>1
[[2,2,2,2,2,2]]=>[[2,2,2,2,2,2]]=>2
[[1,1,1,1,1],[2]]=>[[1,1,1,1,1,2]]=>1
[[1,1,1,1,2],[2]]=>[[1,1,1,1,2,2]]=>1
[[1,1,1,2,2],[2]]=>[[1,1,1,2,2,2]]=>1
[[1,1,2,2,2],[2]]=>[[1,1,2,2,2,2]]=>1
[[1,2,2,2,2],[2]]=>[[1,2,2,2,2,2]]=>1
[[1,1,1,1],[2,2]]=>[[1,1,1,1,2,2]]=>1
[[1,1,1,2],[2,2]]=>[[1,1,1,2,2,2]]=>1
[[1,1,2,2],[2,2]]=>[[1,1,2,2,2,2]]=>1
[[1,1,1],[2,2,2]]=>[[1,1,1,2,2,2]]=>1
[[1,1,1,1,4]]=>[[1,1,1,1,4]]=>1
[[1,1,1,2,4]]=>[[1,1,1,2,4]]=>1
[[1,1,1,3,4]]=>[[1,1,1,3,4]]=>1
[[1,1,1,4,4]]=>[[1,1,1,4,4]]=>1
[[1,1,2,2,4]]=>[[1,1,2,2,4]]=>1
[[1,1,2,3,4]]=>[[1,1,2,3,4]]=>1
[[1,1,2,4,4]]=>[[1,1,2,4,4]]=>1
[[1,1,3,3,4]]=>[[1,1,3,3,4]]=>1
[[1,1,3,4,4]]=>[[1,1,3,4,4]]=>1
[[1,1,4,4,4]]=>[[1,1,4,4,4]]=>1
[[1,2,2,2,4]]=>[[1,2,2,2,4]]=>1
[[1,2,2,3,4]]=>[[1,2,2,3,4]]=>1
[[1,2,2,4,4]]=>[[1,2,2,4,4]]=>1
[[1,2,3,3,4]]=>[[1,2,3,3,4]]=>1
[[1,2,3,4,4]]=>[[1,2,3,4,4]]=>1
[[1,2,4,4,4]]=>[[1,2,4,4,4]]=>1
[[1,3,3,3,4]]=>[[1,3,3,3,4]]=>1
[[1,3,3,4,4]]=>[[1,3,3,4,4]]=>1
[[1,3,4,4,4]]=>[[1,3,4,4,4]]=>1
[[1,4,4,4,4]]=>[[1,4,4,4,4]]=>1
[[2,2,2,2,4]]=>[[2,2,2,2,4]]=>2
[[2,2,2,3,4]]=>[[2,2,2,3,4]]=>2
[[2,2,2,4,4]]=>[[2,2,2,4,4]]=>2
[[2,2,3,3,4]]=>[[2,2,3,3,4]]=>2
[[2,2,3,4,4]]=>[[2,2,3,4,4]]=>2
[[2,2,4,4,4]]=>[[2,2,4,4,4]]=>2
[[2,3,3,3,4]]=>[[2,3,3,3,4]]=>2
[[2,3,3,4,4]]=>[[2,3,3,4,4]]=>2
[[2,3,4,4,4]]=>[[2,3,4,4,4]]=>2
[[2,4,4,4,4]]=>[[2,4,4,4,4]]=>2
[[3,3,3,3,4]]=>[[3,3,3,3,4]]=>3
[[3,3,3,4,4]]=>[[3,3,3,4,4]]=>3
[[3,3,4,4,4]]=>[[3,3,4,4,4]]=>3
[[3,4,4,4,4]]=>[[3,4,4,4,4]]=>3
[[4,4,4,4,4]]=>[[4,4,4,4,4]]=>4
[[1,1,1,1],[4]]=>[[1,1,1,1,4]]=>1
[[1,1,1,2],[4]]=>[[1,1,1,2,4]]=>1
[[1,1,1,4],[2]]=>[[1,1,1,2],[4]]=>1
[[1,1,1,3],[4]]=>[[1,1,1,3,4]]=>1
[[1,1,1,4],[3]]=>[[1,1,1,3],[4]]=>1
[[1,1,1,4],[4]]=>[[1,1,1,4,4]]=>1
[[1,1,2,2],[4]]=>[[1,1,2,2,4]]=>1
[[1,1,2,4],[2]]=>[[1,1,2,2],[4]]=>1
[[1,1,2,3],[4]]=>[[1,1,2,3,4]]=>1
[[1,1,2,4],[3]]=>[[1,1,2,3],[4]]=>1
[[1,1,3,4],[2]]=>[[1,1,2,4],[3]]=>1
[[1,1,2,4],[4]]=>[[1,1,2,4,4]]=>1
[[1,1,4,4],[2]]=>[[1,1,2,4],[4]]=>1
[[1,1,3,3],[4]]=>[[1,1,3,3,4]]=>1
[[1,1,3,4],[3]]=>[[1,1,3,3],[4]]=>1
[[1,1,3,4],[4]]=>[[1,1,3,4,4]]=>1
[[1,1,4,4],[3]]=>[[1,1,3,4],[4]]=>1
[[1,1,4,4],[4]]=>[[1,1,4,4,4]]=>1
[[1,2,2,2],[4]]=>[[1,2,2,2,4]]=>1
[[1,2,2,4],[2]]=>[[1,2,2,2],[4]]=>1
[[1,2,2,3],[4]]=>[[1,2,2,3,4]]=>1
[[1,2,2,4],[3]]=>[[1,2,2,3],[4]]=>1
[[1,2,3,4],[2]]=>[[1,2,2,4],[3]]=>1
[[1,2,2,4],[4]]=>[[1,2,2,4,4]]=>1
[[1,2,4,4],[2]]=>[[1,2,2,4],[4]]=>1
[[1,2,3,3],[4]]=>[[1,2,3,3,4]]=>1
[[1,2,3,4],[3]]=>[[1,2,3,3],[4]]=>1
[[1,3,3,4],[2]]=>[[1,2,3,4],[3]]=>1
[[1,2,3,4],[4]]=>[[1,2,3,4,4]]=>1
[[1,2,4,4],[3]]=>[[1,2,3,4],[4]]=>1
[[1,3,4,4],[2]]=>[[1,2,4,4],[3]]=>1
[[1,2,4,4],[4]]=>[[1,2,4,4,4]]=>1
[[1,4,4,4],[2]]=>[[1,2,4,4],[4]]=>1
[[1,3,3,3],[4]]=>[[1,3,3,3,4]]=>1
[[1,3,3,4],[3]]=>[[1,3,3,3],[4]]=>1
[[1,3,3,4],[4]]=>[[1,3,3,4,4]]=>1
[[1,3,4,4],[3]]=>[[1,3,3,4],[4]]=>1
[[1,3,4,4],[4]]=>[[1,3,4,4,4]]=>1
[[1,4,4,4],[3]]=>[[1,3,4,4],[4]]=>1
[[1,4,4,4],[4]]=>[[1,4,4,4,4]]=>1
[[2,2,2,2],[4]]=>[[2,2,2,2,4]]=>2
[[2,2,2,3],[4]]=>[[2,2,2,3,4]]=>2
[[2,2,2,4],[3]]=>[[2,2,2,3],[4]]=>2
[[2,2,2,4],[4]]=>[[2,2,2,4,4]]=>2
[[2,2,3,3],[4]]=>[[2,2,3,3,4]]=>2
[[2,2,3,4],[3]]=>[[2,2,3,3],[4]]=>2
[[2,2,3,4],[4]]=>[[2,2,3,4,4]]=>2
[[2,2,4,4],[3]]=>[[2,2,3,4],[4]]=>2
[[2,2,4,4],[4]]=>[[2,2,4,4,4]]=>2
[[2,3,3,3],[4]]=>[[2,3,3,3,4]]=>2
[[2,3,3,4],[3]]=>[[2,3,3,3],[4]]=>2
[[2,3,3,4],[4]]=>[[2,3,3,4,4]]=>2
[[2,3,4,4],[3]]=>[[2,3,3,4],[4]]=>2
[[2,3,4,4],[4]]=>[[2,3,4,4,4]]=>2
[[2,4,4,4],[3]]=>[[2,3,4,4],[4]]=>2
[[2,4,4,4],[4]]=>[[2,4,4,4,4]]=>2
[[3,3,3,3],[4]]=>[[3,3,3,3,4]]=>3
[[3,3,3,4],[4]]=>[[3,3,3,4,4]]=>3
[[3,3,4,4],[4]]=>[[3,3,4,4,4]]=>3
[[3,4,4,4],[4]]=>[[3,4,4,4,4]]=>3
[[1,1,1],[2,4]]=>[[1,1,1,2,4]]=>1
[[1,1,1],[3,4]]=>[[1,1,1,3,4]]=>1
[[1,1,1],[4,4]]=>[[1,1,1,4,4]]=>1
[[1,1,2],[2,4]]=>[[1,1,2,2,4]]=>1
[[1,1,4],[2,2]]=>[[1,1,2,2],[4]]=>1
[[1,1,2],[3,4]]=>[[1,1,2,3,4]]=>1
[[1,1,3],[2,4]]=>[[1,1,2,4],[3]]=>1
[[1,1,4],[2,3]]=>[[1,1,2,3],[4]]=>1
[[1,1,2],[4,4]]=>[[1,1,2,4,4]]=>1
[[1,1,4],[2,4]]=>[[1,1,2,4],[4]]=>1
[[1,1,3],[3,4]]=>[[1,1,3,3,4]]=>1
[[1,1,4],[3,3]]=>[[1,1,3,3],[4]]=>1
[[1,1,3],[4,4]]=>[[1,1,3,4,4]]=>1
[[1,1,4],[3,4]]=>[[1,1,3,4],[4]]=>1
[[1,1,4],[4,4]]=>[[1,1,4,4,4]]=>1
[[1,2,2],[2,4]]=>[[1,2,2,2,4]]=>1
[[1,2,2],[3,4]]=>[[1,2,2,3,4]]=>1
[[1,2,3],[2,4]]=>[[1,2,2,4],[3]]=>1
[[1,2,4],[2,3]]=>[[1,2,2,3],[4]]=>1
[[1,2,2],[4,4]]=>[[1,2,2,4,4]]=>1
[[1,2,4],[2,4]]=>[[1,2,2,4],[4]]=>1
[[1,2,3],[3,4]]=>[[1,2,3,3,4]]=>1
[[1,2,4],[3,3]]=>[[1,2,3,3],[4]]=>1
[[1,3,3],[2,4]]=>[[1,2,3,4],[3]]=>1
[[1,2,3],[4,4]]=>[[1,2,3,4,4]]=>1
[[1,2,4],[3,4]]=>[[1,2,3,4],[4]]=>1
[[1,3,4],[2,4]]=>[[1,2,4,4],[3]]=>1
[[1,2,4],[4,4]]=>[[1,2,4,4,4]]=>1
[[1,3,3],[3,4]]=>[[1,3,3,3,4]]=>1
[[1,3,3],[4,4]]=>[[1,3,3,4,4]]=>1
[[1,3,4],[3,4]]=>[[1,3,3,4],[4]]=>1
[[1,3,4],[4,4]]=>[[1,3,4,4,4]]=>1
[[2,2,2],[3,4]]=>[[2,2,2,3,4]]=>2
[[2,2,2],[4,4]]=>[[2,2,2,4,4]]=>2
[[2,2,3],[3,4]]=>[[2,2,3,3,4]]=>2
[[2,2,4],[3,3]]=>[[2,2,3,3],[4]]=>2
[[2,2,3],[4,4]]=>[[2,2,3,4,4]]=>2
[[2,2,4],[3,4]]=>[[2,2,3,4],[4]]=>2
[[2,2,4],[4,4]]=>[[2,2,4,4,4]]=>2
[[2,3,3],[3,4]]=>[[2,3,3,3,4]]=>2
[[2,3,3],[4,4]]=>[[2,3,3,4,4]]=>2
[[2,3,4],[3,4]]=>[[2,3,3,4],[4]]=>2
[[2,3,4],[4,4]]=>[[2,3,4,4,4]]=>2
[[3,3,3],[4,4]]=>[[3,3,3,4,4]]=>3
[[3,3,4],[4,4]]=>[[3,3,4,4,4]]=>3
[[1,1,1],[2],[4]]=>[[1,1,1,2],[4]]=>1
[[1,1,1],[3],[4]]=>[[1,1,1,3],[4]]=>1
[[1,1,2],[2],[4]]=>[[1,1,2,2],[4]]=>1
[[1,1,2],[3],[4]]=>[[1,1,2,3],[4]]=>1
[[1,1,3],[2],[4]]=>[[1,1,2,4],[3]]=>1
[[1,1,4],[2],[3]]=>[[1,1,2],[3],[4]]=>1
[[1,1,4],[2],[4]]=>[[1,1,2,4],[4]]=>1
[[1,1,3],[3],[4]]=>[[1,1,3,3],[4]]=>1
[[1,1,4],[3],[4]]=>[[1,1,3,4],[4]]=>1
[[1,2,2],[2],[4]]=>[[1,2,2,2],[4]]=>1
[[1,2,2],[3],[4]]=>[[1,2,2,3],[4]]=>1
[[1,2,3],[2],[4]]=>[[1,2,2,4],[3]]=>1
[[1,2,4],[2],[3]]=>[[1,2,2],[3],[4]]=>1
[[1,2,4],[2],[4]]=>[[1,2,2,4],[4]]=>1
[[1,2,3],[3],[4]]=>[[1,2,3,3],[4]]=>1
[[1,3,3],[2],[4]]=>[[1,2,3,4],[3]]=>1
[[1,3,4],[2],[3]]=>[[1,2,3],[3],[4]]=>1
[[1,2,4],[3],[4]]=>[[1,2,3,4],[4]]=>1
[[1,3,4],[2],[4]]=>[[1,2,4,4],[3]]=>1
[[1,4,4],[2],[3]]=>[[1,2,4],[3],[4]]=>1
[[1,4,4],[2],[4]]=>[[1,2,4,4],[4]]=>1
[[1,3,3],[3],[4]]=>[[1,3,3,3],[4]]=>1
[[1,3,4],[3],[4]]=>[[1,3,3,4],[4]]=>1
[[1,4,4],[3],[4]]=>[[1,3,4,4],[4]]=>1
[[2,2,2],[3],[4]]=>[[2,2,2,3],[4]]=>2
[[2,2,3],[3],[4]]=>[[2,2,3,3],[4]]=>2
[[2,2,4],[3],[4]]=>[[2,2,3,4],[4]]=>2
[[2,3,3],[3],[4]]=>[[2,3,3,3],[4]]=>2
[[2,3,4],[3],[4]]=>[[2,3,3,4],[4]]=>2
[[2,4,4],[3],[4]]=>[[2,3,4,4],[4]]=>2
[[1,1],[2,2],[4]]=>[[1,1,2,2],[4]]=>1
[[1,1],[2,3],[4]]=>[[1,1,2,3],[4]]=>1
[[1,1],[2,4],[3]]=>[[1,1,2,4],[3]]=>1
[[1,1],[2,4],[4]]=>[[1,1,2,4],[4]]=>1
[[1,1],[3,3],[4]]=>[[1,1,3,3],[4]]=>1
[[1,1],[3,4],[4]]=>[[1,1,3,4],[4]]=>1
[[1,2],[2,3],[4]]=>[[1,2,2,3],[4]]=>1
[[1,2],[2,4],[3]]=>[[1,2,2,4],[3]]=>1
[[1,2],[2,4],[4]]=>[[1,2,2,4],[4]]=>1
[[1,2],[3,3],[4]]=>[[1,2,3,3],[4]]=>1
[[1,3],[2,4],[3]]=>[[1,2,3,4],[3]]=>1
[[1,2],[3,4],[4]]=>[[1,2,3,4],[4]]=>1
[[1,3],[2,4],[4]]=>[[1,2,4,4],[3]]=>1
[[1,3],[3,4],[4]]=>[[1,3,3,4],[4]]=>1
[[2,2],[3,3],[4]]=>[[2,2,3,3],[4]]=>2
[[2,2],[3,4],[4]]=>[[2,2,3,4],[4]]=>2
[[2,3],[3,4],[4]]=>[[2,3,3,4],[4]]=>2
[[1,1],[2],[3],[4]]=>[[1,1,2],[3],[4]]=>1
[[1,2],[2],[3],[4]]=>[[1,2,2],[3],[4]]=>1
[[1,3],[2],[3],[4]]=>[[1,2,3],[3],[4]]=>1
[[1,4],[2],[3],[4]]=>[[1,2,4],[3],[4]]=>1
[[1,1,1,1,1,3]]=>[[1,1,1,1,1,3]]=>1
[[1,1,1,1,2,3]]=>[[1,1,1,1,2,3]]=>1
[[1,1,1,1,3,3]]=>[[1,1,1,1,3,3]]=>1
[[1,1,1,2,2,3]]=>[[1,1,1,2,2,3]]=>1
[[1,1,1,2,3,3]]=>[[1,1,1,2,3,3]]=>1
[[1,1,1,3,3,3]]=>[[1,1,1,3,3,3]]=>1
[[1,1,2,2,2,3]]=>[[1,1,2,2,2,3]]=>1
[[1,1,2,2,3,3]]=>[[1,1,2,2,3,3]]=>1
[[1,1,2,3,3,3]]=>[[1,1,2,3,3,3]]=>1
[[1,1,3,3,3,3]]=>[[1,1,3,3,3,3]]=>1
[[1,2,2,2,2,3]]=>[[1,2,2,2,2,3]]=>1
[[1,2,2,2,3,3]]=>[[1,2,2,2,3,3]]=>1
[[1,2,2,3,3,3]]=>[[1,2,2,3,3,3]]=>1
[[1,2,3,3,3,3]]=>[[1,2,3,3,3,3]]=>1
[[1,3,3,3,3,3]]=>[[1,3,3,3,3,3]]=>1
[[2,2,2,2,2,3]]=>[[2,2,2,2,2,3]]=>2
[[2,2,2,2,3,3]]=>[[2,2,2,2,3,3]]=>2
[[2,2,2,3,3,3]]=>[[2,2,2,3,3,3]]=>2
[[2,2,3,3,3,3]]=>[[2,2,3,3,3,3]]=>2
[[1,1,1,1,1],[3]]=>[[1,1,1,1,1,3]]=>1
[[1,1,1,1,2],[3]]=>[[1,1,1,1,2,3]]=>1
[[1,1,1,1,3],[3]]=>[[1,1,1,1,3,3]]=>1
[[1,1,1,2,2],[3]]=>[[1,1,1,2,2,3]]=>1
[[1,1,1,2,3],[2]]=>[[1,1,1,2,2],[3]]=>1
[[1,1,1,2,3],[3]]=>[[1,1,1,2,3,3]]=>1
[[1,1,1,3,3],[2]]=>[[1,1,1,2,3],[3]]=>1
[[1,1,1,3,3],[3]]=>[[1,1,1,3,3,3]]=>1
[[1,1,2,2,2],[3]]=>[[1,1,2,2,2,3]]=>1
[[1,1,2,2,3],[2]]=>[[1,1,2,2,2],[3]]=>1
[[1,1,2,2,3],[3]]=>[[1,1,2,2,3,3]]=>1
[[1,1,2,3,3],[2]]=>[[1,1,2,2,3],[3]]=>1
[[1,1,2,3,3],[3]]=>[[1,1,2,3,3,3]]=>1
[[1,1,3,3,3],[2]]=>[[1,1,2,3,3],[3]]=>1
[[1,1,3,3,3],[3]]=>[[1,1,3,3,3,3]]=>1
[[1,2,2,2,2],[3]]=>[[1,2,2,2,2,3]]=>1
[[1,2,2,2,3],[3]]=>[[1,2,2,2,3,3]]=>1
[[1,2,2,3,3],[2]]=>[[1,2,2,2,3],[3]]=>1
[[1,2,2,3,3],[3]]=>[[1,2,2,3,3,3]]=>1
[[1,2,3,3,3],[2]]=>[[1,2,2,3,3],[3]]=>1
[[1,2,3,3,3],[3]]=>[[1,2,3,3,3,3]]=>1
[[1,3,3,3,3],[3]]=>[[1,3,3,3,3,3]]=>1
[[2,2,2,2,2],[3]]=>[[2,2,2,2,2,3]]=>2
[[2,2,2,2,3],[3]]=>[[2,2,2,2,3,3]]=>2
[[2,2,2,3,3],[3]]=>[[2,2,2,3,3,3]]=>2
[[2,2,3,3,3],[3]]=>[[2,2,3,3,3,3]]=>2
[[1,1,1,1],[2,3]]=>[[1,1,1,1,2,3]]=>1
[[1,1,1,1],[3,3]]=>[[1,1,1,1,3,3]]=>1
[[1,1,1,2],[2,3]]=>[[1,1,1,2,2,3]]=>1
[[1,1,1,3],[2,2]]=>[[1,1,1,2,2],[3]]=>1
[[1,1,1,2],[3,3]]=>[[1,1,1,2,3,3]]=>1
[[1,1,1,3],[2,3]]=>[[1,1,1,2,3],[3]]=>1
[[1,1,1,3],[3,3]]=>[[1,1,1,3,3,3]]=>1
[[1,1,2,2],[2,3]]=>[[1,1,2,2,2,3]]=>1
[[1,1,2,3],[2,2]]=>[[1,1,2,2,2],[3]]=>1
[[1,1,2,2],[3,3]]=>[[1,1,2,2,3,3]]=>1
[[1,1,2,3],[2,3]]=>[[1,1,2,2,3],[3]]=>1
[[1,1,2,3],[3,3]]=>[[1,1,2,3,3,3]]=>1
[[1,1,3,3],[2,3]]=>[[1,1,2,3,3],[3]]=>1
[[1,1,3,3],[3,3]]=>[[1,1,3,3,3,3]]=>1
[[1,2,2,2],[2,3]]=>[[1,2,2,2,2,3]]=>1
[[1,2,2,2],[3,3]]=>[[1,2,2,2,3,3]]=>1
[[1,2,2,3],[2,3]]=>[[1,2,2,2,3],[3]]=>1
[[1,2,2,3],[3,3]]=>[[1,2,2,3,3,3]]=>1
[[1,2,3,3],[2,3]]=>[[1,2,2,3,3],[3]]=>1
[[1,2,3,3],[3,3]]=>[[1,2,3,3,3,3]]=>1
[[2,2,2,2],[3,3]]=>[[2,2,2,2,3,3]]=>2
[[2,2,2,3],[3,3]]=>[[2,2,2,3,3,3]]=>2
[[2,2,3,3],[3,3]]=>[[2,2,3,3,3,3]]=>2
[[1,1,1,2],[2],[3]]=>[[1,1,1,2,2],[3]]=>1
[[1,1,1,3],[2],[3]]=>[[1,1,1,2,3],[3]]=>1
[[1,1,2,2],[2],[3]]=>[[1,1,2,2,2],[3]]=>1
[[1,1,2,3],[2],[3]]=>[[1,1,2,2,3],[3]]=>1
[[1,1,3,3],[2],[3]]=>[[1,1,2,3,3],[3]]=>1
[[1,2,2,3],[2],[3]]=>[[1,2,2,2,3],[3]]=>1
[[1,2,3,3],[2],[3]]=>[[1,2,2,3,3],[3]]=>1
[[1,1,1],[2,2,3]]=>[[1,1,1,2,2,3]]=>1
[[1,1,1],[2,3,3]]=>[[1,1,1,2,3,3]]=>1
[[1,1,1],[3,3,3]]=>[[1,1,1,3,3,3]]=>1
[[1,1,2],[2,2,3]]=>[[1,1,2,2,2,3]]=>1
[[1,1,2],[2,3,3]]=>[[1,1,2,2,3,3]]=>1
[[1,1,2],[3,3,3]]=>[[1,1,2,3,3,3]]=>1
[[1,2,2],[2,3,3]]=>[[1,2,2,2,3,3]]=>1
[[1,2,2],[3,3,3]]=>[[1,2,2,3,3,3]]=>1
[[2,2,2],[3,3,3]]=>[[2,2,2,3,3,3]]=>2
[[1,1,1],[2,2],[3]]=>[[1,1,1,2,2],[3]]=>1
[[1,1,1],[2,3],[3]]=>[[1,1,1,2,3],[3]]=>1
[[1,1,2],[2,2],[3]]=>[[1,1,2,2,2],[3]]=>1
[[1,1,2],[2,3],[3]]=>[[1,1,2,2,3],[3]]=>1
[[1,1,3],[2,3],[3]]=>[[1,1,2,3,3],[3]]=>1
[[1,2,2],[2,3],[3]]=>[[1,2,2,2,3],[3]]=>1
[[1,2,3],[2,3],[3]]=>[[1,2,2,3,3],[3]]=>1
[[1,1,1,1,5]]=>[[1,1,1,1,5]]=>1
[[1,1,1,2,5]]=>[[1,1,1,2,5]]=>1
[[1,1,1,3,5]]=>[[1,1,1,3,5]]=>1
[[1,1,1,4,5]]=>[[1,1,1,4,5]]=>1
[[1,1,1,5,5]]=>[[1,1,1,5,5]]=>1
[[1,1,2,2,5]]=>[[1,1,2,2,5]]=>1
[[1,1,2,3,5]]=>[[1,1,2,3,5]]=>1
[[1,1,2,4,5]]=>[[1,1,2,4,5]]=>1
[[1,1,2,5,5]]=>[[1,1,2,5,5]]=>1
[[1,1,3,3,5]]=>[[1,1,3,3,5]]=>1
[[1,1,3,4,5]]=>[[1,1,3,4,5]]=>1
[[1,1,3,5,5]]=>[[1,1,3,5,5]]=>1
[[1,1,4,4,5]]=>[[1,1,4,4,5]]=>1
[[1,1,4,5,5]]=>[[1,1,4,5,5]]=>1
[[1,1,5,5,5]]=>[[1,1,5,5,5]]=>1
[[1,2,2,2,5]]=>[[1,2,2,2,5]]=>1
[[1,2,2,3,5]]=>[[1,2,2,3,5]]=>1
[[1,2,2,4,5]]=>[[1,2,2,4,5]]=>1
[[1,2,2,5,5]]=>[[1,2,2,5,5]]=>1
[[1,2,3,3,5]]=>[[1,2,3,3,5]]=>1
[[1,2,3,4,5]]=>[[1,2,3,4,5]]=>1
[[1,2,3,5,5]]=>[[1,2,3,5,5]]=>1
[[1,2,4,4,5]]=>[[1,2,4,4,5]]=>1
[[1,2,4,5,5]]=>[[1,2,4,5,5]]=>1
[[1,2,5,5,5]]=>[[1,2,5,5,5]]=>1
[[1,3,3,3,5]]=>[[1,3,3,3,5]]=>1
[[1,3,3,4,5]]=>[[1,3,3,4,5]]=>1
[[1,3,3,5,5]]=>[[1,3,3,5,5]]=>1
[[1,3,4,4,5]]=>[[1,3,4,4,5]]=>1
[[1,3,4,5,5]]=>[[1,3,4,5,5]]=>1
[[1,3,5,5,5]]=>[[1,3,5,5,5]]=>1
[[1,4,4,4,5]]=>[[1,4,4,4,5]]=>1
[[1,4,4,5,5]]=>[[1,4,4,5,5]]=>1
[[1,4,5,5,5]]=>[[1,4,5,5,5]]=>1
[[1,5,5,5,5]]=>[[1,5,5,5,5]]=>1
[[2,2,2,2,5]]=>[[2,2,2,2,5]]=>2
[[2,2,2,3,5]]=>[[2,2,2,3,5]]=>2
[[2,2,2,4,5]]=>[[2,2,2,4,5]]=>2
[[2,2,2,5,5]]=>[[2,2,2,5,5]]=>2
[[2,2,3,3,5]]=>[[2,2,3,3,5]]=>2
[[2,2,3,4,5]]=>[[2,2,3,4,5]]=>2
[[2,2,3,5,5]]=>[[2,2,3,5,5]]=>2
[[2,2,4,4,5]]=>[[2,2,4,4,5]]=>2
[[2,2,4,5,5]]=>[[2,2,4,5,5]]=>2
[[2,2,5,5,5]]=>[[2,2,5,5,5]]=>2
[[2,3,3,3,5]]=>[[2,3,3,3,5]]=>2
[[2,3,3,4,5]]=>[[2,3,3,4,5]]=>2
[[2,3,3,5,5]]=>[[2,3,3,5,5]]=>2
[[2,3,4,4,5]]=>[[2,3,4,4,5]]=>2
[[2,3,4,5,5]]=>[[2,3,4,5,5]]=>2
[[2,3,5,5,5]]=>[[2,3,5,5,5]]=>2
[[2,4,4,4,5]]=>[[2,4,4,4,5]]=>2
[[2,4,4,5,5]]=>[[2,4,4,5,5]]=>2
[[2,4,5,5,5]]=>[[2,4,5,5,5]]=>2
[[2,5,5,5,5]]=>[[2,5,5,5,5]]=>2
[[3,3,3,3,5]]=>[[3,3,3,3,5]]=>3
[[3,3,3,4,5]]=>[[3,3,3,4,5]]=>3
[[3,3,3,5,5]]=>[[3,3,3,5,5]]=>3
[[3,3,4,4,5]]=>[[3,3,4,4,5]]=>3
[[3,3,4,5,5]]=>[[3,3,4,5,5]]=>3
[[3,3,5,5,5]]=>[[3,3,5,5,5]]=>3
[[3,4,4,4,5]]=>[[3,4,4,4,5]]=>3
[[3,4,4,5,5]]=>[[3,4,4,5,5]]=>3
[[3,4,5,5,5]]=>[[3,4,5,5,5]]=>3
[[3,5,5,5,5]]=>[[3,5,5,5,5]]=>3
[[4,4,4,4,5]]=>[[4,4,4,4,5]]=>4
[[4,4,4,5,5]]=>[[4,4,4,5,5]]=>4
[[4,4,5,5,5]]=>[[4,4,5,5,5]]=>4
[[4,5,5,5,5]]=>[[4,5,5,5,5]]=>4
[[5,5,5,5,5]]=>[[5,5,5,5,5]]=>5
[[1,1,1,1],[5]]=>[[1,1,1,1,5]]=>1
[[1,1,1,2],[5]]=>[[1,1,1,2,5]]=>1
[[1,1,1,5],[2]]=>[[1,1,1,2],[5]]=>1
[[1,1,1,3],[5]]=>[[1,1,1,3,5]]=>1
[[1,1,1,5],[3]]=>[[1,1,1,3],[5]]=>1
[[1,1,1,4],[5]]=>[[1,1,1,4,5]]=>1
[[1,1,1,5],[4]]=>[[1,1,1,4],[5]]=>1
[[1,1,1,5],[5]]=>[[1,1,1,5,5]]=>1
[[1,1,2,2],[5]]=>[[1,1,2,2,5]]=>1
[[1,1,2,5],[2]]=>[[1,1,2,2],[5]]=>1
[[1,1,2,3],[5]]=>[[1,1,2,3,5]]=>1
[[1,1,2,5],[3]]=>[[1,1,2,3],[5]]=>1
[[1,1,3,5],[2]]=>[[1,1,2,5],[3]]=>1
[[1,1,2,4],[5]]=>[[1,1,2,4,5]]=>1
[[1,1,2,5],[4]]=>[[1,1,2,4],[5]]=>1
[[1,1,4,5],[2]]=>[[1,1,2,5],[4]]=>1
[[1,1,2,5],[5]]=>[[1,1,2,5,5]]=>1
[[1,1,5,5],[2]]=>[[1,1,2,5],[5]]=>1
[[1,1,3,3],[5]]=>[[1,1,3,3,5]]=>1
[[1,1,3,5],[3]]=>[[1,1,3,3],[5]]=>1
[[1,1,3,4],[5]]=>[[1,1,3,4,5]]=>1
[[1,1,3,5],[4]]=>[[1,1,3,4],[5]]=>1
[[1,1,4,5],[3]]=>[[1,1,3,5],[4]]=>1
[[1,1,3,5],[5]]=>[[1,1,3,5,5]]=>1
[[1,1,5,5],[3]]=>[[1,1,3,5],[5]]=>1
[[1,1,4,4],[5]]=>[[1,1,4,4,5]]=>1
[[1,1,4,5],[4]]=>[[1,1,4,4],[5]]=>1
[[1,1,4,5],[5]]=>[[1,1,4,5,5]]=>1
[[1,1,5,5],[4]]=>[[1,1,4,5],[5]]=>1
[[1,1,5,5],[5]]=>[[1,1,5,5,5]]=>1
[[1,2,2,2],[5]]=>[[1,2,2,2,5]]=>1
[[1,2,2,5],[2]]=>[[1,2,2,2],[5]]=>1
[[1,2,2,3],[5]]=>[[1,2,2,3,5]]=>1
[[1,2,2,5],[3]]=>[[1,2,2,3],[5]]=>1
[[1,2,3,5],[2]]=>[[1,2,2,5],[3]]=>1
[[1,2,2,4],[5]]=>[[1,2,2,4,5]]=>1
[[1,2,2,5],[4]]=>[[1,2,2,4],[5]]=>1
[[1,2,4,5],[2]]=>[[1,2,2,5],[4]]=>1
[[1,2,2,5],[5]]=>[[1,2,2,5,5]]=>1
[[1,2,5,5],[2]]=>[[1,2,2,5],[5]]=>1
[[1,2,3,3],[5]]=>[[1,2,3,3,5]]=>1
[[1,2,3,5],[3]]=>[[1,2,3,3],[5]]=>1
[[1,3,3,5],[2]]=>[[1,2,3,5],[3]]=>1
[[1,2,3,4],[5]]=>[[1,2,3,4,5]]=>1
[[1,2,3,5],[4]]=>[[1,2,3,4],[5]]=>1
[[1,2,4,5],[3]]=>[[1,2,3,5],[4]]=>1
[[1,3,4,5],[2]]=>[[1,2,4,5],[3]]=>1
[[1,2,3,5],[5]]=>[[1,2,3,5,5]]=>1
[[1,2,5,5],[3]]=>[[1,2,3,5],[5]]=>1
[[1,3,5,5],[2]]=>[[1,2,5,5],[3]]=>1
[[1,2,4,4],[5]]=>[[1,2,4,4,5]]=>1
[[1,2,4,5],[4]]=>[[1,2,4,4],[5]]=>1
[[1,4,4,5],[2]]=>[[1,2,4,5],[4]]=>1
[[1,2,4,5],[5]]=>[[1,2,4,5,5]]=>1
[[1,2,5,5],[4]]=>[[1,2,4,5],[5]]=>1
[[1,4,5,5],[2]]=>[[1,2,5,5],[4]]=>1
[[1,2,5,5],[5]]=>[[1,2,5,5,5]]=>1
[[1,5,5,5],[2]]=>[[1,2,5,5],[5]]=>1
[[1,3,3,3],[5]]=>[[1,3,3,3,5]]=>1
[[1,3,3,5],[3]]=>[[1,3,3,3],[5]]=>1
[[1,3,3,4],[5]]=>[[1,3,3,4,5]]=>1
[[1,3,3,5],[4]]=>[[1,3,3,4],[5]]=>1
[[1,3,4,5],[3]]=>[[1,3,3,5],[4]]=>1
[[1,3,3,5],[5]]=>[[1,3,3,5,5]]=>1
[[1,3,5,5],[3]]=>[[1,3,3,5],[5]]=>1
[[1,3,4,4],[5]]=>[[1,3,4,4,5]]=>1
[[1,3,4,5],[4]]=>[[1,3,4,4],[5]]=>1
[[1,4,4,5],[3]]=>[[1,3,4,5],[4]]=>1
[[1,3,4,5],[5]]=>[[1,3,4,5,5]]=>1
[[1,3,5,5],[4]]=>[[1,3,4,5],[5]]=>1
[[1,4,5,5],[3]]=>[[1,3,5,5],[4]]=>1
[[1,3,5,5],[5]]=>[[1,3,5,5,5]]=>1
[[1,5,5,5],[3]]=>[[1,3,5,5],[5]]=>1
[[1,4,4,4],[5]]=>[[1,4,4,4,5]]=>1
[[1,4,4,5],[4]]=>[[1,4,4,4],[5]]=>1
[[1,4,4,5],[5]]=>[[1,4,4,5,5]]=>1
[[1,4,5,5],[4]]=>[[1,4,4,5],[5]]=>1
[[1,4,5,5],[5]]=>[[1,4,5,5,5]]=>1
[[1,5,5,5],[4]]=>[[1,4,5,5],[5]]=>1
[[1,5,5,5],[5]]=>[[1,5,5,5,5]]=>1
[[2,2,2,2],[5]]=>[[2,2,2,2,5]]=>2
[[2,2,2,3],[5]]=>[[2,2,2,3,5]]=>2
[[2,2,2,5],[3]]=>[[2,2,2,3],[5]]=>2
[[2,2,2,4],[5]]=>[[2,2,2,4,5]]=>2
[[2,2,2,5],[4]]=>[[2,2,2,4],[5]]=>2
[[2,2,2,5],[5]]=>[[2,2,2,5,5]]=>2
[[2,2,3,3],[5]]=>[[2,2,3,3,5]]=>2
[[2,2,3,5],[3]]=>[[2,2,3,3],[5]]=>2
[[2,2,3,4],[5]]=>[[2,2,3,4,5]]=>2
[[2,2,3,5],[4]]=>[[2,2,3,4],[5]]=>2
[[2,2,4,5],[3]]=>[[2,2,3,5],[4]]=>2
[[2,2,3,5],[5]]=>[[2,2,3,5,5]]=>2
[[2,2,5,5],[3]]=>[[2,2,3,5],[5]]=>2
[[2,2,4,4],[5]]=>[[2,2,4,4,5]]=>2
[[2,2,4,5],[4]]=>[[2,2,4,4],[5]]=>2
[[2,2,4,5],[5]]=>[[2,2,4,5,5]]=>2
[[2,2,5,5],[4]]=>[[2,2,4,5],[5]]=>2
[[2,2,5,5],[5]]=>[[2,2,5,5,5]]=>2
[[2,3,3,3],[5]]=>[[2,3,3,3,5]]=>2
[[2,3,3,5],[3]]=>[[2,3,3,3],[5]]=>2
[[2,3,3,4],[5]]=>[[2,3,3,4,5]]=>2
[[2,3,3,5],[4]]=>[[2,3,3,4],[5]]=>2
[[2,3,4,5],[3]]=>[[2,3,3,5],[4]]=>2
[[2,3,3,5],[5]]=>[[2,3,3,5,5]]=>2
[[2,3,5,5],[3]]=>[[2,3,3,5],[5]]=>2
[[2,3,4,4],[5]]=>[[2,3,4,4,5]]=>2
[[2,3,4,5],[4]]=>[[2,3,4,4],[5]]=>2
[[2,4,4,5],[3]]=>[[2,3,4,5],[4]]=>2
[[2,3,4,5],[5]]=>[[2,3,4,5,5]]=>2
[[2,3,5,5],[4]]=>[[2,3,4,5],[5]]=>2
[[2,4,5,5],[3]]=>[[2,3,5,5],[4]]=>2
[[2,3,5,5],[5]]=>[[2,3,5,5,5]]=>2
[[2,5,5,5],[3]]=>[[2,3,5,5],[5]]=>2
[[2,4,4,4],[5]]=>[[2,4,4,4,5]]=>2
[[2,4,4,5],[4]]=>[[2,4,4,4],[5]]=>2
[[2,4,4,5],[5]]=>[[2,4,4,5,5]]=>2
[[2,4,5,5],[4]]=>[[2,4,4,5],[5]]=>2
[[2,4,5,5],[5]]=>[[2,4,5,5,5]]=>2
[[2,5,5,5],[4]]=>[[2,4,5,5],[5]]=>2
[[2,5,5,5],[5]]=>[[2,5,5,5,5]]=>2
[[3,3,3,3],[5]]=>[[3,3,3,3,5]]=>3
[[3,3,3,4],[5]]=>[[3,3,3,4,5]]=>3
[[3,3,3,5],[4]]=>[[3,3,3,4],[5]]=>3
[[3,3,3,5],[5]]=>[[3,3,3,5,5]]=>3
[[3,3,4,4],[5]]=>[[3,3,4,4,5]]=>3
[[3,3,4,5],[4]]=>[[3,3,4,4],[5]]=>3
[[3,3,4,5],[5]]=>[[3,3,4,5,5]]=>3
[[3,3,5,5],[4]]=>[[3,3,4,5],[5]]=>3
[[3,3,5,5],[5]]=>[[3,3,5,5,5]]=>3
[[3,4,4,4],[5]]=>[[3,4,4,4,5]]=>3
[[3,4,4,5],[4]]=>[[3,4,4,4],[5]]=>3
[[3,4,4,5],[5]]=>[[3,4,4,5,5]]=>3
[[3,4,5,5],[4]]=>[[3,4,4,5],[5]]=>3
[[3,4,5,5],[5]]=>[[3,4,5,5,5]]=>3
[[3,5,5,5],[4]]=>[[3,4,5,5],[5]]=>3
[[3,5,5,5],[5]]=>[[3,5,5,5,5]]=>3
[[4,4,4,4],[5]]=>[[4,4,4,4,5]]=>4
[[4,4,4,5],[5]]=>[[4,4,4,5,5]]=>4
[[4,4,5,5],[5]]=>[[4,4,5,5,5]]=>4
[[4,5,5,5],[5]]=>[[4,5,5,5,5]]=>4
[[1,1,1],[2,5]]=>[[1,1,1,2,5]]=>1
[[1,1,1],[3,5]]=>[[1,1,1,3,5]]=>1
[[1,1,1],[4,5]]=>[[1,1,1,4,5]]=>1
[[1,1,1],[5,5]]=>[[1,1,1,5,5]]=>1
[[1,1,2],[2,5]]=>[[1,1,2,2,5]]=>1
[[1,1,5],[2,2]]=>[[1,1,2,2],[5]]=>1
[[1,1,2],[3,5]]=>[[1,1,2,3,5]]=>1
[[1,1,3],[2,5]]=>[[1,1,2,5],[3]]=>1
[[1,1,5],[2,3]]=>[[1,1,2,3],[5]]=>1
[[1,1,2],[4,5]]=>[[1,1,2,4,5]]=>1
[[1,1,4],[2,5]]=>[[1,1,2,5],[4]]=>1
[[1,1,5],[2,4]]=>[[1,1,2,4],[5]]=>1
[[1,1,2],[5,5]]=>[[1,1,2,5,5]]=>1
[[1,1,5],[2,5]]=>[[1,1,2,5],[5]]=>1
[[1,1,3],[3,5]]=>[[1,1,3,3,5]]=>1
[[1,1,5],[3,3]]=>[[1,1,3,3],[5]]=>1
[[1,1,3],[4,5]]=>[[1,1,3,4,5]]=>1
[[1,1,4],[3,5]]=>[[1,1,3,5],[4]]=>1
[[1,1,5],[3,4]]=>[[1,1,3,4],[5]]=>1
[[1,1,3],[5,5]]=>[[1,1,3,5,5]]=>1
[[1,1,5],[3,5]]=>[[1,1,3,5],[5]]=>1
[[1,1,4],[4,5]]=>[[1,1,4,4,5]]=>1
[[1,1,5],[4,4]]=>[[1,1,4,4],[5]]=>1
[[1,1,4],[5,5]]=>[[1,1,4,5,5]]=>1
[[1,1,5],[4,5]]=>[[1,1,4,5],[5]]=>1
[[1,1,5],[5,5]]=>[[1,1,5,5,5]]=>1
[[1,2,2],[2,5]]=>[[1,2,2,2,5]]=>1
[[1,2,2],[3,5]]=>[[1,2,2,3,5]]=>1
[[1,2,3],[2,5]]=>[[1,2,2,5],[3]]=>1
[[1,2,5],[2,3]]=>[[1,2,2,3],[5]]=>1
[[1,2,2],[4,5]]=>[[1,2,2,4,5]]=>1
[[1,2,4],[2,5]]=>[[1,2,2,5],[4]]=>1
[[1,2,5],[2,4]]=>[[1,2,2,4],[5]]=>1
[[1,2,2],[5,5]]=>[[1,2,2,5,5]]=>1
[[1,2,5],[2,5]]=>[[1,2,2,5],[5]]=>1
[[1,2,3],[3,5]]=>[[1,2,3,3,5]]=>1
[[1,2,5],[3,3]]=>[[1,2,3,3],[5]]=>1
[[1,3,3],[2,5]]=>[[1,2,3,5],[3]]=>1
[[1,2,3],[4,5]]=>[[1,2,3,4,5]]=>1
[[1,2,4],[3,5]]=>[[1,2,3,5],[4]]=>1
[[1,2,5],[3,4]]=>[[1,2,3,4],[5]]=>1
[[1,3,4],[2,5]]=>[[1,2,4,5],[3]]=>1
[[1,3,5],[2,4]]=>[[1,2,4],[3,5]]=>5
[[1,2,3],[5,5]]=>[[1,2,3,5,5]]=>1
[[1,2,5],[3,5]]=>[[1,2,3,5],[5]]=>1
[[1,3,5],[2,5]]=>[[1,2,5,5],[3]]=>1
[[1,2,4],[4,5]]=>[[1,2,4,4,5]]=>1
[[1,2,5],[4,4]]=>[[1,2,4,4],[5]]=>1
[[1,4,4],[2,5]]=>[[1,2,4,5],[4]]=>1
[[1,2,4],[5,5]]=>[[1,2,4,5,5]]=>1
[[1,2,5],[4,5]]=>[[1,2,4,5],[5]]=>1
[[1,4,5],[2,5]]=>[[1,2,5,5],[4]]=>1
[[1,2,5],[5,5]]=>[[1,2,5,5,5]]=>1
[[1,3,3],[3,5]]=>[[1,3,3,3,5]]=>1
[[1,3,3],[4,5]]=>[[1,3,3,4,5]]=>1
[[1,3,4],[3,5]]=>[[1,3,3,5],[4]]=>1
[[1,3,5],[3,4]]=>[[1,3,3,4],[5]]=>1
[[1,3,3],[5,5]]=>[[1,3,3,5,5]]=>1
[[1,3,5],[3,5]]=>[[1,3,3,5],[5]]=>1
[[1,3,4],[4,5]]=>[[1,3,4,4,5]]=>1
[[1,3,5],[4,4]]=>[[1,3,4,4],[5]]=>1
[[1,4,4],[3,5]]=>[[1,3,4,5],[4]]=>1
[[1,3,4],[5,5]]=>[[1,3,4,5,5]]=>1
[[1,3,5],[4,5]]=>[[1,3,4,5],[5]]=>1
[[1,4,5],[3,5]]=>[[1,3,5,5],[4]]=>1
[[1,3,5],[5,5]]=>[[1,3,5,5,5]]=>1
[[1,4,4],[4,5]]=>[[1,4,4,4,5]]=>1
[[1,4,4],[5,5]]=>[[1,4,4,5,5]]=>1
[[1,4,5],[4,5]]=>[[1,4,4,5],[5]]=>1
[[1,4,5],[5,5]]=>[[1,4,5,5,5]]=>1
[[2,2,2],[3,5]]=>[[2,2,2,3,5]]=>2
[[2,2,2],[4,5]]=>[[2,2,2,4,5]]=>2
[[2,2,2],[5,5]]=>[[2,2,2,5,5]]=>2
[[2,2,3],[3,5]]=>[[2,2,3,3,5]]=>2
[[2,2,5],[3,3]]=>[[2,2,3,3],[5]]=>2
[[2,2,3],[4,5]]=>[[2,2,3,4,5]]=>2
[[2,2,4],[3,5]]=>[[2,2,3,5],[4]]=>2
[[2,2,5],[3,4]]=>[[2,2,3,4],[5]]=>2
[[2,2,3],[5,5]]=>[[2,2,3,5,5]]=>2
[[2,2,5],[3,5]]=>[[2,2,3,5],[5]]=>2
[[2,2,4],[4,5]]=>[[2,2,4,4,5]]=>2
[[2,2,5],[4,4]]=>[[2,2,4,4],[5]]=>2
[[2,2,4],[5,5]]=>[[2,2,4,5,5]]=>2
[[2,2,5],[4,5]]=>[[2,2,4,5],[5]]=>2
[[2,2,5],[5,5]]=>[[2,2,5,5,5]]=>2
[[2,3,3],[3,5]]=>[[2,3,3,3,5]]=>2
[[2,3,3],[4,5]]=>[[2,3,3,4,5]]=>2
[[2,3,4],[3,5]]=>[[2,3,3,5],[4]]=>2
[[2,3,5],[3,4]]=>[[2,3,3,4],[5]]=>2
[[2,3,3],[5,5]]=>[[2,3,3,5,5]]=>2
[[2,3,5],[3,5]]=>[[2,3,3,5],[5]]=>2
[[2,3,4],[4,5]]=>[[2,3,4,4,5]]=>2
[[2,3,5],[4,4]]=>[[2,3,4,4],[5]]=>2
[[2,4,4],[3,5]]=>[[2,3,4,5],[4]]=>2
[[2,3,4],[5,5]]=>[[2,3,4,5,5]]=>2
[[2,3,5],[4,5]]=>[[2,3,4,5],[5]]=>2
[[2,4,5],[3,5]]=>[[2,3,5,5],[4]]=>2
[[2,3,5],[5,5]]=>[[2,3,5,5,5]]=>2
[[2,4,4],[4,5]]=>[[2,4,4,4,5]]=>2
[[2,4,4],[5,5]]=>[[2,4,4,5,5]]=>2
[[2,4,5],[4,5]]=>[[2,4,4,5],[5]]=>2
[[2,4,5],[5,5]]=>[[2,4,5,5,5]]=>2
[[3,3,3],[4,5]]=>[[3,3,3,4,5]]=>3
[[3,3,3],[5,5]]=>[[3,3,3,5,5]]=>3
[[3,3,4],[4,5]]=>[[3,3,4,4,5]]=>3
[[3,3,5],[4,4]]=>[[3,3,4,4],[5]]=>3
[[3,3,4],[5,5]]=>[[3,3,4,5,5]]=>3
[[3,3,5],[4,5]]=>[[3,3,4,5],[5]]=>3
[[3,3,5],[5,5]]=>[[3,3,5,5,5]]=>3
[[3,4,4],[4,5]]=>[[3,4,4,4,5]]=>3
[[3,4,4],[5,5]]=>[[3,4,4,5,5]]=>3
[[3,4,5],[4,5]]=>[[3,4,4,5],[5]]=>3
[[3,4,5],[5,5]]=>[[3,4,5,5,5]]=>3
[[4,4,4],[5,5]]=>[[4,4,4,5,5]]=>4
[[4,4,5],[5,5]]=>[[4,4,5,5,5]]=>4
[[1,1,1],[2],[5]]=>[[1,1,1,2],[5]]=>1
[[1,1,1],[3],[5]]=>[[1,1,1,3],[5]]=>1
[[1,1,1],[4],[5]]=>[[1,1,1,4],[5]]=>1
[[1,1,2],[2],[5]]=>[[1,1,2,2],[5]]=>1
[[1,1,2],[3],[5]]=>[[1,1,2,3],[5]]=>1
[[1,1,3],[2],[5]]=>[[1,1,2,5],[3]]=>1
[[1,1,5],[2],[3]]=>[[1,1,2],[3],[5]]=>1
[[1,1,2],[4],[5]]=>[[1,1,2,4],[5]]=>1
[[1,1,4],[2],[5]]=>[[1,1,2,5],[4]]=>1
[[1,1,5],[2],[4]]=>[[1,1,2],[4],[5]]=>1
[[1,1,5],[2],[5]]=>[[1,1,2,5],[5]]=>1
[[1,1,3],[3],[5]]=>[[1,1,3,3],[5]]=>1
[[1,1,3],[4],[5]]=>[[1,1,3,4],[5]]=>1
[[1,1,4],[3],[5]]=>[[1,1,3,5],[4]]=>1
[[1,1,5],[3],[4]]=>[[1,1,3],[4],[5]]=>1
[[1,1,5],[3],[5]]=>[[1,1,3,5],[5]]=>1
[[1,1,4],[4],[5]]=>[[1,1,4,4],[5]]=>1
[[1,1,5],[4],[5]]=>[[1,1,4,5],[5]]=>1
[[1,2,2],[2],[5]]=>[[1,2,2,2],[5]]=>1
[[1,2,2],[3],[5]]=>[[1,2,2,3],[5]]=>1
[[1,2,3],[2],[5]]=>[[1,2,2,5],[3]]=>1
[[1,2,5],[2],[3]]=>[[1,2,2],[3],[5]]=>1
[[1,2,2],[4],[5]]=>[[1,2,2,4],[5]]=>1
[[1,2,4],[2],[5]]=>[[1,2,2,5],[4]]=>1
[[1,2,5],[2],[4]]=>[[1,2,2],[4],[5]]=>1
[[1,2,5],[2],[5]]=>[[1,2,2,5],[5]]=>1
[[1,2,3],[3],[5]]=>[[1,2,3,3],[5]]=>1
[[1,3,3],[2],[5]]=>[[1,2,3,5],[3]]=>1
[[1,3,5],[2],[3]]=>[[1,2,3],[3],[5]]=>1
[[1,2,3],[4],[5]]=>[[1,2,3,4],[5]]=>1
[[1,2,4],[3],[5]]=>[[1,2,3,5],[4]]=>1
[[1,2,5],[3],[4]]=>[[1,2,3],[4],[5]]=>1
[[1,3,4],[2],[5]]=>[[1,2,4,5],[3]]=>1
[[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]]=>1
[[1,4,5],[2],[3]]=>[[1,2,5],[3],[4]]=>1
[[1,2,5],[3],[5]]=>[[1,2,3,5],[5]]=>1
[[1,3,5],[2],[5]]=>[[1,2,5,5],[3]]=>1
[[1,5,5],[2],[3]]=>[[1,2,5],[3],[5]]=>1
[[1,2,4],[4],[5]]=>[[1,2,4,4],[5]]=>1
[[1,4,4],[2],[5]]=>[[1,2,4,5],[4]]=>1
[[1,4,5],[2],[4]]=>[[1,2,4],[4],[5]]=>1
[[1,2,5],[4],[5]]=>[[1,2,4,5],[5]]=>1
[[1,4,5],[2],[5]]=>[[1,2,5,5],[4]]=>1
[[1,5,5],[2],[4]]=>[[1,2,5],[4],[5]]=>1
[[1,5,5],[2],[5]]=>[[1,2,5,5],[5]]=>1
[[1,3,3],[3],[5]]=>[[1,3,3,3],[5]]=>1
[[1,3,3],[4],[5]]=>[[1,3,3,4],[5]]=>1
[[1,3,4],[3],[5]]=>[[1,3,3,5],[4]]=>1
[[1,3,5],[3],[4]]=>[[1,3,3],[4],[5]]=>1
[[1,3,5],[3],[5]]=>[[1,3,3,5],[5]]=>1
[[1,3,4],[4],[5]]=>[[1,3,4,4],[5]]=>1
[[1,4,4],[3],[5]]=>[[1,3,4,5],[4]]=>1
[[1,4,5],[3],[4]]=>[[1,3,4],[4],[5]]=>1
[[1,3,5],[4],[5]]=>[[1,3,4,5],[5]]=>1
[[1,4,5],[3],[5]]=>[[1,3,5,5],[4]]=>1
[[1,5,5],[3],[4]]=>[[1,3,5],[4],[5]]=>1
[[1,5,5],[3],[5]]=>[[1,3,5,5],[5]]=>1
[[1,4,4],[4],[5]]=>[[1,4,4,4],[5]]=>1
[[1,4,5],[4],[5]]=>[[1,4,4,5],[5]]=>1
[[1,5,5],[4],[5]]=>[[1,4,5,5],[5]]=>1
[[2,2,2],[3],[5]]=>[[2,2,2,3],[5]]=>2
[[2,2,2],[4],[5]]=>[[2,2,2,4],[5]]=>2
[[2,2,3],[3],[5]]=>[[2,2,3,3],[5]]=>2
[[2,2,3],[4],[5]]=>[[2,2,3,4],[5]]=>2
[[2,2,4],[3],[5]]=>[[2,2,3,5],[4]]=>2
[[2,2,5],[3],[4]]=>[[2,2,3],[4],[5]]=>2
[[2,2,5],[3],[5]]=>[[2,2,3,5],[5]]=>2
[[2,2,4],[4],[5]]=>[[2,2,4,4],[5]]=>2
[[2,2,5],[4],[5]]=>[[2,2,4,5],[5]]=>2
[[2,3,3],[3],[5]]=>[[2,3,3,3],[5]]=>2
[[2,3,3],[4],[5]]=>[[2,3,3,4],[5]]=>2
[[2,3,4],[3],[5]]=>[[2,3,3,5],[4]]=>2
[[2,3,5],[3],[4]]=>[[2,3,3],[4],[5]]=>2
[[2,3,5],[3],[5]]=>[[2,3,3,5],[5]]=>2
[[2,3,4],[4],[5]]=>[[2,3,4,4],[5]]=>2
[[2,4,4],[3],[5]]=>[[2,3,4,5],[4]]=>2
[[2,4,5],[3],[4]]=>[[2,3,4],[4],[5]]=>2
[[2,3,5],[4],[5]]=>[[2,3,4,5],[5]]=>2
[[2,4,5],[3],[5]]=>[[2,3,5,5],[4]]=>2
[[2,5,5],[3],[4]]=>[[2,3,5],[4],[5]]=>2
[[2,5,5],[3],[5]]=>[[2,3,5,5],[5]]=>2
[[2,4,4],[4],[5]]=>[[2,4,4,4],[5]]=>2
[[2,4,5],[4],[5]]=>[[2,4,4,5],[5]]=>2
[[2,5,5],[4],[5]]=>[[2,4,5,5],[5]]=>2
[[3,3,3],[4],[5]]=>[[3,3,3,4],[5]]=>3
[[3,3,4],[4],[5]]=>[[3,3,4,4],[5]]=>3
[[3,3,5],[4],[5]]=>[[3,3,4,5],[5]]=>3
[[3,4,4],[4],[5]]=>[[3,4,4,4],[5]]=>3
[[3,4,5],[4],[5]]=>[[3,4,4,5],[5]]=>3
[[3,5,5],[4],[5]]=>[[3,4,5,5],[5]]=>3
[[1,1],[2,2],[5]]=>[[1,1,2,2],[5]]=>1
[[1,1],[2,3],[5]]=>[[1,1,2,3],[5]]=>1
[[1,1],[2,5],[3]]=>[[1,1,2,5],[3]]=>1
[[1,1],[2,4],[5]]=>[[1,1,2,4],[5]]=>1
[[1,1],[2,5],[4]]=>[[1,1,2,5],[4]]=>1
[[1,1],[2,5],[5]]=>[[1,1,2,5],[5]]=>1
[[1,1],[3,3],[5]]=>[[1,1,3,3],[5]]=>1
[[1,1],[3,4],[5]]=>[[1,1,3,4],[5]]=>1
[[1,1],[3,5],[4]]=>[[1,1,3,5],[4]]=>1
[[1,1],[3,5],[5]]=>[[1,1,3,5],[5]]=>1
[[1,1],[4,4],[5]]=>[[1,1,4,4],[5]]=>1
[[1,1],[4,5],[5]]=>[[1,1,4,5],[5]]=>1
[[1,2],[2,3],[5]]=>[[1,2,2,3],[5]]=>1
[[1,2],[2,5],[3]]=>[[1,2,2,5],[3]]=>1
[[1,2],[2,4],[5]]=>[[1,2,2,4],[5]]=>1
[[1,2],[2,5],[4]]=>[[1,2,2,5],[4]]=>1
[[1,2],[2,5],[5]]=>[[1,2,2,5],[5]]=>1
[[1,2],[3,3],[5]]=>[[1,2,3,3],[5]]=>1
[[1,3],[2,5],[3]]=>[[1,2,3,5],[3]]=>1
[[1,2],[3,4],[5]]=>[[1,2,3,4],[5]]=>1
[[1,2],[3,5],[4]]=>[[1,2,3,5],[4]]=>1
[[1,3],[2,4],[5]]=>[[1,2,4],[3,5]]=>5
[[1,3],[2,5],[4]]=>[[1,2,4,5],[3]]=>1
[[1,4],[2,5],[3]]=>[[1,2,5],[3],[4]]=>1
[[1,2],[3,5],[5]]=>[[1,2,3,5],[5]]=>1
[[1,3],[2,5],[5]]=>[[1,2,5,5],[3]]=>1
[[1,2],[4,4],[5]]=>[[1,2,4,4],[5]]=>1
[[1,4],[2,5],[4]]=>[[1,2,4,5],[4]]=>1
[[1,2],[4,5],[5]]=>[[1,2,4,5],[5]]=>1
[[1,4],[2,5],[5]]=>[[1,2,5,5],[4]]=>1
[[1,3],[3,4],[5]]=>[[1,3,3,4],[5]]=>1
[[1,3],[3,5],[4]]=>[[1,3,3,5],[4]]=>1
[[1,3],[3,5],[5]]=>[[1,3,3,5],[5]]=>1
[[1,3],[4,4],[5]]=>[[1,3,4,4],[5]]=>1
[[1,4],[3,5],[4]]=>[[1,3,4,5],[4]]=>1
[[1,3],[4,5],[5]]=>[[1,3,4,5],[5]]=>1
[[1,4],[3,5],[5]]=>[[1,3,5,5],[4]]=>1
[[1,4],[4,5],[5]]=>[[1,4,4,5],[5]]=>1
[[2,2],[3,3],[5]]=>[[2,2,3,3],[5]]=>2
[[2,2],[3,4],[5]]=>[[2,2,3,4],[5]]=>2
[[2,2],[3,5],[4]]=>[[2,2,3,5],[4]]=>2
[[2,2],[3,5],[5]]=>[[2,2,3,5],[5]]=>2
[[2,2],[4,4],[5]]=>[[2,2,4,4],[5]]=>2
[[2,2],[4,5],[5]]=>[[2,2,4,5],[5]]=>2
[[2,3],[3,4],[5]]=>[[2,3,3,4],[5]]=>2
[[2,3],[3,5],[4]]=>[[2,3,3,5],[4]]=>2
[[2,3],[3,5],[5]]=>[[2,3,3,5],[5]]=>2
[[2,3],[4,4],[5]]=>[[2,3,4,4],[5]]=>2
[[2,4],[3,5],[4]]=>[[2,3,4,5],[4]]=>2
[[2,3],[4,5],[5]]=>[[2,3,4,5],[5]]=>2
[[2,4],[3,5],[5]]=>[[2,3,5,5],[4]]=>2
[[2,4],[4,5],[5]]=>[[2,4,4,5],[5]]=>2
[[3,3],[4,4],[5]]=>[[3,3,4,4],[5]]=>3
[[3,3],[4,5],[5]]=>[[3,3,4,5],[5]]=>3
[[3,4],[4,5],[5]]=>[[3,4,4,5],[5]]=>3
[[1,1],[2],[3],[5]]=>[[1,1,2],[3],[5]]=>1
[[1,1],[2],[4],[5]]=>[[1,1,2],[4],[5]]=>1
[[1,1],[3],[4],[5]]=>[[1,1,3],[4],[5]]=>1
[[1,2],[2],[3],[5]]=>[[1,2,2],[3],[5]]=>1
[[1,2],[2],[4],[5]]=>[[1,2,2],[4],[5]]=>1
[[1,3],[2],[3],[5]]=>[[1,2,3],[3],[5]]=>1
[[1,2],[3],[4],[5]]=>[[1,2,3],[4],[5]]=>1
[[1,3],[2],[4],[5]]=>[[1,2,4],[3],[5]]=>1
[[1,4],[2],[3],[5]]=>[[1,2,5],[3],[4]]=>1
[[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]=>1
[[1,5],[2],[3],[5]]=>[[1,2,5],[3],[5]]=>1
[[1,4],[2],[4],[5]]=>[[1,2,4],[4],[5]]=>1
[[1,5],[2],[4],[5]]=>[[1,2,5],[4],[5]]=>1
[[1,3],[3],[4],[5]]=>[[1,3,3],[4],[5]]=>1
[[1,4],[3],[4],[5]]=>[[1,3,4],[4],[5]]=>1
[[1,5],[3],[4],[5]]=>[[1,3,5],[4],[5]]=>1
[[2,2],[3],[4],[5]]=>[[2,2,3],[4],[5]]=>2
[[2,3],[3],[4],[5]]=>[[2,3,3],[4],[5]]=>2
[[2,4],[3],[4],[5]]=>[[2,3,4],[4],[5]]=>2
[[2,5],[3],[4],[5]]=>[[2,3,5],[4],[5]]=>2
[[1],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5]]=>1
[[1,1,1,1,1,4]]=>[[1,1,1,1,1,4]]=>1
[[1,1,1,1,2,4]]=>[[1,1,1,1,2,4]]=>1
[[1,1,1,1,3,4]]=>[[1,1,1,1,3,4]]=>1
[[1,1,1,1,4,4]]=>[[1,1,1,1,4,4]]=>1
[[1,1,1,2,2,4]]=>[[1,1,1,2,2,4]]=>1
[[1,1,1,2,3,4]]=>[[1,1,1,2,3,4]]=>1
[[1,1,1,2,4,4]]=>[[1,1,1,2,4,4]]=>1
[[1,1,1,3,3,4]]=>[[1,1,1,3,3,4]]=>1
[[1,1,1,3,4,4]]=>[[1,1,1,3,4,4]]=>1
[[1,1,1,4,4,4]]=>[[1,1,1,4,4,4]]=>1
[[1,1,2,2,2,4]]=>[[1,1,2,2,2,4]]=>1
[[1,1,2,2,3,4]]=>[[1,1,2,2,3,4]]=>1
[[1,1,2,2,4,4]]=>[[1,1,2,2,4,4]]=>1
[[1,1,2,3,3,4]]=>[[1,1,2,3,3,4]]=>1
[[1,1,2,3,4,4]]=>[[1,1,2,3,4,4]]=>1
[[1,1,2,4,4,4]]=>[[1,1,2,4,4,4]]=>1
[[1,1,3,3,3,4]]=>[[1,1,3,3,3,4]]=>1
[[1,1,3,3,4,4]]=>[[1,1,3,3,4,4]]=>1
[[1,1,3,4,4,4]]=>[[1,1,3,4,4,4]]=>1
[[1,1,4,4,4,4]]=>[[1,1,4,4,4,4]]=>1
[[1,2,2,2,2,4]]=>[[1,2,2,2,2,4]]=>1
[[1,2,2,2,3,4]]=>[[1,2,2,2,3,4]]=>1
[[1,2,2,2,4,4]]=>[[1,2,2,2,4,4]]=>1
[[1,2,2,3,3,4]]=>[[1,2,2,3,3,4]]=>1
[[1,2,2,3,4,4]]=>[[1,2,2,3,4,4]]=>1
[[1,2,2,4,4,4]]=>[[1,2,2,4,4,4]]=>1
[[1,2,3,3,3,4]]=>[[1,2,3,3,3,4]]=>1
[[1,2,3,3,4,4]]=>[[1,2,3,3,4,4]]=>1
[[1,2,3,4,4,4]]=>[[1,2,3,4,4,4]]=>1
[[1,2,4,4,4,4]]=>[[1,2,4,4,4,4]]=>1
[[1,3,3,3,3,4]]=>[[1,3,3,3,3,4]]=>1
[[1,3,3,3,4,4]]=>[[1,3,3,3,4,4]]=>1
[[1,3,3,4,4,4]]=>[[1,3,3,4,4,4]]=>1
[[1,3,4,4,4,4]]=>[[1,3,4,4,4,4]]=>1
[[1,4,4,4,4,4]]=>[[1,4,4,4,4,4]]=>1
[[2,2,2,2,2,4]]=>[[2,2,2,2,2,4]]=>2
[[2,2,2,2,3,4]]=>[[2,2,2,2,3,4]]=>2
[[2,2,2,2,4,4]]=>[[2,2,2,2,4,4]]=>2
[[2,2,2,3,3,4]]=>[[2,2,2,3,3,4]]=>2
[[2,2,2,3,4,4]]=>[[2,2,2,3,4,4]]=>2
[[2,2,2,4,4,4]]=>[[2,2,2,4,4,4]]=>2
[[2,2,3,3,3,4]]=>[[2,2,3,3,3,4]]=>2
[[2,2,3,3,4,4]]=>[[2,2,3,3,4,4]]=>2
[[2,2,3,4,4,4]]=>[[2,2,3,4,4,4]]=>2
[[2,2,4,4,4,4]]=>[[2,2,4,4,4,4]]=>2
[[1,1,1,1,1],[4]]=>[[1,1,1,1,1,4]]=>1
[[1,1,1,1,2],[4]]=>[[1,1,1,1,2,4]]=>1
[[1,1,1,1,3],[4]]=>[[1,1,1,1,3,4]]=>1
[[1,1,1,1,4],[4]]=>[[1,1,1,1,4,4]]=>1
[[1,1,1,2,2],[4]]=>[[1,1,1,2,2,4]]=>1
[[1,1,1,2,3],[4]]=>[[1,1,1,2,3,4]]=>1
[[1,1,1,2,4],[4]]=>[[1,1,1,2,4,4]]=>1
[[1,1,1,3,3],[4]]=>[[1,1,1,3,3,4]]=>1
[[1,1,1,3,4],[4]]=>[[1,1,1,3,4,4]]=>1
[[1,1,1,4,4],[4]]=>[[1,1,1,4,4,4]]=>1
[[1,1,2,2,2],[4]]=>[[1,1,2,2,2,4]]=>1
[[1,1,2,2,3],[4]]=>[[1,1,2,2,3,4]]=>1
[[1,1,2,2,4],[4]]=>[[1,1,2,2,4,4]]=>1
[[1,1,2,3,3],[4]]=>[[1,1,2,3,3,4]]=>1
[[1,1,2,3,4],[4]]=>[[1,1,2,3,4,4]]=>1
[[1,1,2,4,4],[4]]=>[[1,1,2,4,4,4]]=>1
[[1,1,3,3,3],[4]]=>[[1,1,3,3,3,4]]=>1
[[1,1,3,3,4],[4]]=>[[1,1,3,3,4,4]]=>1
[[1,1,3,4,4],[4]]=>[[1,1,3,4,4,4]]=>1
[[1,1,4,4,4],[4]]=>[[1,1,4,4,4,4]]=>1
[[1,2,2,2,2],[4]]=>[[1,2,2,2,2,4]]=>1
[[1,2,2,2,3],[4]]=>[[1,2,2,2,3,4]]=>1
[[1,2,2,2,4],[4]]=>[[1,2,2,2,4,4]]=>1
[[1,2,2,3,3],[4]]=>[[1,2,2,3,3,4]]=>1
[[1,2,2,3,4],[4]]=>[[1,2,2,3,4,4]]=>1
[[1,2,2,4,4],[4]]=>[[1,2,2,4,4,4]]=>1
[[1,2,3,3,3],[4]]=>[[1,2,3,3,3,4]]=>1
[[1,2,3,3,4],[4]]=>[[1,2,3,3,4,4]]=>1
[[1,2,3,4,4],[4]]=>[[1,2,3,4,4,4]]=>1
[[1,2,4,4,4],[4]]=>[[1,2,4,4,4,4]]=>1
[[1,3,3,3,3],[4]]=>[[1,3,3,3,3,4]]=>1
[[1,3,3,3,4],[4]]=>[[1,3,3,3,4,4]]=>1
[[1,3,3,4,4],[4]]=>[[1,3,3,4,4,4]]=>1
[[1,3,4,4,4],[4]]=>[[1,3,4,4,4,4]]=>1
[[1,4,4,4,4],[4]]=>[[1,4,4,4,4,4]]=>1
[[2,2,2,2,2],[4]]=>[[2,2,2,2,2,4]]=>2
[[2,2,2,2,3],[4]]=>[[2,2,2,2,3,4]]=>2
[[2,2,2,2,4],[4]]=>[[2,2,2,2,4,4]]=>2
[[2,2,2,3,3],[4]]=>[[2,2,2,3,3,4]]=>2
[[2,2,2,3,4],[4]]=>[[2,2,2,3,4,4]]=>2
[[2,2,2,4,4],[4]]=>[[2,2,2,4,4,4]]=>2
[[2,2,3,3,3],[4]]=>[[2,2,3,3,3,4]]=>2
[[2,2,3,3,4],[4]]=>[[2,2,3,3,4,4]]=>2
[[2,2,3,4,4],[4]]=>[[2,2,3,4,4,4]]=>2
[[2,2,4,4,4],[4]]=>[[2,2,4,4,4,4]]=>2
[[1,1,1,1],[2,4]]=>[[1,1,1,1,2,4]]=>1
[[1,1,1,1],[3,4]]=>[[1,1,1,1,3,4]]=>1
[[1,1,1,1],[4,4]]=>[[1,1,1,1,4,4]]=>1
[[1,1,1,2],[2,4]]=>[[1,1,1,2,2,4]]=>1
[[1,1,1,2],[3,4]]=>[[1,1,1,2,3,4]]=>1
[[1,1,1,2],[4,4]]=>[[1,1,1,2,4,4]]=>1
[[1,1,1,3],[3,4]]=>[[1,1,1,3,3,4]]=>1
[[1,1,1,3],[4,4]]=>[[1,1,1,3,4,4]]=>1
[[1,1,1,4],[4,4]]=>[[1,1,1,4,4,4]]=>1
[[1,1,2,2],[2,4]]=>[[1,1,2,2,2,4]]=>1
[[1,1,2,2],[3,4]]=>[[1,1,2,2,3,4]]=>1
[[1,1,2,2],[4,4]]=>[[1,1,2,2,4,4]]=>1
[[1,1,2,3],[3,4]]=>[[1,1,2,3,3,4]]=>1
[[1,1,2,3],[4,4]]=>[[1,1,2,3,4,4]]=>1
[[1,1,2,4],[4,4]]=>[[1,1,2,4,4,4]]=>1
[[1,1,3,3],[3,4]]=>[[1,1,3,3,3,4]]=>1
[[1,1,3,3],[4,4]]=>[[1,1,3,3,4,4]]=>1
[[1,1,3,4],[4,4]]=>[[1,1,3,4,4,4]]=>1
[[1,1,4,4],[4,4]]=>[[1,1,4,4,4,4]]=>1
[[1,2,2,2],[2,4]]=>[[1,2,2,2,2,4]]=>1
[[1,2,2,2],[3,4]]=>[[1,2,2,2,3,4]]=>1
[[1,2,2,2],[4,4]]=>[[1,2,2,2,4,4]]=>1
[[1,2,2,3],[3,4]]=>[[1,2,2,3,3,4]]=>1
[[1,2,2,3],[4,4]]=>[[1,2,2,3,4,4]]=>1
[[1,2,2,4],[4,4]]=>[[1,2,2,4,4,4]]=>1
[[1,2,3,3],[3,4]]=>[[1,2,3,3,3,4]]=>1
[[1,2,3,3],[4,4]]=>[[1,2,3,3,4,4]]=>1
[[1,2,3,4],[4,4]]=>[[1,2,3,4,4,4]]=>1
[[1,2,4,4],[4,4]]=>[[1,2,4,4,4,4]]=>1
[[1,3,3,3],[3,4]]=>[[1,3,3,3,3,4]]=>1
[[1,3,3,3],[4,4]]=>[[1,3,3,3,4,4]]=>1
[[1,3,3,4],[4,4]]=>[[1,3,3,4,4,4]]=>1
[[1,3,4,4],[4,4]]=>[[1,3,4,4,4,4]]=>1
[[2,2,2,2],[3,4]]=>[[2,2,2,2,3,4]]=>2
[[2,2,2,2],[4,4]]=>[[2,2,2,2,4,4]]=>2
[[2,2,2,3],[3,4]]=>[[2,2,2,3,3,4]]=>2
[[2,2,2,3],[4,4]]=>[[2,2,2,3,4,4]]=>2
[[2,2,2,4],[4,4]]=>[[2,2,2,4,4,4]]=>2
[[2,2,3,3],[3,4]]=>[[2,2,3,3,3,4]]=>2
[[2,2,3,3],[4,4]]=>[[2,2,3,3,4,4]]=>2
[[2,2,3,4],[4,4]]=>[[2,2,3,4,4,4]]=>2
[[2,2,4,4],[4,4]]=>[[2,2,4,4,4,4]]=>2
[[1,1,1],[2,2,4]]=>[[1,1,1,2,2,4]]=>1
[[1,1,1],[2,3,4]]=>[[1,1,1,2,3,4]]=>1
[[1,1,1],[2,4,4]]=>[[1,1,1,2,4,4]]=>1
[[1,1,1],[3,3,4]]=>[[1,1,1,3,3,4]]=>1
[[1,1,1],[3,4,4]]=>[[1,1,1,3,4,4]]=>1
[[1,1,1],[4,4,4]]=>[[1,1,1,4,4,4]]=>1
[[1,1,2],[2,2,4]]=>[[1,1,2,2,2,4]]=>1
[[1,1,2],[2,3,4]]=>[[1,1,2,2,3,4]]=>1
[[1,1,2],[2,4,4]]=>[[1,1,2,2,4,4]]=>1
[[1,1,2],[3,3,4]]=>[[1,1,2,3,3,4]]=>1
[[1,1,2],[3,4,4]]=>[[1,1,2,3,4,4]]=>1
[[1,1,2],[4,4,4]]=>[[1,1,2,4,4,4]]=>1
[[1,1,3],[3,3,4]]=>[[1,1,3,3,3,4]]=>1
[[1,1,3],[3,4,4]]=>[[1,1,3,3,4,4]]=>1
[[1,1,3],[4,4,4]]=>[[1,1,3,4,4,4]]=>1
[[1,2,2],[2,3,4]]=>[[1,2,2,2,3,4]]=>1
[[1,2,2],[2,4,4]]=>[[1,2,2,2,4,4]]=>1
[[1,2,2],[3,3,4]]=>[[1,2,2,3,3,4]]=>1
[[1,2,2],[3,4,4]]=>[[1,2,2,3,4,4]]=>1
[[1,2,2],[4,4,4]]=>[[1,2,2,4,4,4]]=>1
[[1,2,3],[3,3,4]]=>[[1,2,3,3,3,4]]=>1
[[1,2,3],[3,4,4]]=>[[1,2,3,3,4,4]]=>1
[[1,2,3],[4,4,4]]=>[[1,2,3,4,4,4]]=>1
[[1,3,3],[3,4,4]]=>[[1,3,3,3,4,4]]=>1
[[1,3,3],[4,4,4]]=>[[1,3,3,4,4,4]]=>1
[[2,2,2],[3,3,4]]=>[[2,2,2,3,3,4]]=>2
[[2,2,2],[3,4,4]]=>[[2,2,2,3,4,4]]=>2
[[2,2,2],[4,4,4]]=>[[2,2,2,4,4,4]]=>2
[[2,2,3],[3,3,4]]=>[[2,2,3,3,3,4]]=>2
[[2,2,3],[3,4,4]]=>[[2,2,3,3,4,4]]=>2
[[2,2,3],[4,4,4]]=>[[2,2,3,4,4,4]]=>2
[[1]]=>[[1]]=>1
[[1,1,1,1],[2,2,2],[3,3],[4]]=>[[1,1,1,1,2,2,2],[3,3],[4]]=>3
[[1,1,1,2],[2,2,2],[3,3],[4]]=>[[1,1,1,2,2,2,2],[3,3],[4]]=>3
[[1,1,1,1],[2,2,3],[3,3],[4]]=>[[1,1,1,1,2,2,3],[3,3],[4]]=>3
[[1,1,1,2],[2,2,3],[3,3],[4]]=>[[1,1,1,2,2,2,3],[3,3],[4]]=>3
[[1,1,1,3],[2,2,3],[3,3],[4]]=>[[1,1,1,2,2,3,3],[3,3],[4]]=>3
[[1,1,2,2],[2,2,3],[3,3],[4]]=>[[1,1,2,2,2,2,3],[3,3],[4]]=>3
[[1,1,2,3],[2,2,3],[3,3],[4]]=>[[1,1,2,2,2,3,3],[3,3],[4]]=>3
[[1,1,1,1],[2,2,2],[3,4],[4]]=>[[1,1,1,1,2,2,2],[3,4],[4]]=>4
[[1,1,1,2],[2,2,2],[3,4],[4]]=>[[1,1,1,2,2,2,2],[3,4],[4]]=>4
[[1,1,1,1],[2,2,3],[3,4],[4]]=>[[1,1,1,1,2,2,3],[3,4],[4]]=>4
[[1,1,1,2],[2,2,3],[3,4],[4]]=>[[1,1,1,2,2,2,3],[3,4],[4]]=>4
[[1,1,1,3],[2,2,3],[3,4],[4]]=>[[1,1,1,2,2,3],[3,3,4],[4]]=>3
[[1,1,2,2],[2,2,3],[3,4],[4]]=>[[1,1,2,2,2,2,3],[3,4],[4]]=>4
[[1,1,2,3],[2,2,3],[3,4],[4]]=>[[1,1,2,2,2,3],[3,3,4],[4]]=>3
[[1,1,1,1],[2,2,4],[3,4],[4]]=>[[1,1,1,1,2,2,4],[3,4],[4]]=>4
[[1,1,1,2],[2,2,4],[3,4],[4]]=>[[1,1,1,2,2,2,4],[3,4],[4]]=>4
[[1,1,1,3],[2,2,4],[3,4],[4]]=>[[1,1,1,2,2,4,4],[3,3],[4]]=>3
[[1,1,1,4],[2,2,4],[3,4],[4]]=>[[1,1,1,2,2,4,4],[3,4],[4]]=>4
[[1,1,2,2],[2,2,4],[3,4],[4]]=>[[1,1,2,2,2,2,4],[3,4],[4]]=>4
[[1,1,2,3],[2,2,4],[3,4],[4]]=>[[1,1,2,2,2,4,4],[3,3],[4]]=>3
[[1,1,2,4],[2,2,4],[3,4],[4]]=>[[1,1,2,2,2,4,4],[3,4],[4]]=>4
[[1,1,1,1],[2,3,3],[3,4],[4]]=>[[1,1,1,1,2,3,3],[3,4],[4]]=>4
[[1,1,1,2],[2,3,3],[3,4],[4]]=>[[1,1,1,2,2,3,3],[3,4],[4]]=>4
[[1,1,1,3],[2,3,3],[3,4],[4]]=>[[1,1,1,2,3,3,3],[3,4],[4]]=>4
[[1,1,2,2],[2,3,3],[3,4],[4]]=>[[1,1,2,2,2,3,3],[3,4],[4]]=>4
[[1,1,2,3],[2,3,3],[3,4],[4]]=>[[1,1,2,2,3,3,3],[3,4],[4]]=>4
[[1,1,1,1],[2,3,4],[3,4],[4]]=>[[1,1,1,1,2,3,4],[3,4],[4]]=>4
[[1,1,1,2],[2,3,4],[3,4],[4]]=>[[1,1,1,2,2,3,4],[3,4],[4]]=>4
[[1,1,1,3],[2,3,4],[3,4],[4]]=>[[1,1,1,2,3,3,4],[3,4],[4]]=>4
[[1,1,1,4],[2,3,4],[3,4],[4]]=>[[1,1,1,2,3,4,4],[3,4],[4]]=>4
[[1,1,2,2],[2,3,4],[3,4],[4]]=>[[1,1,2,2,2,3,4],[3,4],[4]]=>4
[[1,1,2,3],[2,3,4],[3,4],[4]]=>[[1,1,2,2,3,3,4],[3,4],[4]]=>4
[[1,1,2,4],[2,3,4],[3,4],[4]]=>[[1,1,2,2,3,4,4],[3,4],[4]]=>4
[[1,1,3,3],[2,3,4],[3,4],[4]]=>[[1,1,2,3,3,3,4],[3,4],[4]]=>4
[[1,1,3,4],[2,3,4],[3,4],[4]]=>[[1,1,2,3,3,4,4],[3,4],[4]]=>4
[[1,2,2,2],[2,3,3],[3,4],[4]]=>[[1,2,2,2,2,3,3],[3,4],[4]]=>4
[[1,2,2,3],[2,3,3],[3,4],[4]]=>[[1,2,2,2,3,3,3],[3,4],[4]]=>4
[[1,2,2,2],[2,3,4],[3,4],[4]]=>[[1,2,2,2,2,3,4],[3,4],[4]]=>4
[[1,2,2,3],[2,3,4],[3,4],[4]]=>[[1,2,2,2,3,3,4],[3,4],[4]]=>4
[[1,2,2,4],[2,3,4],[3,4],[4]]=>[[1,2,2,2,3,4,4],[3,4],[4]]=>4
[[1,2,3,3],[2,3,4],[3,4],[4]]=>[[1,2,2,3,3,3,4],[3,4],[4]]=>4
[[1,2,3,4],[2,3,4],[3,4],[4]]=>[[1,2,2,3,3,4,4],[3,4],[4]]=>4
[[2]]=>[[2]]=>2
[[1,1]]=>[[1,1]]=>1
[[3]]=>[[3]]=>3
[[1,1,1]]=>[[1,1,1]]=>1
[[4]]=>[[4]]=>4
[[1,1,1,1]]=>[[1,1,1,1]]=>1
[[5]]=>[[5]]=>5
[[1,1,1,1,1]]=>[[1,1,1,1,1]]=>1
[[6]]=>[[6]]=>6
[[1,1,1,1,1,1]]=>[[1,1,1,1,1,1]]=>1
[[1,2,3,4,5,6]]=>[[1,2,3,4,5,6]]=>1
[[1,2,3,4,5],[6]]=>[[1,2,3,4,5,6]]=>1
[[1,2,3,4,6],[5]]=>[[1,2,3,4,5],[6]]=>1
[[1,2,3,4],[5],[6]]=>[[1,2,3,4,5],[6]]=>1
[[1,2,3,5,6],[4]]=>[[1,2,3,4,6],[5]]=>1
[[1,2,3,5],[4,6]]=>[[1,2,3,4,6],[5]]=>1
[[1,2,3,5],[4],[6]]=>[[1,2,3,4,6],[5]]=>1
[[1,2,3,4],[5,6]]=>[[1,2,3,4,5,6]]=>1
[[1,2,3,6],[4],[5]]=>[[1,2,3,4],[5],[6]]=>1
[[1,2,3],[4],[5],[6]]=>[[1,2,3,4],[5],[6]]=>1
[[1,2,4,5,6],[3]]=>[[1,2,3,5,6],[4]]=>1
[[1,2,4,5],[3,6]]=>[[1,2,3,5,6],[4]]=>1
[[1,2,4,6],[3,5]]=>[[1,2,3,5],[4,6]]=>6
[[1,2,4],[3,5],[6]]=>[[1,2,3,5],[4,6]]=>6
[[1,2,4,5],[3],[6]]=>[[1,2,3,5,6],[4]]=>1
[[1,2,4,6],[3],[5]]=>[[1,2,3,5],[4],[6]]=>1
[[1,2,4],[3],[5],[6]]=>[[1,2,3,5],[4],[6]]=>1
[[1,2,3,6],[4,5]]=>[[1,2,3,4,5],[6]]=>1
[[1,2,3],[4,5],[6]]=>[[1,2,3,4,5],[6]]=>1
[[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]]=>1
[[1,2,5],[3,6],[4]]=>[[1,2,3,6],[4],[5]]=>1
[[1,2,5],[3],[4],[6]]=>[[1,2,3,6],[4],[5]]=>1
[[1,2,3],[4,6],[5]]=>[[1,2,3,4,6],[5]]=>1
[[1,2,4],[3,6],[5]]=>[[1,2,3,5,6],[4]]=>1
[[1,2,6],[3],[4],[5]]=>[[1,2,3],[4],[5],[6]]=>1
[[1,2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6]]=>1
[[1,3,4,5,6],[2]]=>[[1,2,4,5,6],[3]]=>1
[[1,3,4,5],[2,6]]=>[[1,2,4,5,6],[3]]=>1
[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]=>6
[[1,3,4],[2,5],[6]]=>[[1,2,4,5],[3,6]]=>6
[[1,3,5,6],[2,4]]=>[[1,2,4,6],[3,5]]=>5
[[1,3,5],[2,4,6]]=>[[1,2,4,6],[3,5]]=>5
[[1,3,5],[2,4],[6]]=>[[1,2,4,6],[3,5]]=>5
[[1,3,4],[2,5,6]]=>[[1,2,4,5,6],[3]]=>1
[[1,3,6],[2,4],[5]]=>[[1,2,4],[3,5],[6]]=>5
[[1,3],[2,4],[5],[6]]=>[[1,2,4],[3,5],[6]]=>5
[[1,3,4,5],[2],[6]]=>[[1,2,4,5,6],[3]]=>1
[[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]=>1
[[1,3,4],[2],[5],[6]]=>[[1,2,4,5],[3],[6]]=>1
[[1,3,5,6],[2],[4]]=>[[1,2,4,6],[3],[5]]=>1
[[1,3,5],[2,6],[4]]=>[[1,2,4,6],[3],[5]]=>1
[[1,3,5],[2],[4],[6]]=>[[1,2,4,6],[3],[5]]=>1
[[1,3,4],[2,6],[5]]=>[[1,2,4,5,6],[3]]=>1
[[1,3,6],[2],[4],[5]]=>[[1,2,4],[3],[5],[6]]=>1
[[1,3],[2],[4],[5],[6]]=>[[1,2,4],[3],[5],[6]]=>1
[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]=>6
[[1,2,5],[3,4,6]]=>[[1,2,3,4,6],[5]]=>1
[[1,2,5],[3,4],[6]]=>[[1,2,3,4],[5,6]]=>6
[[1,2,4],[3,5,6]]=>[[1,2,3,5,6],[4]]=>1
[[1,2,6],[3,4],[5]]=>[[1,2,3,4],[5],[6]]=>1
[[1,2],[3,4],[5],[6]]=>[[1,2,3,4],[5],[6]]=>1
[[1,4,5,6],[2],[3]]=>[[1,2,5,6],[3],[4]]=>1
[[1,4,5],[2,6],[3]]=>[[1,2,5,6],[3],[4]]=>1
[[1,4,6],[2,5],[3]]=>[[1,2,5],[3,6],[4]]=>6
[[1,4],[2,5],[3,6]]=>[[1,2,5],[3,6],[4]]=>6
[[1,4],[2,5],[3],[6]]=>[[1,2,5],[3,6],[4]]=>6
[[1,4,5],[2],[3],[6]]=>[[1,2,5,6],[3],[4]]=>1
[[1,4,6],[2],[3],[5]]=>[[1,2,5],[3],[4],[6]]=>1
[[1,4],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6]]=>1
[[1,2,3],[4,5,6]]=>[[1,2,3,4,5,6]]=>1
[[1,2,6],[3,5],[4]]=>[[1,2,3,5],[4],[6]]=>1
[[1,2],[3,5],[4],[6]]=>[[1,2,3,5],[4],[6]]=>1
[[1,3,6],[2,5],[4]]=>[[1,2,4,5],[3],[6]]=>1
[[1,3],[2,5],[4,6]]=>[[1,2,4,5],[3,6]]=>6
[[1,3],[2,5],[4],[6]]=>[[1,2,4,5],[3],[6]]=>1
[[1,2],[3,5],[4,6]]=>[[1,2,3,5],[4,6]]=>6
[[1,5,6],[2],[3],[4]]=>[[1,2,6],[3],[4],[5]]=>1
[[1,5],[2,6],[3],[4]]=>[[1,2,6],[3],[4],[5]]=>1
[[1,5],[2],[3],[4],[6]]=>[[1,2,6],[3],[4],[5]]=>1
[[1,2],[3,6],[4],[5]]=>[[1,2,3,6],[4],[5]]=>1
[[1,3],[2,4],[5,6]]=>[[1,2,4,6],[3,5]]=>5
[[1,3],[2,6],[4],[5]]=>[[1,2,4,6],[3],[5]]=>1
[[1,2],[3,4],[5,6]]=>[[1,2,3,4],[5,6]]=>6
[[1,4],[2,6],[3],[5]]=>[[1,2,5,6],[3],[4]]=>1
[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>1
[[1],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6]]=>1
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Description
The last entry on the main diagonal of a semistandard tableau.
Map
catabolism
Description
Remove the first row of the semistandard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater or equal to than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than or equal to $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater or equal to than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than or equal to $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
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