Identifier
Mp00106:
Standard tableaux
—catabolism⟶
Standard tableaux
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Images
=>
Cc0007;cc-rep-0Cc0007;cc-rep-1Cc0018;cc-rep-2Cc0019;cc-rep-3
[[1]]=>[[1]]=>[[1]]=>[[1]]
[[1,2]]=>[[1,2]]=>[[2,0],[1]]=>[[1,2]]
[[1],[2]]=>[[1,2]]=>[[2,0],[1]]=>[[1,2]]
[[1,2,3]]=>[[1,2,3]]=>[[3,0,0],[2,0],[1]]=>[[1,2,3]]
[[1,3],[2]]=>[[1,2],[3]]=>[[2,1,0],[2,0],[1]]=>[[1,2],[3]]
[[1,2],[3]]=>[[1,2,3]]=>[[3,0,0],[2,0],[1]]=>[[1,2,3]]
[[1],[2],[3]]=>[[1,2],[3]]=>[[2,1,0],[2,0],[1]]=>[[1,2],[3]]
[[1,2,3,4]]=>[[1,2,3,4]]=>[[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4]]
[[1,3,4],[2]]=>[[1,2,4],[3]]=>[[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3]]
[[1,2,4],[3]]=>[[1,2,3],[4]]=>[[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4]]
[[1,2,3],[4]]=>[[1,2,3,4]]=>[[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4]]
[[1,3],[2,4]]=>[[1,2,4],[3]]=>[[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3]]
[[1,2],[3,4]]=>[[1,2,3,4]]=>[[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4]]
[[1,4],[2],[3]]=>[[1,2],[3],[4]]=>[[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4]]
[[1,3],[2],[4]]=>[[1,2,4],[3]]=>[[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3]]
[[1,2],[3],[4]]=>[[1,2,3],[4]]=>[[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4]]
[[1],[2],[3],[4]]=>[[1,2],[3],[4]]=>[[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4]]
[[1,2,3,4,5]]=>[[1,2,3,4,5]]=>[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5]]
[[1,3,4,5],[2]]=>[[1,2,4,5],[3]]=>[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3]]
[[1,2,4,5],[3]]=>[[1,2,3,5],[4]]=>[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4]]
[[1,2,3,5],[4]]=>[[1,2,3,4],[5]]=>[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5]]
[[1,2,3,4],[5]]=>[[1,2,3,4,5]]=>[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5]]
[[1,3,5],[2,4]]=>[[1,2,4],[3,5]]=>[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5]]
[[1,2,5],[3,4]]=>[[1,2,3,4],[5]]=>[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5]]
[[1,3,4],[2,5]]=>[[1,2,4,5],[3]]=>[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3]]
[[1,2,4],[3,5]]=>[[1,2,3,5],[4]]=>[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4]]
[[1,2,3],[4,5]]=>[[1,2,3,4,5]]=>[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5]]
[[1,4,5],[2],[3]]=>[[1,2,5],[3],[4]]=>[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3],[4]]
[[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]]=>[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3],[5]]
[[1,2,5],[3],[4]]=>[[1,2,3],[4],[5]]=>[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5]]
[[1,3,4],[2],[5]]=>[[1,2,4,5],[3]]=>[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3]]
[[1,2,4],[3],[5]]=>[[1,2,3,5],[4]]=>[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4]]
[[1,2,3],[4],[5]]=>[[1,2,3,4],[5]]=>[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5]]
[[1,4],[2,5],[3]]=>[[1,2,5],[3],[4]]=>[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3],[4]]
[[1,3],[2,5],[4]]=>[[1,2,4,5],[3]]=>[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3]]
[[1,2],[3,5],[4]]=>[[1,2,3,5],[4]]=>[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4]]
[[1,3],[2,4],[5]]=>[[1,2,4],[3,5]]=>[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5]]
[[1,2],[3,4],[5]]=>[[1,2,3,4],[5]]=>[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5]]
[[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]=>[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5]]
[[1,4],[2],[3],[5]]=>[[1,2,5],[3],[4]]=>[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3],[4]]
[[1,3],[2],[4],[5]]=>[[1,2,4],[3],[5]]=>[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3],[5]]
[[1,2],[3],[4],[5]]=>[[1,2,3],[4],[5]]=>[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5]]
[[1],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5]]=>[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5]]
[[1,2,3,4,5,6]]=>[[1,2,3,4,5,6]]=>[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6]]
[[1,3,4,5,6],[2]]=>[[1,2,4,5,6],[3]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6],[3]]
[[1,2,4,5,6],[3]]=>[[1,2,3,5,6],[4]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,6],[4]]
[[1,2,3,5,6],[4]]=>[[1,2,3,4,6],[5]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5]]
[[1,2,3,4,6],[5]]=>[[1,2,3,4,5],[6]]=>[[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6]]
[[1,2,3,4,5],[6]]=>[[1,2,3,4,5,6]]=>[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6]]
[[1,3,5,6],[2,4]]=>[[1,2,4,6],[3,5]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5]]
[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6]]
[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3,6]]
[[1,2,4,6],[3,5]]=>[[1,2,3,5],[4,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6]]
[[1,2,3,6],[4,5]]=>[[1,2,3,4,5],[6]]=>[[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6]]
[[1,3,4,5],[2,6]]=>[[1,2,4,5,6],[3]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6],[3]]
[[1,2,4,5],[3,6]]=>[[1,2,3,5,6],[4]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,6],[4]]
[[1,2,3,5],[4,6]]=>[[1,2,3,4,6],[5]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5]]
[[1,2,3,4],[5,6]]=>[[1,2,3,4,5,6]]=>[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6]]
[[1,4,5,6],[2],[3]]=>[[1,2,5,6],[3],[4]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6],[3],[4]]
[[1,3,5,6],[2],[4]]=>[[1,2,4,6],[3],[5]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3],[5]]
[[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4],[5]]
[[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3],[6]]
[[1,2,4,6],[3],[5]]=>[[1,2,3,5],[4],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4],[6]]
[[1,2,3,6],[4],[5]]=>[[1,2,3,4],[5],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6]]
[[1,3,4,5],[2],[6]]=>[[1,2,4,5,6],[3]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6],[3]]
[[1,2,4,5],[3],[6]]=>[[1,2,3,5,6],[4]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,6],[4]]
[[1,2,3,5],[4],[6]]=>[[1,2,3,4,6],[5]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5]]
[[1,2,3,4],[5],[6]]=>[[1,2,3,4,5],[6]]=>[[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6]]
[[1,3,5],[2,4,6]]=>[[1,2,4,6],[3,5]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5]]
[[1,2,5],[3,4,6]]=>[[1,2,3,4,6],[5]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5]]
[[1,3,4],[2,5,6]]=>[[1,2,4,5,6],[3]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6],[3]]
[[1,2,4],[3,5,6]]=>[[1,2,3,5,6],[4]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,6],[4]]
[[1,2,3],[4,5,6]]=>[[1,2,3,4,5,6]]=>[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6]]
[[1,4,6],[2,5],[3]]=>[[1,2,5],[3,6],[4]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4]]
[[1,3,6],[2,5],[4]]=>[[1,2,4,5],[3],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3],[6]]
[[1,2,6],[3,5],[4]]=>[[1,2,3,5],[4],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4],[6]]
[[1,3,6],[2,4],[5]]=>[[1,2,4],[3,5],[6]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5],[6]]
[[1,2,6],[3,4],[5]]=>[[1,2,3,4],[5],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6]]
[[1,4,5],[2,6],[3]]=>[[1,2,5,6],[3],[4]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6],[3],[4]]
[[1,3,5],[2,6],[4]]=>[[1,2,4,6],[3],[5]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3],[5]]
[[1,2,5],[3,6],[4]]=>[[1,2,3,6],[4],[5]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4],[5]]
[[1,3,4],[2,6],[5]]=>[[1,2,4,5,6],[3]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6],[3]]
[[1,2,4],[3,6],[5]]=>[[1,2,3,5,6],[4]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,6],[4]]
[[1,2,3],[4,6],[5]]=>[[1,2,3,4,6],[5]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5]]
[[1,3,5],[2,4],[6]]=>[[1,2,4,6],[3,5]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5]]
[[1,2,5],[3,4],[6]]=>[[1,2,3,4],[5,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6]]
[[1,3,4],[2,5],[6]]=>[[1,2,4,5],[3,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3,6]]
[[1,2,4],[3,5],[6]]=>[[1,2,3,5],[4,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6]]
[[1,2,3],[4,5],[6]]=>[[1,2,3,4,5],[6]]=>[[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6]]
[[1,5,6],[2],[3],[4]]=>[[1,2,6],[3],[4],[5]]=>[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6],[3],[4],[5]]
[[1,4,6],[2],[3],[5]]=>[[1,2,5],[3],[4],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3],[4],[6]]
[[1,3,6],[2],[4],[5]]=>[[1,2,4],[3],[5],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3],[5],[6]]
[[1,2,6],[3],[4],[5]]=>[[1,2,3],[4],[5],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5],[6]]
[[1,4,5],[2],[3],[6]]=>[[1,2,5,6],[3],[4]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6],[3],[4]]
[[1,3,5],[2],[4],[6]]=>[[1,2,4,6],[3],[5]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3],[5]]
[[1,2,5],[3],[4],[6]]=>[[1,2,3,6],[4],[5]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4],[5]]
[[1,3,4],[2],[5],[6]]=>[[1,2,4,5],[3],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3],[6]]
[[1,2,4],[3],[5],[6]]=>[[1,2,3,5],[4],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4],[6]]
[[1,2,3],[4],[5],[6]]=>[[1,2,3,4],[5],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6]]
[[1,4],[2,5],[3,6]]=>[[1,2,5],[3,6],[4]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4]]
[[1,3],[2,5],[4,6]]=>[[1,2,4,5],[3,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3,6]]
[[1,2],[3,5],[4,6]]=>[[1,2,3,5],[4,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6]]
[[1,3],[2,4],[5,6]]=>[[1,2,4,6],[3,5]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5]]
[[1,2],[3,4],[5,6]]=>[[1,2,3,4],[5,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6]]
[[1,5],[2,6],[3],[4]]=>[[1,2,6],[3],[4],[5]]=>[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6],[3],[4],[5]]
[[1,4],[2,6],[3],[5]]=>[[1,2,5,6],[3],[4]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6],[3],[4]]
[[1,3],[2,6],[4],[5]]=>[[1,2,4,6],[3],[5]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3],[5]]
[[1,2],[3,6],[4],[5]]=>[[1,2,3,6],[4],[5]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4],[5]]
[[1,4],[2,5],[3],[6]]=>[[1,2,5],[3,6],[4]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4]]
[[1,3],[2,5],[4],[6]]=>[[1,2,4,5],[3],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3],[6]]
[[1,2],[3,5],[4],[6]]=>[[1,2,3,5],[4],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4],[6]]
[[1,3],[2,4],[5],[6]]=>[[1,2,4],[3,5],[6]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5],[6]]
[[1,2],[3,4],[5],[6]]=>[[1,2,3,4],[5],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6]]
[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6]]
[[1,5],[2],[3],[4],[6]]=>[[1,2,6],[3],[4],[5]]=>[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6],[3],[4],[5]]
[[1,4],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3],[4],[6]]
[[1,3],[2],[4],[5],[6]]=>[[1,2,4],[3],[5],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3],[5],[6]]
[[1,2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5],[6]]
[[1],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6]]
[[1,2,3,4,5,6,7]]=>[[1,2,3,4,5,6,7]]=>[[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7]]
[[1,3,4,5,6,7],[2]]=>[[1,2,4,5,6,7],[3]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7],[3]]
[[1,2,3,4,6,7],[5]]=>[[1,2,3,4,5,7],[6]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6]]
[[1,2,3,4,5,7],[6]]=>[[1,2,3,4,5,6],[7]]=>[[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7]]
[[1,2,3,4,5,6],[7]]=>[[1,2,3,4,5,6,7]]=>[[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7]]
[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,7],[5,6]]=>[[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5,6]]
[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,5],[6,7]]=>[[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7]]
[[1,2,3,5,7],[4,6]]=>[[1,2,3,4,6],[5,7]]=>[[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7]]
[[1,2,3,4,7],[5,6]]=>[[1,2,3,4,5,6],[7]]=>[[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7]]
[[1,3,4,5,6],[2,7]]=>[[1,2,4,5,6,7],[3]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7],[3]]
[[1,2,3,4,6],[5,7]]=>[[1,2,3,4,5,7],[6]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6]]
[[1,2,3,4,5],[6,7]]=>[[1,2,3,4,5,6,7]]=>[[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7]]
[[1,4,5,6,7],[2],[3]]=>[[1,2,5,6,7],[3],[4]]=>[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7],[3],[4]]
[[1,2,3,6,7],[4],[5]]=>[[1,2,3,4,7],[5],[6]]=>[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5],[6]]
[[1,2,3,4,7],[5],[6]]=>[[1,2,3,4,5],[6],[7]]=>[[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7]]
[[1,3,4,5,6],[2],[7]]=>[[1,2,4,5,6,7],[3]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7],[3]]
[[1,2,3,4,6],[5],[7]]=>[[1,2,3,4,5,7],[6]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6]]
[[1,2,3,4,5],[6],[7]]=>[[1,2,3,4,5,6],[7]]=>[[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7]]
[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]=>[[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5,7]]
[[1,2,5,7],[3,4,6]]=>[[1,2,3,4,6],[5,7]]=>[[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7]]
[[1,2,3,7],[4,5,6]]=>[[1,2,3,4,5,6],[7]]=>[[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7]]
[[1,2,5,6],[3,4,7]]=>[[1,2,3,4,7],[5,6]]=>[[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5,6]]
[[1,2,3,6],[4,5,7]]=>[[1,2,3,4,5,7],[6]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6]]
[[1,3,4,5],[2,6,7]]=>[[1,2,4,5,6,7],[3]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7],[3]]
[[1,2,3,4],[5,6,7]]=>[[1,2,3,4,5,6,7]]=>[[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7]]
[[1,2,5,7],[3,4],[6]]=>[[1,2,3,4],[5,6],[7]]=>[[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7]]
[[1,2,4,7],[3,5],[6]]=>[[1,2,3,5],[4,6],[7]]=>[[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7]]
[[1,2,3,7],[4,5],[6]]=>[[1,2,3,4,5],[6],[7]]=>[[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7]]
[[1,4,5,6],[2,7],[3]]=>[[1,2,5,6,7],[3],[4]]=>[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7],[3],[4]]
[[1,2,3,6],[4,7],[5]]=>[[1,2,3,4,7],[5],[6]]=>[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5],[6]]
[[1,3,4,5],[2,7],[6]]=>[[1,2,4,5,6,7],[3]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7],[3]]
[[1,2,3,4],[5,7],[6]]=>[[1,2,3,4,5,7],[6]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6]]
[[1,2,5,6],[3,4],[7]]=>[[1,2,3,4,7],[5,6]]=>[[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5,6]]
[[1,2,3,6],[4,5],[7]]=>[[1,2,3,4,5],[6,7]]=>[[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7]]
[[1,2,3,5],[4,6],[7]]=>[[1,2,3,4,6],[5,7]]=>[[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7]]
[[1,2,3,4],[5,6],[7]]=>[[1,2,3,4,5,6],[7]]=>[[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7]]
[[1,5,6,7],[2],[3],[4]]=>[[1,2,6,7],[3],[4],[5]]=>[[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7],[3],[4],[5]]
[[1,2,6,7],[3],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]=>[[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,7],[4],[5],[6]]
[[1,2,3,7],[4],[5],[6]]=>[[1,2,3,4],[5],[6],[7]]=>[[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7]]
[[1,4,5,6],[2],[3],[7]]=>[[1,2,5,6,7],[3],[4]]=>[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7],[3],[4]]
[[1,2,3,6],[4],[5],[7]]=>[[1,2,3,4,7],[5],[6]]=>[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5],[6]]
[[1,2,3,4],[5],[6],[7]]=>[[1,2,3,4,5],[6],[7]]=>[[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7]]
[[1,2,6],[3,4,7],[5]]=>[[1,2,3,4,7],[5],[6]]=>[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5],[6]]
[[1,4,5],[2,6,7],[3]]=>[[1,2,5,6,7],[3],[4]]=>[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7],[3],[4]]
[[1,3,4],[2,6,7],[5]]=>[[1,2,4,5,6,7],[3]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7],[3]]
[[1,2,5],[3,4,7],[6]]=>[[1,2,3,4,7],[5,6]]=>[[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5,6]]
[[1,2,3],[4,5,7],[6]]=>[[1,2,3,4,5,7],[6]]=>[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6]]
[[1,3,5],[2,4,6],[7]]=>[[1,2,4,6],[3,5,7]]=>[[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5,7]]
[[1,2,5],[3,4,6],[7]]=>[[1,2,3,4,6],[5,7]]=>[[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7]]
[[1,2,3],[4,5,6],[7]]=>[[1,2,3,4,5,6],[7]]=>[[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7]]
[[1,4,7],[2,5],[3,6]]=>[[1,2,5],[3,6],[4,7]]=>[[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4,7]]
[[1,2,7],[3,5],[4,6]]=>[[1,2,3,5],[4,6],[7]]=>[[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7]]
[[1,2,7],[3,4],[5,6]]=>[[1,2,3,4],[5,6],[7]]=>[[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7]]
[[1,2,3],[4,6],[5,7]]=>[[1,2,3,4,6],[5,7]]=>[[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7]]
[[1,2,5],[3,4],[6,7]]=>[[1,2,3,4,7],[5,6]]=>[[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5,6]]
[[1,2,3],[4,5],[6,7]]=>[[1,2,3,4,5],[6,7]]=>[[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7]]
[[1,3,7],[2,4],[5],[6]]=>[[1,2,4],[3,5],[6],[7]]=>[[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5],[6],[7]]
[[1,2,7],[3,4],[5],[6]]=>[[1,2,3,4],[5],[6],[7]]=>[[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7]]
[[1,5,6],[2,7],[3],[4]]=>[[1,2,6,7],[3],[4],[5]]=>[[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7],[3],[4],[5]]
[[1,2,6],[3,7],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]=>[[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,7],[4],[5],[6]]
[[1,4,5],[2,7],[3],[6]]=>[[1,2,5,6,7],[3],[4]]=>[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7],[3],[4]]
[[1,2,3],[4,7],[5],[6]]=>[[1,2,3,4,7],[5],[6]]=>[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5],[6]]
[[1,2,5],[3,4],[6],[7]]=>[[1,2,3,4],[5,6],[7]]=>[[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7]]
[[1,2,4],[3,5],[6],[7]]=>[[1,2,3,5],[4,6],[7]]=>[[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7]]
[[1,2,3],[4,5],[6],[7]]=>[[1,2,3,4,5],[6],[7]]=>[[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7]]
[[1,6,7],[2],[3],[4],[5]]=>[[1,2,7],[3],[4],[5],[6]]=>[[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7],[3],[4],[5],[6]]
[[1,2,7],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7]]=>[[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5],[6],[7]]
[[1,5,6],[2],[3],[4],[7]]=>[[1,2,6,7],[3],[4],[5]]=>[[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7],[3],[4],[5]]
[[1,2,6],[3],[4],[5],[7]]=>[[1,2,3,7],[4],[5],[6]]=>[[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,7],[4],[5],[6]]
[[1,2,3],[4],[5],[6],[7]]=>[[1,2,3,4],[5],[6],[7]]=>[[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7]]
[[1,4],[2,5],[3,6],[7]]=>[[1,2,5],[3,6],[4,7]]=>[[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4,7]]
[[1,2],[3,5],[4,6],[7]]=>[[1,2,3,5],[4,6],[7]]=>[[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7]]
[[1,2],[3,4],[5,6],[7]]=>[[1,2,3,4],[5,6],[7]]=>[[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7]]
[[1,6],[2,7],[3],[4],[5]]=>[[1,2,7],[3],[4],[5],[6]]=>[[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7],[3],[4],[5],[6]]
[[1,5],[2,7],[3],[4],[6]]=>[[1,2,6,7],[3],[4],[5]]=>[[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7],[3],[4],[5]]
[[1,2],[3,7],[4],[5],[6]]=>[[1,2,3,7],[4],[5],[6]]=>[[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,7],[4],[5],[6]]
[[1,3],[2,4],[5],[6],[7]]=>[[1,2,4],[3,5],[6],[7]]=>[[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5],[6],[7]]
[[1,2],[3,4],[5],[6],[7]]=>[[1,2,3,4],[5],[6],[7]]=>[[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7]]
[[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]=>[[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6],[7]]
[[1,6],[2],[3],[4],[5],[7]]=>[[1,2,7],[3],[4],[5],[6]]=>[[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7],[3],[4],[5],[6]]
[[1,2],[3],[4],[5],[6],[7]]=>[[1,2,3],[4],[5],[6],[7]]=>[[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5],[6],[7]]
[[1],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7]]=>[[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6],[7]]
[[1,2,3,4,5,6,7,8]]=>[[1,2,3,4,5,6,7,8]]=>[[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8]]
[[1,3,4,5,6,7,8],[2]]=>[[1,2,4,5,6,7,8],[3]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7,8],[3]]
[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,4,5,6,8],[7]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,8],[7]]
[[1,2,3,4,5,6,8],[7]]=>[[1,2,3,4,5,6,7],[8]]=>[[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8]]
[[1,2,3,4,5,6,7],[8]]=>[[1,2,3,4,5,6,7,8]]=>[[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8]]
[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]=>[[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6,7]]
[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,5,6],[7,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8]]
[[1,2,3,4,6,8],[5,7]]=>[[1,2,3,4,5,7],[6,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6,8]]
[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,4,5,6,7],[8]]=>[[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8]]
[[1,3,4,5,6,7],[2,8]]=>[[1,2,4,5,6,7,8],[3]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7,8],[3]]
[[1,2,3,4,5,7],[6,8]]=>[[1,2,3,4,5,6,8],[7]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,8],[7]]
[[1,2,3,4,5,6],[7,8]]=>[[1,2,3,4,5,6,7,8]]=>[[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8]]
[[1,4,5,6,7,8],[2],[3]]=>[[1,2,5,6,7,8],[3],[4]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8],[3],[4]]
[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,4,5,8],[6],[7]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6],[7]]
[[1,2,3,4,5,8],[6],[7]]=>[[1,2,3,4,5,6],[7],[8]]=>[[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8]]
[[1,3,4,5,6,7],[2],[8]]=>[[1,2,4,5,6,7,8],[3]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7,8],[3]]
[[1,2,3,4,5,7],[6],[8]]=>[[1,2,3,4,5,6,8],[7]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,8],[7]]
[[1,2,3,4,5,6],[7],[8]]=>[[1,2,3,4,5,6,7],[8]]=>[[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8]]
[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5,6],[7,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8]]
[[1,2,4,6,8],[3,5,7]]=>[[1,2,3,5,7],[4,6,8]]=>[[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,7],[4,6,8]]
[[1,2,3,6,8],[4,5,7]]=>[[1,2,3,4,5,7],[6,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6,8]]
[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,5,6,7],[8]]=>[[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8]]
[[1,2,3,6,7],[4,5,8]]=>[[1,2,3,4,5,8],[6,7]]=>[[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6,7]]
[[1,2,3,4,7],[5,6,8]]=>[[1,2,3,4,5,6,8],[7]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,8],[7]]
[[1,3,4,5,6],[2,7,8]]=>[[1,2,4,5,6,7,8],[3]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7,8],[3]]
[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,4,5,6,7,8]]=>[[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8]]
[[1,2,5,7,8],[3,4],[6]]=>[[1,2,3,4,8],[5,6],[7]]=>[[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5,6],[7]]
[[1,2,3,6,8],[4,5],[7]]=>[[1,2,3,4,5],[6,7],[8]]=>[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8]]
[[1,2,3,5,8],[4,6],[7]]=>[[1,2,3,4,6],[5,7],[8]]=>[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7],[8]]
[[1,2,3,4,8],[5,6],[7]]=>[[1,2,3,4,5,6],[7],[8]]=>[[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8]]
[[1,4,5,6,7],[2,8],[3]]=>[[1,2,5,6,7,8],[3],[4]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8],[3],[4]]
[[1,2,3,4,7],[5,8],[6]]=>[[1,2,3,4,5,8],[6],[7]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6],[7]]
[[1,3,4,5,6],[2,8],[7]]=>[[1,2,4,5,6,7,8],[3]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7,8],[3]]
[[1,2,3,4,5],[6,8],[7]]=>[[1,2,3,4,5,6,8],[7]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,8],[7]]
[[1,2,3,6,7],[4,5],[8]]=>[[1,2,3,4,5,8],[6,7]]=>[[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6,7]]
[[1,2,3,4,7],[5,6],[8]]=>[[1,2,3,4,5,6],[7,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8]]
[[1,2,3,4,6],[5,7],[8]]=>[[1,2,3,4,5,7],[6,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6,8]]
[[1,2,3,4,5],[6,7],[8]]=>[[1,2,3,4,5,6,7],[8]]=>[[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8]]
[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,6,7,8],[3],[4],[5]]=>[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8],[3],[4],[5]]
[[1,2,3,7,8],[4],[5],[6]]=>[[1,2,3,4,8],[5],[6],[7]]=>[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5],[6],[7]]
[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,3,4,5],[6],[7],[8]]=>[[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7],[8]]
[[1,4,5,6,7],[2],[3],[8]]=>[[1,2,5,6,7,8],[3],[4]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8],[3],[4]]
[[1,2,3,4,7],[5],[6],[8]]=>[[1,2,3,4,5,8],[6],[7]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6],[7]]
[[1,2,3,4,5],[6],[7],[8]]=>[[1,2,3,4,5,6],[7],[8]]=>[[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8]]
[[1,2,3,7],[4,5,6,8]]=>[[1,2,3,4,5,6,8],[7]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,8],[7]]
[[1,3,4,5],[2,6,7,8]]=>[[1,2,4,5,6,7,8],[3]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7,8],[3]]
[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4,5,6,7,8]]=>[[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8]]
[[1,3,5,8],[2,4,6],[7]]=>[[1,2,4,6],[3,5,7],[8]]=>[[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5,7],[8]]
[[1,2,5,8],[3,4,6],[7]]=>[[1,2,3,4,6],[5,7],[8]]=>[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7],[8]]
[[1,2,3,8],[4,5,6],[7]]=>[[1,2,3,4,5,6],[7],[8]]=>[[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8]]
[[1,2,5,7],[3,4,8],[6]]=>[[1,2,3,4,8],[5,6],[7]]=>[[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5,6],[7]]
[[1,2,3,7],[4,5,8],[6]]=>[[1,2,3,4,5,8],[6],[7]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6],[7]]
[[1,4,5,6],[2,7,8],[3]]=>[[1,2,5,6,7,8],[3],[4]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8],[3],[4]]
[[1,3,4,5],[2,7,8],[6]]=>[[1,2,4,5,6,7,8],[3]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7,8],[3]]
[[1,2,3,6],[4,5,8],[7]]=>[[1,2,3,4,5,8],[6,7]]=>[[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6,7]]
[[1,2,3,4],[5,6,8],[7]]=>[[1,2,3,4,5,6,8],[7]]=>[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,8],[7]]
[[1,2,3,7],[4,5,6],[8]]=>[[1,2,3,4,5,6],[7,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8]]
[[1,2,4,6],[3,5,7],[8]]=>[[1,2,3,5,7],[4,6,8]]=>[[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,7],[4,6,8]]
[[1,2,3,6],[4,5,7],[8]]=>[[1,2,3,4,5,7],[6,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6,8]]
[[1,2,3,4],[5,6,7],[8]]=>[[1,2,3,4,5,6,7],[8]]=>[[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8]]
[[1,2,7,8],[3,4],[5,6]]=>[[1,2,3,4],[5,6],[7,8]]=>[[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7,8]]
[[1,2,5,8],[3,6],[4,7]]=>[[1,2,3,6],[4,7],[5,8]]=>[[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4,7],[5,8]]
[[1,2,3,8],[4,6],[5,7]]=>[[1,2,3,4,6],[5,7],[8]]=>[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7],[8]]
[[1,2,3,8],[4,5],[6,7]]=>[[1,2,3,4,5],[6,7],[8]]=>[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8]]
[[1,2,5,7],[3,4],[6,8]]=>[[1,2,3,4,8],[5,6],[7]]=>[[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5,6],[7]]
[[1,2,3,4],[5,7],[6,8]]=>[[1,2,3,4,5,7],[6,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6,8]]
[[1,2,3,6],[4,5],[7,8]]=>[[1,2,3,4,5,8],[6,7]]=>[[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6,7]]
[[1,2,3,4],[5,6],[7,8]]=>[[1,2,3,4,5,6],[7,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8]]
[[1,2,5,8],[3,4],[6],[7]]=>[[1,2,3,4],[5,6],[7],[8]]=>[[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7],[8]]
[[1,2,4,8],[3,5],[6],[7]]=>[[1,2,3,5],[4,6],[7],[8]]=>[[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7],[8]]
[[1,2,3,8],[4,5],[6],[7]]=>[[1,2,3,4,5],[6],[7],[8]]=>[[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7],[8]]
[[1,5,6,7],[2,8],[3],[4]]=>[[1,2,6,7,8],[3],[4],[5]]=>[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8],[3],[4],[5]]
[[1,2,3,7],[4,8],[5],[6]]=>[[1,2,3,4,8],[5],[6],[7]]=>[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5],[6],[7]]
[[1,4,5,6],[2,8],[3],[7]]=>[[1,2,5,6,7,8],[3],[4]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8],[3],[4]]
[[1,2,3,4],[5,8],[6],[7]]=>[[1,2,3,4,5,8],[6],[7]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6],[7]]
[[1,2,5,7],[3,4],[6],[8]]=>[[1,2,3,4,8],[5,6],[7]]=>[[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5,6],[7]]
[[1,2,3,6],[4,5],[7],[8]]=>[[1,2,3,4,5],[6,7],[8]]=>[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8]]
[[1,2,3,5],[4,6],[7],[8]]=>[[1,2,3,4,6],[5,7],[8]]=>[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7],[8]]
[[1,2,3,4],[5,6],[7],[8]]=>[[1,2,3,4,5,6],[7],[8]]=>[[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8]]
[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,7,8],[3],[4],[5],[6]]=>[[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8],[3],[4],[5],[6]]
[[1,2,7,8],[3],[4],[5],[6]]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,8],[4],[5],[6],[7]]
[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7],[8]]
[[1,5,6,7],[2],[3],[4],[8]]=>[[1,2,6,7,8],[3],[4],[5]]=>[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8],[3],[4],[5]]
[[1,2,3,7],[4],[5],[6],[8]]=>[[1,2,3,4,8],[5],[6],[7]]=>[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5],[6],[7]]
[[1,2,3,4],[5],[6],[7],[8]]=>[[1,2,3,4,5],[6],[7],[8]]=>[[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7],[8]]
[[1,2,7],[3,4,8],[5,6]]=>[[1,2,3,4,8],[5,6],[7]]=>[[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5,6],[7]]
[[1,2,3],[4,5,8],[6,7]]=>[[1,2,3,4,5,8],[6,7]]=>[[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6,7]]
[[1,2,4],[3,5,7],[6,8]]=>[[1,2,3,5,7],[4,6,8]]=>[[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,7],[4,6,8]]
[[1,2,3],[4,5,7],[6,8]]=>[[1,2,3,4,5,7],[6,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6,8]]
[[1,2,3],[4,5,6],[7,8]]=>[[1,2,3,4,5,6],[7,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8]]
[[1,2,7],[3,4,8],[5],[6]]=>[[1,2,3,4,8],[5],[6],[7]]=>[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5],[6],[7]]
[[1,5,6],[2,7,8],[3],[4]]=>[[1,2,6,7,8],[3],[4],[5]]=>[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8],[3],[4],[5]]
[[1,4,5],[2,7,8],[3],[6]]=>[[1,2,5,6,7,8],[3],[4]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8],[3],[4]]
[[1,2,5],[3,4,8],[6],[7]]=>[[1,2,3,4,8],[5,6],[7]]=>[[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5,6],[7]]
[[1,2,3],[4,5,8],[6],[7]]=>[[1,2,3,4,5,8],[6],[7]]=>[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6],[7]]
[[1,3,5],[2,4,6],[7],[8]]=>[[1,2,4,6],[3,5,7],[8]]=>[[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5,7],[8]]
[[1,2,5],[3,4,6],[7],[8]]=>[[1,2,3,4,6],[5,7],[8]]=>[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7],[8]]
[[1,2,3],[4,5,6],[7],[8]]=>[[1,2,3,4,5,6],[7],[8]]=>[[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8]]
[[1,4,8],[2,5],[3,6],[7]]=>[[1,2,5],[3,6],[4,7],[8]]=>[[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4,7],[8]]
[[1,2,8],[3,5],[4,6],[7]]=>[[1,2,3,5],[4,6],[7],[8]]=>[[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7],[8]]
[[1,2,8],[3,4],[5,6],[7]]=>[[1,2,3,4],[5,6],[7],[8]]=>[[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7],[8]]
[[1,2,5],[3,4],[6,8],[7]]=>[[1,2,3,4,8],[5,6],[7]]=>[[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5,6],[7]]
[[1,2,7],[3,4],[5,6],[8]]=>[[1,2,3,4],[5,6],[7,8]]=>[[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7,8]]
[[1,2,5],[3,6],[4,7],[8]]=>[[1,2,3,6],[4,7],[5,8]]=>[[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4,7],[5,8]]
[[1,2,3],[4,6],[5,7],[8]]=>[[1,2,3,4,6],[5,7],[8]]=>[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7],[8]]
[[1,2,3],[4,5],[6,7],[8]]=>[[1,2,3,4,5],[6,7],[8]]=>[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8]]
[[1,3,8],[2,4],[5],[6],[7]]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5],[6],[7],[8]]
[[1,2,8],[3,4],[5],[6],[7]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7],[8]]
[[1,6,7],[2,8],[3],[4],[5]]=>[[1,2,7,8],[3],[4],[5],[6]]=>[[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8],[3],[4],[5],[6]]
[[1,2,7],[3,8],[4],[5],[6]]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,8],[4],[5],[6],[7]]
[[1,5,6],[2,8],[3],[4],[7]]=>[[1,2,6,7,8],[3],[4],[5]]=>[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8],[3],[4],[5]]
[[1,2,3],[4,8],[5],[6],[7]]=>[[1,2,3,4,8],[5],[6],[7]]=>[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,8],[5],[6],[7]]
[[1,2,5],[3,4],[6],[7],[8]]=>[[1,2,3,4],[5,6],[7],[8]]=>[[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7],[8]]
[[1,2,4],[3,5],[6],[7],[8]]=>[[1,2,3,5],[4,6],[7],[8]]=>[[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7],[8]]
[[1,2,3],[4,5],[6],[7],[8]]=>[[1,2,3,4,5],[6],[7],[8]]=>[[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7],[8]]
[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,8],[3],[4],[5],[6],[7]]
[[1,2,8],[3],[4],[5],[6],[7]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5],[6],[7],[8]]
[[1,6,7],[2],[3],[4],[5],[8]]=>[[1,2,7,8],[3],[4],[5],[6]]=>[[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8],[3],[4],[5],[6]]
[[1,2,7],[3],[4],[5],[6],[8]]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,8],[4],[5],[6],[7]]
[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7],[8]]
[[1,2],[3,6],[4,7],[5,8]]=>[[1,2,3,6],[4,7],[5,8]]=>[[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4,7],[5,8]]
[[1,2],[3,4],[5,6],[7,8]]=>[[1,2,3,4],[5,6],[7,8]]=>[[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7,8]]
[[1,4],[2,5],[3,6],[7],[8]]=>[[1,2,5],[3,6],[4,7],[8]]=>[[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4,7],[8]]
[[1,2],[3,5],[4,6],[7],[8]]=>[[1,2,3,5],[4,6],[7],[8]]=>[[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7],[8]]
[[1,2],[3,4],[5,6],[7],[8]]=>[[1,2,3,4],[5,6],[7],[8]]=>[[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7],[8]]
[[1,7],[2,8],[3],[4],[5],[6]]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,8],[3],[4],[5],[6],[7]]
[[1,6],[2,8],[3],[4],[5],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]=>[[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8],[3],[4],[5],[6]]
[[1,2],[3,8],[4],[5],[6],[7]]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,8],[4],[5],[6],[7]]
[[1,3],[2,4],[5],[6],[7],[8]]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5],[6],[7],[8]]
[[1,2],[3,4],[5],[6],[7],[8]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7],[8]]
[[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6],[7],[8]]
[[1,7],[2],[3],[4],[5],[6],[8]]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,8],[3],[4],[5],[6],[7]]
[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5],[6],[7],[8]]
[[1],[2],[3],[4],[5],[6],[7],[8]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6],[7],[8]]
[[1,3,4,5,6],[2,7,8,9,10]]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[[9,1,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7,8,9,10],[3]]
[[1,2,3,4,9],[5,6,7,8,10]]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[9,1,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,10],[9]]
[[1,2,3,4,5],[6,7,8,9,10]]=>[[1,2,3,4,5,6,7,8,9,10]]=>[[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9,10]]
[[1,2,3,4,5,6,7,8,9]]=>[[1,2,3,4,5,6,7,8,9]]=>[[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9]]
[[1,2,3,4,5,6,7,8],[9]]=>[[1,2,3,4,5,6,7,8,9]]=>[[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9]]
[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,3,4,5,6,7,8,9]]=>[[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9]]
[[1,2,3,4,5,6,7],[8],[9]]=>[[1,2,3,4,5,6,7,8],[9]]=>[[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9]]
[[1,2,3,4,5,6],[7,8,9]]=>[[1,2,3,4,5,6,7,8,9]]=>[[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9]]
[[1,2,3,4,5,6],[7,8],[9]]=>[[1,2,3,4,5,6,7,8],[9]]=>[[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9]]
[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8],[9]]
[[1,2,3,4,5],[6,7,8,9]]=>[[1,2,3,4,5,6,7,8,9]]=>[[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9]]
[[1,2,3,4,5],[6,7,8],[9]]=>[[1,2,3,4,5,6,7,8],[9]]=>[[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9]]
[[1,2,3,4,5],[6,7],[8,9]]=>[[1,2,3,4,5,6,7],[8,9]]=>[[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8,9]]
[[1,2,3,4,5],[6,7],[8],[9]]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8],[9]]
[[1,2,3,4,5],[6],[7],[8],[9]]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8],[9]]
[[1,2,3,4],[5,6,7,8],[9]]=>[[1,2,3,4,5,6,7,8],[9]]=>[[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9]]
[[1,2,3,4],[5,6,7],[8,9]]=>[[1,2,3,4,5,6,7],[8,9]]=>[[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8,9]]
[[1,2,3,4],[5,6,7],[8],[9]]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8],[9]]
[[1,2,3,4],[5,6],[7,8],[9]]=>[[1,2,3,4,5,6],[7,8],[9]]=>[[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8],[9]]
[[1,2,3,4],[5,6],[7],[8],[9]]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8],[9]]
[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7],[8],[9]]
[[1,2,3],[4,5,6],[7,8,9]]=>[[1,2,3,4,5,6],[7,8,9]]=>[[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8,9]]
[[1,2,3],[4,5,6],[7,8],[9]]=>[[1,2,3,4,5,6],[7,8],[9]]=>[[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8],[9]]
[[1,2,3],[4,5,6],[7],[8],[9]]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8],[9]]
[[1,2,3],[4,5],[6,7],[8,9]]=>[[1,2,3,4,5],[6,7],[8,9]]=>[[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8,9]]
[[1,2,3],[4,5],[6,7],[8],[9]]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8],[9]]
[[1,2,3],[4,5],[6],[7],[8],[9]]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7],[8],[9]]
[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7],[8],[9]]
[[1,2],[3,4],[5,6],[7,8],[9]]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7,8],[9]]
[[1,2],[3,4],[5,6],[7],[8],[9]]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7],[8],[9]]
[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7],[8],[9]]
[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]
[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]
[[1,2,3,4,5,6,7,8,9,10]]=>[[1,2,3,4,5,6,7,8,9,10]]=>[[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9,10]]
[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,2,3,4,5,6,7,8,9,10]]=>[[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9,10]]
[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,3,4,5,6,7,8,9,10]]=>[[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9,10]]
[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[[1,2,3,4,5,6,7],[8,9,10]]=>[[1,2,3,4,5,6,7,8,9,10]]=>[[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9,10]]
[[1,2,3,4,5,6,7],[8,9],[10]]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9],[10]]
[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,5,6,7,8,9,10]]=>[[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9,10]]
[[1,2,3,4,5,6],[7,8,9],[10]]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[[1,2,3,4,5,6],[7,8],[9,10]]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[[1,2,3,4,5,6],[7,8],[9],[10]]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9],[10]]
[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[7,1,1,1,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8],[9],[10]]
[[1,2,3,4,5],[6,7,8,9],[10]]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[[1,2,3,4,5],[6,7,8],[9,10]]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[[1,2,3,4,5],[6,7,8],[9],[10]]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9],[10]]
[[1,2,3,4,5],[6,7],[8,9],[10]]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8,9],[10]]
[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[7,1,1,1,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8],[9],[10]]
[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[6,1,1,1,1,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]
[[1,2,3,4],[5,6,7,8],[9,10]]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[[1,2,3,4],[5,6,7,8],[9],[10]]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9],[10]]
[[1,2,3,4],[5,6,7],[8,9,10]]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[[7,3,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8,9,10]]
[[1,2,3,4],[5,6,7],[8,9],[10]]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8,9],[10]]
[[1,2,3,4],[5,6,7],[8],[9],[10]]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[7,1,1,1,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8],[9],[10]]
[[1,2,3,4],[5,6],[7,8],[9,10]]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[[6,2,2,0,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8],[9,10]]
[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>[[6,2,1,1,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8],[9],[10]]
[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[6,1,1,1,1,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]
[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[5,1,1,1,1,1,0,0,0,0],[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]
[[1,2,3],[4,5,6],[7,8,9],[10]]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[[6,3,1,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8,9],[10]]
[[1,2,3],[4,5,6],[7,8],[9,10]]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[[6,2,2,0,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8],[9,10]]
[[1,2,3],[4,5,6],[7,8],[9],[10]]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>[[6,2,1,1,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8],[9],[10]]
[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[6,1,1,1,1,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]
[[1,2,3],[4,5],[6,7],[8,9],[10]]=>[[1,2,3,4,5],[6,7],[8,9],[10]]=>[[5,2,2,1,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8,9],[10]]
[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]
[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[5,1,1,1,1,1,0,0,0,0],[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]
[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[[4,2,2,2,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7,8],[9,10]]
[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]
[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[[3,1,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]
[[1,3,4,5,6,7,8,9],[2]]=>[[1,2,4,5,6,7,8,9],[3]]=>[[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7,8,9],[3]]
[[1,4,5,6,7,8,9],[2],[3]]=>[[1,2,5,6,7,8,9],[3],[4]]=>[[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8,9],[3],[4]]
[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]=>[[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8,9]]
[[1,5,6,7,8,9],[2],[3],[4]]=>[[1,2,6,7,8,9],[3],[4],[5]]=>[[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8,9],[3],[4],[5]]
[[1,2,3,4,9],[5,6,7,8]]=>[[1,2,3,4,5,6,7,8],[9]]=>[[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9]]
[[1,2,7,8,9],[3,4],[5,6]]=>[[1,2,3,4,9],[5,6],[7,8]]=>[[5,2,2,0,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,9],[5,6],[7,8]]
[[1,6,7,8,9],[2],[3],[4],[5]]=>[[1,2,7,8,9],[3],[4],[5],[6]]=>[[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8,9],[3],[4],[5],[6]]
[[1,3,4,5],[2,7,8,9],[6]]=>[[1,2,4,5,6,7,8,9],[3]]=>[[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7,8,9],[3]]
[[1,7,8,9],[2],[3],[4],[5],[6]]=>[[1,2,8,9],[3],[4],[5],[6],[7]]=>[[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,8,9],[3],[4],[5],[6],[7]]
[[1,5,6],[2,8,9],[3],[4],[7]]=>[[1,2,6,7,8,9],[3],[4],[5]]=>[[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8,9],[3],[4],[5]]
[[1,2,9],[3,4],[5,6],[7,8]]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7,8],[9]]
[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[[3,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]
[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[[1,2,8,9],[3],[4],[5],[6],[7]]=>[[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,8,9],[3],[4],[5],[6],[7]]
[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]
[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[[9,1,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6,7,8,9,10],[3]]
[[1,4,5,6,7,8,9,10],[2],[3]]=>[[1,2,5,6,7,8,9,10],[3],[4]]=>[[8,1,1,0,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8,9,10],[3],[4]]
[[1,2,3,7,8,9,10],[4,5,6]]=>[[1,2,3,4,5,6,10],[7,8,9]]=>[[7,3,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,10],[7,8,9]]
[[1,5,6,7,8,9,10],[2],[3],[4]]=>[[1,2,6,7,8,9,10],[3],[4],[5]]=>[[7,1,1,1,0,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8,9,10],[3],[4],[5]]
[[1,2,3,4,9,10],[5,6,7,8]]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]=>[[6,1,1,1,1,0,0,0,0,0],[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]
[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[[1,2,8,9,10],[3],[4],[5],[6],[7]]=>[[5,1,1,1,1,1,0,0,0,0],[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,8,9,10],[3],[4],[5],[6],[7]]
[[1,4,5,6],[2,8,9,10],[3],[7]]=>[[1,2,5,6,7,8,9,10],[3],[4]]=>[[8,1,1,0,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8,9,10],[3],[4]]
[[1,2,3,10],[4,5,6],[7,8,9]]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[[6,3,1,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8,9],[10]]
[[1,2,9,10],[3,4],[5,6],[7,8]]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[[4,2,2,2,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7,8],[9,10]]
[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[[1,2,9,10],[3],[4],[5],[6],[7],[8]]=>[[4,1,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,9,10],[3],[4],[5],[6],[7],[8]]
[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]=>[[6,1,1,1,1,0,0,0,0,0],[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[[3,1,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[[1,2,9,10],[3],[4],[5],[6],[7],[8]]=>[[4,1,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,9,10],[3],[4],[5],[6],[7],[8]]
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]
[[1,8],[2,9],[3],[4],[5],[6],[7]]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[[3,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]
[[1,5,9],[2,6],[3,7],[4,8]]=>[[1,2,6],[3,7],[4,8],[5,9]]=>[[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6],[3,7],[4,8],[5,9]]
[[1,3,5,7,9],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7,9]]=>[[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6,8],[3,5,7,9]]
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[[3,1,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]
[[1,4,7,10],[2,5,8],[3,6,9]]=>[[1,2,5,8],[3,6,9],[4,7,10]]=>[[4,3,3,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,8],[3,6,9],[4,7,10]]
[[1,3],[2,4],[5],[6],[7],[8],[9]]=>[[1,2,4],[3,5],[6],[7],[8],[9]]=>[[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5],[6],[7],[8],[9]]
[[1,4],[2,5],[3,6],[7],[8],[9]]=>[[1,2,5],[3,6],[4,7],[8],[9]]=>[[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4,7],[8],[9]]
[[1,2,4],[3,5],[6],[7],[8],[9]]=>[[1,2,3,5],[4,6],[7],[8],[9]]=>[[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7],[8],[9]]
[[1,5],[2,6],[3,7],[4,8],[9]]=>[[1,2,6],[3,7],[4,8],[5,9]]=>[[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6],[3,7],[4,8],[5,9]]
[[1,2,5],[3,6],[4,7],[8],[9]]=>[[1,2,3,6],[4,7],[5,8],[9]]=>[[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4,7],[5,8],[9]]
[[1,3,5],[2,4,6],[7],[8],[9]]=>[[1,2,4,6],[3,5,7],[8],[9]]=>[[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5,7],[8],[9]]
[[1,2,3,5],[4,6],[7],[8],[9]]=>[[1,2,3,4,6],[5,7],[8],[9]]=>[[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7],[8],[9]]
[[1,3,6],[2,4,7],[5,8],[9]]=>[[1,2,4,7],[3,5,8],[6,9]]=>[[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,7],[3,5,8],[6,9]]
[[1,2,3,6],[4,7],[5,8],[9]]=>[[1,2,3,4,7],[5,8],[6,9]]=>[[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5,8],[6,9]]
[[1,2,4,6],[3,5,7],[8],[9]]=>[[1,2,3,5,7],[4,6,8],[9]]=>[[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,7],[4,6,8],[9]]
[[1,2,3,4,6],[5,7],[8],[9]]=>[[1,2,3,4,5,7],[6,8],[9]]=>[[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6,8],[9]]
[[1,3,5,7],[2,4,6,8],[9]]=>[[1,2,4,6,8],[3,5,7,9]]=>[[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6,8],[3,5,7,9]]
[[1,2,3,5,7],[4,6,8],[9]]=>[[1,2,3,4,6,8],[5,7,9]]=>[[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6,8],[5,7,9]]
[[1,2,3,4,5,7],[6,8],[9]]=>[[1,2,3,4,5,6,8],[7,9]]=>[[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,8],[7,9]]
[[1,2,3,4,5,6,8],[7,9]]=>[[1,2,3,4,5,6,7,9],[8]]=>[[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,9],[8]]
[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>[[1,2,4],[3,5],[6],[7],[8],[9],[10]]=>[[3,2,1,1,1,1,1,0,0,0],[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5],[6],[7],[8],[9],[10]]
[[1,4],[2,5],[3,6],[7],[8],[9],[10]]=>[[1,2,5],[3,6],[4,7],[8],[9],[10]]=>[[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4,7],[8],[9],[10]]
[[1,2,4],[3,5],[6],[7],[8],[9],[10]]=>[[1,2,3,5],[4,6],[7],[8],[9],[10]]=>[[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7],[8],[9],[10]]
[[1,5],[2,6],[3,7],[4,8],[9],[10]]=>[[1,2,6],[3,7],[4,8],[5,9],[10]]=>[[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6],[3,7],[4,8],[5,9],[10]]
[[1,2,5],[3,6],[4,7],[8],[9],[10]]=>[[1,2,3,6],[4,7],[5,8],[9],[10]]=>[[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4,7],[5,8],[9],[10]]
[[1,3,5],[2,4,6],[7],[8],[9],[10]]=>[[1,2,4,6],[3,5,7],[8],[9],[10]]=>[[4,3,1,1,1,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5,7],[8],[9],[10]]
[[1,2,3,5],[4,6],[7],[8],[9],[10]]=>[[1,2,3,4,6],[5,7],[8],[9],[10]]=>[[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7],[8],[9],[10]]
[[1,2,6],[3,7],[4,8],[5,9],[10]]=>[[1,2,3,7],[4,8],[5,9],[6,10]]=>[[4,2,2,2,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,7],[4,8],[5,9],[6,10]]
[[1,3,6],[2,4,7],[5,8],[9],[10]]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[[4,3,2,1,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,7],[3,5,8],[6,9],[10]]
[[1,2,3,6],[4,7],[5,8],[9],[10]]=>[[1,2,3,4,7],[5,8],[6,9],[10]]=>[[5,2,2,1,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5,8],[6,9],[10]]
[[1,2,4,6],[3,5,7],[8],[9],[10]]=>[[1,2,3,5,7],[4,6,8],[9],[10]]=>[[5,3,1,1,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,7],[4,6,8],[9],[10]]
[[1,2,3,4,6],[5,7],[8],[9],[10]]=>[[1,2,3,4,5,7],[6,8],[9],[10]]=>[[6,2,1,1,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6,8],[9],[10]]
[[1,4,7],[2,5,8],[3,6,9],[10]]=>[[1,2,5,8],[3,6,9],[4,7,10]]=>[[4,3,3,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,8],[3,6,9],[4,7,10]]
[[1,2,4,7],[3,5,8],[6,9],[10]]=>[[1,2,3,5,8],[4,6,9],[7,10]]=>[[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,8],[4,6,9],[7,10]]
[[1,2,3,4,7],[5,8],[6,9],[10]]=>[[1,2,3,4,5,8],[6,9],[7,10]]=>[[6,2,2,0,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6,9],[7,10]]
[[1,3,5,7],[2,4,6,8],[9],[10]]=>[[1,2,4,6,8],[3,5,7,9],[10]]=>[[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6,8],[3,5,7,9],[10]]
[[1,2,3,5,7],[4,6,8],[9],[10]]=>[[1,2,3,4,6,8],[5,7,9],[10]]=>[[6,3,1,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6,8],[5,7,9],[10]]
[[1,2,3,4,5,7],[6,8],[9],[10]]=>[[1,2,3,4,5,6,8],[7,9],[10]]=>[[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,8],[7,9],[10]]
[[1,2,4,6,8],[3,5,7,9],[10]]=>[[1,2,3,5,7,9],[4,6,8,10]]=>[[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,7,9],[4,6,8,10]]
[[1,2,3,4,6,8],[5,7,9],[10]]=>[[1,2,3,4,5,7,9],[6,8,10]]=>[[7,3,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7,9],[6,8,10]]
[[1,2,3,4,5,6,8],[7,9],[10]]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,9],[8,10]]
[[1,2,3,4,5,6,7,9],[8,10]]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[9,1,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,10],[9]]
[[1,2],[3,7],[4,8],[5,9],[6,10]]=>[[1,2,3,7],[4,8],[5,9],[6,10]]=>[[4,2,2,2,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,7],[4,8],[5,9],[6,10]]
[[1,2,3,4,5,6,7,9],[8]]=>[[1,2,3,4,5,6,7,8],[9]]=>[[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9]]
[[1,2,3,4,5,6,9],[7,8]]=>[[1,2,3,4,5,6,7,8],[9]]=>[[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9]]
[[1,2,3,4,5,6,9],[7],[8]]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8],[9]]
[[1,2,3,4,5,9],[6,7,8]]=>[[1,2,3,4,5,6,7,8],[9]]=>[[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9]]
[[1,2,3,4,5,9],[6,7],[8]]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8],[9]]
[[1,2,3,4,5,9],[6],[7],[8]]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8],[9]]
[[1,2,3,4,9],[5,6,7],[8]]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8],[9]]
[[1,2,3,4,9],[5,6],[7,8]]=>[[1,2,3,4,5,6],[7,8],[9]]=>[[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8],[9]]
[[1,2,3,4,9],[5,6],[7],[8]]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8],[9]]
[[1,2,3,4,9],[5],[6],[7],[8]]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7],[8],[9]]
[[1,2,3,9],[4,5,6],[7,8]]=>[[1,2,3,4,5,6],[7,8],[9]]=>[[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8],[9]]
[[1,2,3,9],[4,5,6],[7],[8]]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7],[8],[9]]
[[1,2,3,9],[4,5],[6,7],[8]]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8],[9]]
[[1,2,3,9],[4,5],[6],[7],[8]]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6],[7],[8],[9]]
[[1,2,3,9],[4],[5],[6],[7],[8]]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7],[8],[9]]
[[1,2,9],[3,4],[5,6],[7],[8]]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7],[8],[9]]
[[1,2,9],[3,4],[5],[6],[7],[8]]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6],[7],[8],[9]]
[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]
[[1,2,3,4,5,6,7,8,10],[9]]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[[1,2,3,4,5,6,7,10],[8,9]]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,9],[10]]
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[[1,2,4,6,8,10],[3,5,7,9]]=>[[1,2,3,5,7,9],[4,6,8,10]]=>[[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,7,9],[4,6,8,10]]
[[1,2,3,4,6,8,10],[5,7,9]]=>[[1,2,3,4,5,7,9],[6,8,10]]=>[[7,3,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7,9],[6,8,10]]
[[1,2,3,4,5,6,8,10],[7,9]]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,9],[8,10]]
[[1,2,3,4,5,6,9,10],[7,8]]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[[1,2,3,4,5,6,7,9,10],[8]]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[9,1,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,10],[9]]
[[1,4,5,6,7,8],[2],[3],[9]]=>[[1,2,5,6,7,8,9],[3],[4]]=>[[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8,9],[3],[4]]
[[1,2,3,7,8],[4,5,6],[9]]=>[[1,2,3,4,5,6],[7,8,9]]=>[[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8,9]]
[[1,5,6,7,8],[2],[3],[4],[9]]=>[[1,2,6,7,8,9],[3],[4],[5]]=>[[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8,9],[3],[4],[5]]
[[1,2,7,8],[3,4],[5,6],[9]]=>[[1,2,3,4,9],[5,6],[7,8]]=>[[5,2,2,0,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,9],[5,6],[7,8]]
[[1,6,7,8],[2],[3],[4],[5],[9]]=>[[1,2,7,8,9],[3],[4],[5],[6]]=>[[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8,9],[3],[4],[5],[6]]
[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[[1,2,8,9],[3],[4],[5],[6],[7]]=>[[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,8,9],[3],[4],[5],[6],[7]]
[[1,4,5,6,7,8,9],[2],[3],[10]]=>[[1,2,5,6,7,8,9,10],[3],[4]]=>[[8,1,1,0,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8,9,10],[3],[4]]
[[1,2,3,7,8,9],[4,5,6,10]]=>[[1,2,3,4,5,6,10],[7,8,9]]=>[[7,3,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,10],[7,8,9]]
[[1,2,3,7,8,9],[4,5,6],[10]]=>[[1,2,3,4,5,6,10],[7,8,9]]=>[[7,3,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,10],[7,8,9]]
[[1,5,6,7,8,9],[2],[3],[4],[10]]=>[[1,2,6,7,8,9,10],[3],[4],[5]]=>[[7,1,1,1,0,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8,9,10],[3],[4],[5]]
[[1,2,3,4,9],[5,6,7,8],[10]]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[[1,6,7,8,9],[2],[3],[4],[5],[10]]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]=>[[6,1,1,1,1,0,0,0,0,0],[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]
[[1,7,8,9],[2],[3],[4],[5],[6],[10]]=>[[1,2,8,9,10],[3],[4],[5],[6],[7]]=>[[5,1,1,1,1,1,0,0,0,0],[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,8,9,10],[3],[4],[5],[6],[7]]
[[1,2,9],[3,4],[5,6],[7,8],[10]]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[[4,2,2,2,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7,8],[9,10]]
[[1,8,9],[2],[3],[4],[5],[6],[7],[10]]=>[[1,2,9,10],[3],[4],[5],[6],[7],[8]]=>[[4,1,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,9,10],[3],[4],[5],[6],[7],[8]]
[[1,2,3,4,8,9],[5,6,7]]=>[[1,2,3,4,5,6,7],[8,9]]=>[[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8,9]]
[[1,2,3,8,9],[4,5],[6,7]]=>[[1,2,3,4,5],[6,7],[8,9]]=>[[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8,9]]
[[1,2,3,4,8,9,10],[5,6,7]]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[[7,3,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8,9,10]]
[[1,2,3,4,9,10],[5,6],[7,8]]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[[6,2,2,0,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8],[9,10]]
[[1,2,3,4],[5,6,7,9],[8]]=>[[1,2,3,4,5,6,7,9],[8]]=>[[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,9],[8]]
[[1,2,3,4,5,6,8],[7],[9]]=>[[1,2,3,4,5,6,7,9],[8]]=>[[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,9],[8]]
[[1,2,3,5,7,9],[4,6,8]]=>[[1,2,3,4,6,8],[5,7,9]]=>[[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6,8],[5,7,9]]
[[1,2,3,4,5,7,9],[6,8]]=>[[1,2,3,4,5,6,8],[7,9]]=>[[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,8],[7,9]]
[[1,2,3,4,5,6,7,9],[8],[10]]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[9,1,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,10],[9]]
[[1,2,6,10],[3,7],[4,8],[5,9]]=>[[1,2,3,7],[4,8],[5,9],[6,10]]=>[[4,2,2,2,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,7],[4,8],[5,9],[6,10]]
[[1,2,3,4],[5,8],[6,9],[7,10]]=>[[1,2,3,4,5,8],[6,9],[7,10]]=>[[6,2,2,0,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6,9],[7,10]]
[[1,2,3,4,5,6],[7,9],[8]]=>[[1,2,3,4,5,6,7,9],[8]]=>[[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,9],[8]]
[[1,2,3,4,5,6,7],[8,10],[9]]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[9,1,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7,8,10],[9]]
[[1,3,9],[2,4],[5],[6],[7],[8]]=>[[1,2,4],[3,5],[6],[7],[8],[9]]=>[[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5],[6],[7],[8],[9]]
[[1,4,9],[2,5],[3,6],[7],[8]]=>[[1,2,5],[3,6],[4,7],[8],[9]]=>[[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4,7],[8],[9]]
[[1,2,4,9],[3,5],[6],[7],[8]]=>[[1,2,3,5],[4,6],[7],[8],[9]]=>[[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7],[8],[9]]
[[1,2,5,9],[3,6],[4,7],[8]]=>[[1,2,3,6],[4,7],[5,8],[9]]=>[[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4,7],[5,8],[9]]
[[1,3,5,9],[2,4,6],[7],[8]]=>[[1,2,4,6],[3,5,7],[8],[9]]=>[[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5,7],[8],[9]]
[[1,2,3,5,9],[4,6],[7],[8]]=>[[1,2,3,4,6],[5,7],[8],[9]]=>[[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7],[8],[9]]
[[1,3,6,9],[2,4,7],[5,8]]=>[[1,2,4,7],[3,5,8],[6,9]]=>[[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,7],[3,5,8],[6,9]]
[[1,2,3,6,9],[4,7],[5,8]]=>[[1,2,3,4,7],[5,8],[6,9]]=>[[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5,8],[6,9]]
[[1,2,4,6,9],[3,5,7],[8]]=>[[1,2,3,5,7],[4,6,8],[9]]=>[[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,7],[4,6,8],[9]]
[[1,2,3,4,6,9],[5,7],[8]]=>[[1,2,3,4,5,7],[6,8],[9]]=>[[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6,8],[9]]
[[1,3,10],[2,4],[5],[6],[7],[8],[9]]=>[[1,2,4],[3,5],[6],[7],[8],[9],[10]]=>[[3,2,1,1,1,1,1,0,0,0],[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5],[6],[7],[8],[9],[10]]
[[1,4,10],[2,5],[3,6],[7],[8],[9]]=>[[1,2,5],[3,6],[4,7],[8],[9],[10]]=>[[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4,7],[8],[9],[10]]
[[1,2,4,10],[3,5],[6],[7],[8],[9]]=>[[1,2,3,5],[4,6],[7],[8],[9],[10]]=>[[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6],[7],[8],[9],[10]]
[[1,5,10],[2,6],[3,7],[4,8],[9]]=>[[1,2,6],[3,7],[4,8],[5,9],[10]]=>[[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6],[3,7],[4,8],[5,9],[10]]
[[1,2,5,10],[3,6],[4,7],[8],[9]]=>[[1,2,3,6],[4,7],[5,8],[9],[10]]=>[[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4,7],[5,8],[9],[10]]
[[1,3,5,10],[2,4,6],[7],[8],[9]]=>[[1,2,4,6],[3,5,7],[8],[9],[10]]=>[[4,3,1,1,1,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5,7],[8],[9],[10]]
[[1,2,3,5,10],[4,6],[7],[8],[9]]=>[[1,2,3,4,6],[5,7],[8],[9],[10]]=>[[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5,7],[8],[9],[10]]
[[1,3,6,10],[2,4,7],[5,8],[9]]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[[4,3,2,1,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,7],[3,5,8],[6,9],[10]]
[[1,2,3,6,10],[4,7],[5,8],[9]]=>[[1,2,3,4,7],[5,8],[6,9],[10]]=>[[5,2,2,1,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,7],[5,8],[6,9],[10]]
[[1,2,4,6,10],[3,5,7],[8],[9]]=>[[1,2,3,5,7],[4,6,8],[9],[10]]=>[[5,3,1,1,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,7],[4,6,8],[9],[10]]
[[1,2,3,4,6,10],[5,7],[8],[9]]=>[[1,2,3,4,5,7],[6,8],[9],[10]]=>[[6,2,1,1,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7],[6,8],[9],[10]]
[[1,2,4,7,10],[3,5,8],[6,9]]=>[[1,2,3,5,8],[4,6,9],[7,10]]=>[[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,8],[4,6,9],[7,10]]
[[1,2,3,4,7,10],[5,8],[6,9]]=>[[1,2,3,4,5,8],[6,9],[7,10]]=>[[6,2,2,0,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,8],[6,9],[7,10]]
[[1,3,5,7,10],[2,4,6,8],[9]]=>[[1,2,4,6,8],[3,5,7,9],[10]]=>[[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6,8],[3,5,7,9],[10]]
[[1,2,3,5,7,10],[4,6,8],[9]]=>[[1,2,3,4,6,8],[5,7,9],[10]]=>[[6,3,1,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6,8],[5,7,9],[10]]
[[1,2,3,4,5,7,10],[6,8],[9]]=>[[1,2,3,4,5,6,8],[7,9],[10]]=>[[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,8],[7,9],[10]]
[[1,2,3,4,5,8,9],[6,7]]=>[[1,2,3,4,5,6,7],[8,9]]=>[[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8,9]]
[[1,2,3,4,7,9],[5,6],[8]]=>[[1,2,3,4,5,6],[7,8],[9]]=>[[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8],[9]]
[[1,2,3,4,7,10],[5,6],[8],[9]]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>[[6,2,1,1,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8],[9],[10]]
[[1,2,3,5],[4,6,8],[7,9]]=>[[1,2,3,4,6,8],[5,7,9]]=>[[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6,8],[5,7,9]]
[[1,2,3,4,6],[5,7,9],[8,10]]=>[[1,2,3,4,5,7,9],[6,8,10]]=>[[7,3,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,7,9],[6,8,10]]
[[1,4,5,6],[2,8,9],[3],[7]]=>[[1,2,5,6,7,8,9],[3],[4]]=>[[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8,9],[3],[4]]
[[1,2,3,6,9],[4,5],[7],[8]]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8],[9]]
[[1,2,7,9],[3,4],[5,6],[8]]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7,8],[9]]
[[1,2,5,9],[3,4],[6],[7],[8]]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7],[8],[9]]
[[1,2,3,4,5,8,10],[6,7],[9]]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6,7],[8,9],[10]]
[[1,2,3,7,8,10],[4,5,6],[9]]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[[6,3,1,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6],[7,8,9],[10]]
[[1,2,3,8,10],[4,5],[6,7],[9]]=>[[1,2,3,4,5],[6,7],[8,9],[10]]=>[[5,2,2,1,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8,9],[10]]
[[1,2,3,6,10],[4,5],[7],[8],[9]]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]
[[1,2,7,10],[3,4],[5,6],[8],[9]]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]
[[1,2,5,10],[3,4],[6],[7],[8],[9]]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]
[[1,6,7],[2,9],[3],[4],[5],[8]]=>[[1,2,7,8,9],[3],[4],[5],[6]]=>[[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8,9],[3],[4],[5],[6]]
[[1,5,6,7],[2,9,10],[3],[4],[8]]=>[[1,2,6,7,8,9,10],[3],[4],[5]]=>[[7,1,1,1,0,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8,9,10],[3],[4],[5]]
[[1,7,8],[2,10],[3],[4],[5],[6],[9]]=>[[1,2,8,9,10],[3],[4],[5],[6],[7]]=>[[5,1,1,1,1,1,0,0,0,0],[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,8,9,10],[3],[4],[5],[6],[7]]
[[1,5,6,7],[2,8,9,10],[3],[4]]=>[[1,2,6,7,8,9,10],[3],[4],[5]]=>[[7,1,1,1,0,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8,9,10],[3],[4],[5]]
[[1,6,7,8,9],[2,10],[3],[4],[5]]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]=>[[6,1,1,1,1,0,0,0,0,0],[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]
[[1,4,5,6,7,8],[2,9],[3]]=>[[1,2,5,6,7,8,9],[3],[4]]=>[[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8,9],[3],[4]]
[[1,5,6,7,8],[2,9],[3],[4]]=>[[1,2,6,7,8,9],[3],[4],[5]]=>[[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8,9],[3],[4],[5]]
[[1,6,7,8],[2,9],[3],[4],[5]]=>[[1,2,7,8,9],[3],[4],[5],[6]]=>[[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,7,8,9],[3],[4],[5],[6]]
[[1,7,8],[2,9],[3],[4],[5],[6]]=>[[1,2,8,9],[3],[4],[5],[6],[7]]=>[[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,8,9],[3],[4],[5],[6],[7]]
[[1,4,5,6,7,8,9],[2,10],[3]]=>[[1,2,5,6,7,8,9,10],[3],[4]]=>[[8,1,1,0,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6,7,8,9,10],[3],[4]]
[[1,5,6,7,8,9],[2,10],[3],[4]]=>[[1,2,6,7,8,9,10],[3],[4],[5]]=>[[7,1,1,1,0,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6,7,8,9,10],[3],[4],[5]]
[[1,7,8,9],[2,10],[3],[4],[5],[6]]=>[[1,2,8,9,10],[3],[4],[5],[6],[7]]=>[[5,1,1,1,1,1,0,0,0,0],[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,8,9,10],[3],[4],[5],[6],[7]]
[[1,8,9],[2,10],[3],[4],[5],[6],[7]]=>[[1,2,9,10],[3],[4],[5],[6],[7],[8]]=>[[4,1,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,9,10],[3],[4],[5],[6],[7],[8]]
Map
catabolism
Description
Remove the first row of the standard 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 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 $y$. 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 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 $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
Map
to Gelfand-Tsetlin pattern
Description
Sends a tableau to its corresponding Gelfand-Tsetlin pattern.
To obtain this Gelfand-Tsetlin pattern, fill in the first row of the pattern with the shape of the tableau.
Then remove the maximal entry from the tableau to obtain a smaller tableau, and repeat the process until the tableau is empty.
To obtain this Gelfand-Tsetlin pattern, fill in the first row of the pattern with the shape of the tableau.
Then remove the maximal entry from the tableau to obtain a smaller tableau, and repeat the process until the tableau is empty.
Map
to semistandard tableau
Description
Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let $G$ be a Gelfand-Tsetlin pattern and let $\lambda^{(k)}$ be its $(n-k+1)$-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
$$ \lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)}, $$
where $\lambda^{(0)}$ is the empty partition.
Each skew shape $\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau $T(G)$ by inserting $k$ into the cells of the skew shape $\lambda^{(k)} / \lambda^{(k-1)}$, for $k=1,\dots,n$.
Let $G$ be a Gelfand-Tsetlin pattern and let $\lambda^{(k)}$ be its $(n-k+1)$-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
$$ \lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)}, $$
where $\lambda^{(0)}$ is the empty partition.
Each skew shape $\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau $T(G)$ by inserting $k$ into the cells of the skew shape $\lambda^{(k)} / \lambda^{(k-1)}$, for $k=1,\dots,n$.
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