Identifier
Images
=>
Cc0005;cc-rep-0Cc0028;cc-rep-1
[1,0]=>[[1],[]]
[1,0,1,0]=>[[1,1],[]]
[1,1,0,0]=>[[2],[]]
[1,0,1,0,1,0]=>[[1,1,1],[]]
[1,0,1,1,0,0]=>[[2,1],[]]
[1,1,0,0,1,0]=>[[2,2],[1]]
[1,1,0,1,0,0]=>[[3],[]]
[1,1,1,0,0,0]=>[[2,2],[]]
[1,0,1,0,1,0,1,0]=>[[1,1,1,1],[]]
[1,0,1,0,1,1,0,0]=>[[2,1,1],[]]
[1,0,1,1,0,0,1,0]=>[[2,2,1],[1]]
[1,0,1,1,0,1,0,0]=>[[3,1],[]]
[1,0,1,1,1,0,0,0]=>[[2,2,1],[]]
[1,1,0,0,1,0,1,0]=>[[2,2,2],[1,1]]
[1,1,0,0,1,1,0,0]=>[[3,2],[1]]
[1,1,0,1,0,0,1,0]=>[[3,3],[2]]
[1,1,0,1,0,1,0,0]=>[[4],[]]
[1,1,0,1,1,0,0,0]=>[[3,3],[1]]
[1,1,1,0,0,0,1,0]=>[[2,2,2],[1]]
[1,1,1,0,0,1,0,0]=>[[3,2],[]]
[1,1,1,0,1,0,0,0]=>[[2,2,2],[]]
[1,1,1,1,0,0,0,0]=>[[3,3],[]]
[1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1],[]]
[1,0,1,0,1,1,0,0,1,0]=>[[2,2,1,1],[1]]
[1,0,1,0,1,1,0,1,0,0]=>[[3,1,1],[]]
[1,0,1,0,1,1,1,0,0,0]=>[[2,2,1,1],[]]
[1,0,1,1,0,0,1,0,1,0]=>[[2,2,2,1],[1,1]]
[1,0,1,1,0,0,1,1,0,0]=>[[3,2,1],[1]]
[1,0,1,1,0,1,0,0,1,0]=>[[3,3,1],[2]]
[1,0,1,1,0,1,0,1,0,0]=>[[4,1],[]]
[1,0,1,1,0,1,1,0,0,0]=>[[3,3,1],[1]]
[1,0,1,1,1,0,0,0,1,0]=>[[2,2,2,1],[1]]
[1,0,1,1,1,0,0,1,0,0]=>[[3,2,1],[]]
[1,0,1,1,1,0,1,0,0,0]=>[[2,2,2,1],[]]
[1,0,1,1,1,1,0,0,0,0]=>[[3,3,1],[]]
[1,1,0,0,1,0,1,0,1,0]=>[[2,2,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,0,0]=>[[3,2,2],[1,1]]
[1,1,0,0,1,1,0,0,1,0]=>[[3,3,2],[2,1]]
[1,1,0,0,1,1,0,1,0,0]=>[[4,2],[1]]
[1,1,0,0,1,1,1,0,0,0]=>[[3,3,2],[1,1]]
[1,1,0,1,0,0,1,0,1,0]=>[[3,3,3],[2,2]]
[1,1,0,1,0,0,1,1,0,0]=>[[4,3],[2]]
[1,1,0,1,0,1,0,0,1,0]=>[[4,4],[3]]
[1,1,0,1,0,1,0,1,0,0]=>[[5],[]]
[1,1,0,1,0,1,1,0,0,0]=>[[4,4],[2]]
[1,1,0,1,1,0,0,0,1,0]=>[[3,3,3],[2,1]]
[1,1,0,1,1,0,0,1,0,0]=>[[4,3],[1]]
[1,1,0,1,1,0,1,0,0,0]=>[[3,3,3],[1,1]]
[1,1,0,1,1,1,0,0,0,0]=>[[4,4],[1]]
[1,1,1,0,0,0,1,0,1,0]=>[[2,2,2,2],[1,1]]
[1,1,1,0,0,0,1,1,0,0]=>[[3,2,2],[1]]
[1,1,1,0,0,1,0,0,1,0]=>[[3,3,2],[2]]
[1,1,1,0,0,1,0,1,0,0]=>[[4,2],[]]
[1,1,1,0,0,1,1,0,0,0]=>[[3,3,2],[1]]
[1,1,1,0,1,0,0,0,1,0]=>[[2,2,2,2],[1]]
[1,1,1,0,1,0,0,1,0,0]=>[[3,2,2],[]]
[1,1,1,0,1,0,1,0,0,0]=>[[2,2,2,2],[]]
[1,1,1,0,1,1,0,0,0,0]=>[[3,3,2],[]]
[1,1,1,1,0,0,0,0,1,0]=>[[3,3,3],[2]]
[1,1,1,1,0,0,0,1,0,0]=>[[4,3],[]]
[1,1,1,1,0,0,1,0,0,0]=>[[3,3,3],[1]]
[1,1,1,1,0,1,0,0,0,0]=>[[4,4],[]]
[1,1,1,1,1,0,0,0,0,0]=>[[3,3,3],[]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[[2,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[[3,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[[2,2,1,1,1],[]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[[2,2,2,1,1],[1,1]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[[3,2,1,1],[1]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[[3,3,1,1],[2]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[[4,1,1],[]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[[3,3,1,1],[1]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[[2,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[[3,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[[2,2,2,1,1],[]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[[3,3,1,1],[]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[[2,2,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[[3,2,2,1],[1,1]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[[3,3,2,1],[2,1]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[[4,2,1],[1]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[[3,3,2,1],[1,1]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[[3,3,3,1],[2,2]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[[4,3,1],[2]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[[4,4,1],[3]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[[5,1],[]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[[4,4,1],[2]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[[3,3,3,1],[2,1]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[[4,3,1],[1]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[[3,3,3,1],[1,1]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[[4,4,1],[1]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[[2,2,2,2,1],[1,1]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[[3,2,2,1],[1]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[[3,3,2,1],[2]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[[4,2,1],[]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[[3,3,2,1],[1]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[[2,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[[3,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[[2,2,2,2,1],[]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[[3,3,2,1],[]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[[3,3,3,1],[2]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[[4,3,1],[]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[[3,3,3,1],[1]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[[4,4,1],[]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[[3,3,3,1],[]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[[4,2,2],[1,1]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[3,3,2,2],[1,1,1]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2],[2,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[[4,3,2],[2,1]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[[4,4,2],[3,1]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[5,2],[1]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[4,4,2],[2,1]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[3,3,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[4,3,2],[1,1]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[3,3,3,2],[1,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[4,4,2],[1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3],[2,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[4,3,3],[2,2]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[4,4,3],[3,2]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[5,3],[2]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[4,4,3],[2,2]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[4,4,4],[3,3]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[5,4],[3]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[5,5],[4]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[[6],[]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[[5,5],[3]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[4,4,4],[3,2]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[[5,4],[2]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[[4,4,4],[2,2]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[[5,5],[2]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[3,3,3,3],[2,2,1]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[4,3,3],[2,1]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[4,4,3],[3,1]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[[5,3],[1]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[[4,4,3],[2,1]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[3,3,3,3],[2,1,1]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[[4,3,3],[1,1]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3],[1,1,1]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[[4,4,3],[1,1]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[4,4,4],[3,1]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[[5,4],[1]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[[4,4,4],[2,1]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[[5,5],[1]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[[4,4,4],[1,1]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[2,2,2,2,2],[1,1,1]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[3,2,2,2],[1,1]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[3,3,2,2],[2,1]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[4,2,2],[1]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[3,3,2,2],[1,1]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[3,3,3,2],[2,2]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[4,3,2],[2]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[4,4,2],[3]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[[5,2],[]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[[4,4,2],[2]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[3,3,3,2],[2,1]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[[4,3,2],[1]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[[3,3,3,2],[1,1]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[[4,4,2],[1]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[2,2,2,2,2],[1,1]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[3,2,2,2],[1]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[3,3,2,2],[2]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[[4,2,2],[]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[[3,3,2,2],[1]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[2,2,2,2,2],[1]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2],[]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[[3,3,2,2],[]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[3,3,3,2],[2]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[[4,3,2],[]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[[3,3,3,2],[1]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[[4,4,2],[]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[[3,3,3,2],[]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[3,3,3,3],[2,2]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[4,3,3],[2]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[4,4,3],[3]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[[5,3],[]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[[4,4,3],[2]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[3,3,3,3],[2,1]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[[4,3,3],[1]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[[3,3,3,3],[1,1]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[[4,4,3],[1]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[4,4,4],[3]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[[5,4],[]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[[4,4,4],[2]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[[5,5],[]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[[4,4,4],[1]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[3,3,3,3],[2]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[[4,3,3],[]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[[3,3,3,3],[1]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[[4,4,3],[]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[[3,3,3,3],[]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[[4,4,4],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[2,2,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[3,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[2,2,1,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[2,2,2,1,1,1],[1,1]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[3,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[3,3,1,1,1],[2]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[4,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[3,3,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[2,2,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[3,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[2,2,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[3,3,1,1,1],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[2,2,2,2,1,1],[1,1,1]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[3,2,2,1,1],[1,1]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[3,3,2,1,1],[2,1]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[4,2,1,1],[1]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[3,3,2,1,1],[1,1]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[3,3,3,1,1],[2,2]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[4,3,1,1],[2]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[4,4,1,1],[3]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[5,1,1],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[4,4,1,1],[2]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[3,3,3,1,1],[2,1]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[4,3,1,1],[1]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[3,3,3,1,1],[1,1]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[4,4,1,1],[1]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[2,2,2,2,1,1],[1,1]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[3,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[3,3,2,1,1],[2]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[4,2,1,1],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[3,3,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[2,2,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[3,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[2,2,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[3,3,2,1,1],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[3,3,3,1,1],[2]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[4,3,1,1],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[3,3,3,1,1],[1]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[4,4,1,1],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[3,3,3,1,1],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,1],[1,1,1,1]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,1],[2,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[4,2,2,1],[1,1]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[3,3,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2,1],[2,2,1]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[4,3,2,1],[2,1]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[4,4,2,1],[3,1]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[5,2,1],[1]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[4,4,2,1],[2,1]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[3,3,3,2,1],[2,1,1]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[4,3,2,1],[1,1]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[3,3,3,2,1],[1,1,1]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[4,4,2,1],[1,1]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3,1],[2,2,2]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[4,3,3,1],[2,2]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[4,4,3,1],[3,2]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[5,3,1],[2]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[4,4,3,1],[2,2]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[4,4,4,1],[3,3]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[5,4,1],[3]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[5,5,1],[4]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[6,1],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[5,5,1],[3]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[4,4,4,1],[3,2]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[5,4,1],[2]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[4,4,4,1],[2,2]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[5,5,1],[2]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[3,3,3,3,1],[2,2,1]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[4,3,3,1],[2,1]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[4,4,3,1],[3,1]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[5,3,1],[1]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[4,4,3,1],[2,1]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[3,3,3,3,1],[2,1,1]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[4,3,3,1],[1,1]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3,1],[1,1,1]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[4,4,3,1],[1,1]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[4,4,4,1],[3,1]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[5,4,1],[1]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[4,4,4,1],[2,1]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[5,5,1],[1]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[4,4,4,1],[1,1]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[2,2,2,2,2,1],[1,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[3,2,2,2,1],[1,1]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[3,3,2,2,1],[2,1]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[4,2,2,1],[1]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[3,3,2,2,1],[1,1]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[3,3,3,2,1],[2,2]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[4,3,2,1],[2]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[4,4,2,1],[3]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[5,2,1],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[4,4,2,1],[2]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[3,3,3,2,1],[2,1]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[4,3,2,1],[1]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[3,3,3,2,1],[1,1]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[4,4,2,1],[1]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[2,2,2,2,2,1],[1,1]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[3,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[3,3,2,2,1],[2]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[4,2,2,1],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[3,3,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[2,2,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[3,3,2,2,1],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[3,3,3,2,1],[2]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[4,3,2,1],[]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[3,3,3,2,1],[1]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[4,4,2,1],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[3,3,3,2,1],[]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[3,3,3,3,1],[2,2]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[4,3,3,1],[2]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[4,4,3,1],[3]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[5,3,1],[]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[4,4,3,1],[2]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[3,3,3,3,1],[2,1]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[4,3,3,1],[1]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[3,3,3,3,1],[1,1]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[4,4,3,1],[1]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[4,4,4,1],[3]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[5,4,1],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[4,4,4,1],[2]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[5,5,1],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[4,4,4,1],[1]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[3,3,3,3,1],[2]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[4,3,3,1],[]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[3,3,3,3,1],[1]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[4,4,3,1],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[3,3,3,3,1],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[4,4,4,1],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2],[1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[4,2,2,2],[1,1,1]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[3,3,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2,2],[2,2,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[4,3,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[4,4,2,2],[3,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[5,2,2],[1,1]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[4,4,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[3,3,3,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[4,3,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[3,3,3,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[4,4,2,2],[1,1,1]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3,2],[2,2,2,1]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[4,3,3,2],[2,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[4,4,3,2],[3,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[5,3,2],[2,1]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[4,4,3,2],[2,2,1]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[4,4,4,2],[3,3,1]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[5,4,2],[3,1]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[5,5,2],[4,1]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[6,2],[1]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[5,5,2],[3,1]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[4,4,4,2],[3,2,1]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[5,4,2],[2,1]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[4,4,4,2],[2,2,1]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[5,5,2],[2,1]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[3,3,3,3,2],[2,2,1,1]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[4,3,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[4,4,3,2],[3,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[5,3,2],[1,1]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[4,4,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[3,3,3,3,2],[2,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[4,3,3,2],[1,1,1]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3,2],[1,1,1,1]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[4,4,3,2],[1,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[4,4,4,2],[3,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[5,4,2],[1,1]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[4,4,4,2],[2,1,1]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[5,5,2],[1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[4,4,4,2],[1,1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3],[2,2,2,2]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[4,3,3,3],[2,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[4,4,3,3],[3,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[5,3,3],[2,2]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[4,4,3,3],[2,2,2]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[4,4,4,3],[3,3,2]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[5,4,3],[3,2]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[5,5,3],[4,2]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[6,3],[2]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[5,5,3],[3,2]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[4,4,4,3],[3,2,2]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[5,4,3],[2,2]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[4,4,4,3],[2,2,2]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[5,5,3],[2,2]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[4,4,4,4],[3,3,3]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[5,4,4],[3,3]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[5,5,4],[4,3]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[6,4],[3]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[5,5,4],[3,3]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[5,5,5],[4,4]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[6,5],[4]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[6,6],[5]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[6,6],[4]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[5,5,5],[4,3]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[6,5],[3]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[5,5,5],[3,3]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[6,6],[3]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[4,4,4,4],[3,3,2]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[5,4,4],[3,2]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[5,5,4],[4,2]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[6,4],[2]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[5,5,4],[3,2]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[4,4,4,4],[3,2,2]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[5,4,4],[2,2]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[4,4,4,4],[2,2,2]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[5,5,4],[2,2]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[5,5,5],[4,2]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[6,5],[2]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[5,5,5],[3,2]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[6,6],[2]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[5,5,5],[2,2]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[3,3,3,3,3],[2,2,2,1]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[4,3,3,3],[2,2,1]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[4,4,3,3],[3,2,1]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[5,3,3],[2,1]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3],[2,2,1]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[4,4,4,3],[3,3,1]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[5,4,3],[3,1]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[5,5,3],[4,1]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[6,3],[1]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[5,5,3],[3,1]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[4,4,4,3],[3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[5,4,3],[2,1]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3],[2,2,1]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[5,5,3],[2,1]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[3,3,3,3,3],[2,2,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[4,3,3,3],[2,1,1]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[4,4,3,3],[3,1,1]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[5,3,3],[1,1]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3],[2,1,1]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[3,3,3,3,3],[2,1,1,1]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3],[1,1,1]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3],[1,1,1,1]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3],[1,1,1]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[4,4,4,3],[3,1,1]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[5,4,3],[1,1]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3],[2,1,1]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[5,5,3],[1,1]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3],[1,1,1]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[4,4,4,4],[3,3,1]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[5,4,4],[3,1]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[5,5,4],[4,1]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[6,4],[1]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[5,5,4],[3,1]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[4,4,4,4],[3,2,1]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[5,4,4],[2,1]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4],[2,2,1]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[5,5,4],[2,1]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[5,5,5],[4,1]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[6,5],[1]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[5,5,5],[3,1]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[6,6],[1]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[5,5,5],[2,1]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4],[3,1,1]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[5,4,4],[1,1]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4],[2,1,1]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[5,5,4],[1,1]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4],[1,1,1]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[5,5,5],[1,1]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2],[1,1,1,1]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,2],[1,1,1]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,2],[2,1,1]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[4,2,2,2],[1,1]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[3,3,2,2,2],[1,1,1]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2,2],[2,2,1]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[4,3,2,2],[2,1]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[4,4,2,2],[3,1]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[5,2,2],[1]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[4,4,2,2],[2,1]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[3,3,3,2,2],[2,1,1]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[4,3,2,2],[1,1]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[3,3,3,2,2],[1,1,1]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[4,4,2,2],[1,1]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3,2],[2,2,2]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[4,3,3,2],[2,2]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[4,4,3,2],[3,2]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[5,3,2],[2]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[4,4,3,2],[2,2]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[4,4,4,2],[3,3]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[5,4,2],[3]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[5,5,2],[4]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[6,2],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[5,5,2],[3]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[4,4,4,2],[3,2]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[5,4,2],[2]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[4,4,4,2],[2,2]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[5,5,2],[2]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[3,3,3,3,2],[2,2,1]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[4,3,3,2],[2,1]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[4,4,3,2],[3,1]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[5,3,2],[1]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[4,4,3,2],[2,1]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[3,3,3,3,2],[2,1,1]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[4,3,3,2],[1,1]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3,2],[1,1,1]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[4,4,3,2],[1,1]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[4,4,4,2],[3,1]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[5,4,2],[1]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[4,4,4,2],[2,1]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[5,5,2],[1]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[4,4,4,2],[1,1]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2],[1,1,1]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[3,2,2,2,2],[1,1]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[3,3,2,2,2],[2,1]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[4,2,2,2],[1]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[3,3,2,2,2],[1,1]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[3,3,3,2,2],[2,2]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[4,3,2,2],[2]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[4,4,2,2],[3]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[5,2,2],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[4,4,2,2],[2]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[3,3,3,2,2],[2,1]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[4,3,2,2],[1]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[3,3,3,2,2],[1,1]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[4,4,2,2],[1]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[2,2,2,2,2,2],[1,1]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[3,2,2,2,2],[1]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[3,3,2,2,2],[2]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[4,2,2,2],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[3,3,2,2,2],[1]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[2,2,2,2,2,2],[1]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[3,3,2,2,2],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[3,3,3,2,2],[2]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[4,3,2,2],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[3,3,3,2,2],[1]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[4,4,2,2],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[3,3,3,2,2],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[3,3,3,3,2],[2,2]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[4,3,3,2],[2]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[4,4,3,2],[3]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[5,3,2],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[4,4,3,2],[2]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[3,3,3,3,2],[2,1]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[4,3,3,2],[1]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[3,3,3,3,2],[1,1]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[4,4,3,2],[1]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[4,4,4,2],[3]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[5,4,2],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[4,4,4,2],[2]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[5,5,2],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[4,4,4,2],[1]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[3,3,3,3,2],[2]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[4,3,3,2],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[3,3,3,3,2],[1]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[4,4,3,2],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[3,3,3,3,2],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[4,4,4,2],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[3,3,3,3,3],[2,2,2]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[4,3,3,3],[2,2]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[4,4,3,3],[3,2]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[5,3,3],[2]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3],[2,2]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[4,4,4,3],[3,3]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[5,4,3],[3]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[5,5,3],[4]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[6,3],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[5,5,3],[3]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[4,4,4,3],[3,2]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[5,4,3],[2]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3],[2,2]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[5,5,3],[2]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[3,3,3,3,3],[2,2,1]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[4,3,3,3],[2,1]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[4,4,3,3],[3,1]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[5,3,3],[1]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3],[2,1]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[3,3,3,3,3],[2,1,1]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3],[1,1]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3],[1,1,1]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3],[1,1]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[4,4,4,3],[3,1]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[5,4,3],[1]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3],[2,1]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[5,5,3],[1]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3],[1,1]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[4,4,4,4],[3,3]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[5,4,4],[3]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[5,5,4],[4]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[6,4],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[5,5,4],[3]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[4,4,4,4],[3,2]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[5,4,4],[2]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4],[2,2]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[5,5,4],[2]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[5,5,5],[4]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[6,5],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[5,5,5],[3]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[6,6],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[5,5,5],[2]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4],[3,1]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[5,4,4],[1]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4],[2,1]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[5,5,4],[1]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4],[1,1]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[5,5,5],[1]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[3,3,3,3,3],[2,2]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[4,3,3,3],[2]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[4,4,3,3],[3]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[5,3,3],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[4,4,3,3],[2]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[3,3,3,3,3],[2,1]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[4,3,3,3],[1]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[3,3,3,3,3],[1,1]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[4,4,3,3],[1]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[4,4,4,3],[3]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[5,4,3],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[4,4,4,3],[2]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[5,5,3],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[4,4,4,3],[1]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[3,3,3,3,3],[2]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[4,3,3,3],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[3,3,3,3,3],[1]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[4,4,3,3],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[3,3,3,3,3],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[4,4,4,3],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[4,4,4,4],[3]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[5,4,4],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[4,4,4,4],[2]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[5,5,4],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[4,4,4,4],[1]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[5,5,5],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[4,4,4,4],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[2,2,1,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[3,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[2,2,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[2,2,2,1,1,1,1],[1,1]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[3,2,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[3,3,1,1,1,1],[2]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[4,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[3,3,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[2,2,2,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[3,2,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[2,2,2,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[3,3,1,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[2,2,2,2,1,1,1],[1,1,1]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[3,2,2,1,1,1],[1,1]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[3,3,2,1,1,1],[2,1]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[4,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[3,3,2,1,1,1],[1,1]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[3,3,3,1,1,1],[2,2]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[4,3,1,1,1],[2]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[4,4,1,1,1],[3]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[5,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[4,4,1,1,1],[2]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[3,3,3,1,1,1],[2,1]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[4,3,1,1,1],[1]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[3,3,3,1,1,1],[1,1]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[4,4,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[2,2,2,2,1,1,1],[1,1]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[3,2,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[3,3,2,1,1,1],[2]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[4,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[3,3,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[2,2,2,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[3,2,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[2,2,2,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[3,3,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[3,3,3,1,1,1],[2]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[4,3,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[3,3,3,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[4,4,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[3,3,3,1,1,1],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,1,1],[1,1,1,1]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,1,1],[1,1,1]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,1,1],[2,1,1]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[4,2,2,1,1],[1,1]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[3,3,2,2,1,1],[1,1,1]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2,1,1],[2,2,1]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[4,3,2,1,1],[2,1]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[4,4,2,1,1],[3,1]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[5,2,1,1],[1]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[4,4,2,1,1],[2,1]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[3,3,3,2,1,1],[2,1,1]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[4,3,2,1,1],[1,1]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[3,3,3,2,1,1],[1,1,1]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[4,4,2,1,1],[1,1]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3,1,1],[2,2,2]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[4,3,3,1,1],[2,2]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[4,4,3,1,1],[3,2]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[5,3,1,1],[2]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[4,4,3,1,1],[2,2]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[4,4,4,1,1],[3,3]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[5,4,1,1],[3]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[5,5,1,1],[4]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[6,1,1],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[5,5,1,1],[3]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[4,4,4,1,1],[3,2]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[5,4,1,1],[2]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[4,4,4,1,1],[2,2]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[5,5,1,1],[2]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[3,3,3,3,1,1],[2,2,1]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[4,3,3,1,1],[2,1]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[4,4,3,1,1],[3,1]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[5,3,1,1],[1]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[4,4,3,1,1],[2,1]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[3,3,3,3,1,1],[2,1,1]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[4,3,3,1,1],[1,1]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3,1,1],[1,1,1]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[4,4,3,1,1],[1,1]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[4,4,4,1,1],[3,1]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[5,4,1,1],[1]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[4,4,4,1,1],[2,1]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[5,5,1,1],[1]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[4,4,4,1,1],[1,1]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[2,2,2,2,2,1,1],[1,1,1]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[3,2,2,2,1,1],[1,1]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[3,3,2,2,1,1],[2,1]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[4,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[3,3,2,2,1,1],[1,1]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[3,3,3,2,1,1],[2,2]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[4,3,2,1,1],[2]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[4,4,2,1,1],[3]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[5,2,1,1],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[4,4,2,1,1],[2]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[3,3,3,2,1,1],[2,1]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[4,3,2,1,1],[1]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[3,3,3,2,1,1],[1,1]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[4,4,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[2,2,2,2,2,1,1],[1,1]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[3,2,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[3,3,2,2,1,1],[2]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[4,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[3,3,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[2,2,2,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[3,3,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[3,3,3,2,1,1],[2]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[4,3,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[3,3,3,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[4,4,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[3,3,3,2,1,1],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[3,3,3,3,1,1],[2,2]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[4,3,3,1,1],[2]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[4,4,3,1,1],[3]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[5,3,1,1],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[4,4,3,1,1],[2]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[3,3,3,3,1,1],[2,1]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[4,3,3,1,1],[1]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[3,3,3,3,1,1],[1,1]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[4,4,3,1,1],[1]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[4,4,4,1,1],[3]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[5,4,1,1],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[4,4,4,1,1],[2]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[5,5,1,1],[]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[4,4,4,1,1],[1]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[3,3,3,3,1,1],[2]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[4,3,3,1,1],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[3,3,3,3,1,1],[1]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[4,4,3,1,1],[]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[3,3,3,3,1,1],[]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[4,4,4,1,1],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,2,1],[1,1,1,1]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,2,1],[2,1,1,1]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[4,2,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[3,3,2,2,2,1],[1,1,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2,2,1],[2,2,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[4,3,2,2,1],[2,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[4,4,2,2,1],[3,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[5,2,2,1],[1,1]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[4,4,2,2,1],[2,1,1]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[3,3,3,2,2,1],[2,1,1,1]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[4,3,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[3,3,3,2,2,1],[1,1,1,1]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[4,4,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3,2,1],[2,2,2,1]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[4,3,3,2,1],[2,2,1]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[4,4,3,2,1],[3,2,1]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[5,3,2,1],[2,1]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[4,4,3,2,1],[2,2,1]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[4,4,4,2,1],[3,3,1]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[5,4,2,1],[3,1]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[5,5,2,1],[4,1]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[6,2,1],[1]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[5,5,2,1],[3,1]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[4,4,4,2,1],[3,2,1]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[5,4,2,1],[2,1]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[4,4,4,2,1],[2,2,1]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[5,5,2,1],[2,1]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[3,3,3,3,2,1],[2,2,1,1]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[4,3,3,2,1],[2,1,1]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[4,4,3,2,1],[3,1,1]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[5,3,2,1],[1,1]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[4,4,3,2,1],[2,1,1]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[3,3,3,3,2,1],[2,1,1,1]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[4,3,3,2,1],[1,1,1]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3,2,1],[1,1,1,1]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[4,4,3,2,1],[1,1,1]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[4,4,4,2,1],[3,1,1]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[5,4,2,1],[1,1]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[4,4,4,2,1],[2,1,1]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[5,5,2,1],[1,1]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[4,4,4,2,1],[1,1,1]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,1],[2,2,2,2]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[4,3,3,3,1],[2,2,2]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[4,4,3,3,1],[3,2,2]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[5,3,3,1],[2,2]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[4,4,3,3,1],[2,2,2]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[4,4,4,3,1],[3,3,2]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[5,4,3,1],[3,2]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[5,5,3,1],[4,2]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[6,3,1],[2]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[5,5,3,1],[3,2]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[4,4,4,3,1],[3,2,2]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[5,4,3,1],[2,2]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[4,4,4,3,1],[2,2,2]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[5,5,3,1],[2,2]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[4,4,4,4,1],[3,3,3]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[5,4,4,1],[3,3]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[5,5,4,1],[4,3]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[6,4,1],[3]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[5,5,4,1],[3,3]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[5,5,5,1],[4,4]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[6,5,1],[4]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[6,6,1],[5]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7,1],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[6,6,1],[4]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[5,5,5,1],[4,3]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[6,5,1],[3]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[5,5,5,1],[3,3]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[6,6,1],[3]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[4,4,4,4,1],[3,3,2]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[5,4,4,1],[3,2]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[5,5,4,1],[4,2]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[6,4,1],[2]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[5,5,4,1],[3,2]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[4,4,4,4,1],[3,2,2]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[5,4,4,1],[2,2]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[4,4,4,4,1],[2,2,2]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[5,5,4,1],[2,2]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[5,5,5,1],[4,2]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[6,5,1],[2]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[5,5,5,1],[3,2]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[6,6,1],[2]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[5,5,5,1],[2,2]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[3,3,3,3,3,1],[2,2,2,1]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[4,3,3,3,1],[2,2,1]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[4,4,3,3,1],[3,2,1]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[5,3,3,1],[2,1]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3,1],[2,2,1]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[4,4,4,3,1],[3,3,1]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[5,4,3,1],[3,1]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[5,5,3,1],[4,1]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[6,3,1],[1]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[5,5,3,1],[3,1]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[4,4,4,3,1],[3,2,1]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[5,4,3,1],[2,1]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3,1],[2,2,1]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[5,5,3,1],[2,1]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[3,3,3,3,3,1],[2,2,1,1]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[4,3,3,3,1],[2,1,1]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[4,4,3,3,1],[3,1,1]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[5,3,3,1],[1,1]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3,1],[2,1,1]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[3,3,3,3,3,1],[2,1,1,1]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3,1],[1,1,1]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,1],[1,1,1,1]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3,1],[1,1,1]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[4,4,4,3,1],[3,1,1]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[5,4,3,1],[1,1]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3,1],[2,1,1]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[5,5,3,1],[1,1]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3,1],[1,1,1]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[4,4,4,4,1],[3,3,1]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[5,4,4,1],[3,1]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[5,5,4,1],[4,1]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[6,4,1],[1]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[5,5,4,1],[3,1]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[4,4,4,4,1],[3,2,1]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[5,4,4,1],[2,1]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4,1],[2,2,1]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[5,5,4,1],[2,1]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[5,5,5,1],[4,1]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[6,5,1],[1]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[5,5,5,1],[3,1]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[6,6,1],[1]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[5,5,5,1],[2,1]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4,1],[3,1,1]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[5,4,4,1],[1,1]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4,1],[2,1,1]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[5,5,4,1],[1,1]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4,1],[1,1,1]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[5,5,5,1],[1,1]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,1],[1,1,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,2,1],[1,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,2,1],[2,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[4,2,2,2,1],[1,1]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[3,3,2,2,2,1],[1,1,1]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2,2,1],[2,2,1]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[4,3,2,2,1],[2,1]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[4,4,2,2,1],[3,1]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[5,2,2,1],[1]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[4,4,2,2,1],[2,1]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[3,3,3,2,2,1],[2,1,1]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[4,3,2,2,1],[1,1]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[3,3,3,2,2,1],[1,1,1]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[4,4,2,2,1],[1,1]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3,2,1],[2,2,2]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[4,3,3,2,1],[2,2]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[4,4,3,2,1],[3,2]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[5,3,2,1],[2]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[4,4,3,2,1],[2,2]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[4,4,4,2,1],[3,3]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[5,4,2,1],[3]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[5,5,2,1],[4]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[6,2,1],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[5,5,2,1],[3]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[4,4,4,2,1],[3,2]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[5,4,2,1],[2]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[4,4,4,2,1],[2,2]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[5,5,2,1],[2]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[3,3,3,3,2,1],[2,2,1]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[4,3,3,2,1],[2,1]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[4,4,3,2,1],[3,1]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[5,3,2,1],[1]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[4,4,3,2,1],[2,1]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[3,3,3,3,2,1],[2,1,1]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[4,3,3,2,1],[1,1]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3,2,1],[1,1,1]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[4,4,3,2,1],[1,1]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[4,4,4,2,1],[3,1]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[5,4,2,1],[1]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[4,4,4,2,1],[2,1]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[5,5,2,1],[1]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[4,4,4,2,1],[1,1]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,1],[1,1,1]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[3,2,2,2,2,1],[1,1]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[3,3,2,2,2,1],[2,1]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[4,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[3,3,2,2,2,1],[1,1]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[3,3,3,2,2,1],[2,2]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[4,3,2,2,1],[2]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[4,4,2,2,1],[3]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[5,2,2,1],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[4,4,2,2,1],[2]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[3,3,3,2,2,1],[2,1]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[4,3,2,2,1],[1]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[3,3,3,2,2,1],[1,1]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[4,4,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[2,2,2,2,2,2,1],[1,1]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[3,2,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[3,3,2,2,2,1],[2]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[4,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[3,3,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[2,2,2,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[3,3,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[3,3,3,2,2,1],[2]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[4,3,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[3,3,3,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[4,4,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[3,3,3,2,2,1],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[3,3,3,3,2,1],[2,2]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[4,3,3,2,1],[2]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[4,4,3,2,1],[3]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[5,3,2,1],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[4,4,3,2,1],[2]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[3,3,3,3,2,1],[2,1]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[4,3,3,2,1],[1]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[3,3,3,3,2,1],[1,1]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[4,4,3,2,1],[1]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[4,4,4,2,1],[3]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[5,4,2,1],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[4,4,4,2,1],[2]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[5,5,2,1],[]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[4,4,4,2,1],[1]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[3,3,3,3,2,1],[2]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[4,3,3,2,1],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[3,3,3,3,2,1],[1]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[4,4,3,2,1],[]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[3,3,3,3,2,1],[]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[4,4,4,2,1],[]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[3,3,3,3,3,1],[2,2,2]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[4,3,3,3,1],[2,2]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[4,4,3,3,1],[3,2]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[5,3,3,1],[2]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3,1],[2,2]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[4,4,4,3,1],[3,3]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[5,4,3,1],[3]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[5,5,3,1],[4]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[6,3,1],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[5,5,3,1],[3]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[4,4,4,3,1],[3,2]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[5,4,3,1],[2]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3,1],[2,2]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[5,5,3,1],[2]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[3,3,3,3,3,1],[2,2,1]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[4,3,3,3,1],[2,1]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[4,4,3,3,1],[3,1]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[5,3,3,1],[1]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3,1],[2,1]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[3,3,3,3,3,1],[2,1,1]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3,1],[1,1]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,1],[1,1,1]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3,1],[1,1]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[4,4,4,3,1],[3,1]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[5,4,3,1],[1]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3,1],[2,1]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[5,5,3,1],[1]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3,1],[1,1]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[4,4,4,4,1],[3,3]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[5,4,4,1],[3]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[5,5,4,1],[4]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[6,4,1],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[5,5,4,1],[3]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[4,4,4,4,1],[3,2]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[5,4,4,1],[2]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4,1],[2,2]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[5,5,4,1],[2]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[5,5,5,1],[4]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[6,5,1],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[5,5,5,1],[3]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[6,6,1],[]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[5,5,5,1],[2]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4,1],[3,1]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[5,4,4,1],[1]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4,1],[2,1]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[5,5,4,1],[1]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4,1],[1,1]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[5,5,5,1],[1]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[3,3,3,3,3,1],[2,2]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[4,3,3,3,1],[2]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[4,4,3,3,1],[3]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[5,3,3,1],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[4,4,3,3,1],[2]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[3,3,3,3,3,1],[2,1]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[4,3,3,3,1],[1]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[3,3,3,3,3,1],[1,1]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[4,4,3,3,1],[1]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[4,4,4,3,1],[3]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[5,4,3,1],[]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[4,4,4,3,1],[2]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[5,5,3,1],[]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[4,4,4,3,1],[1]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[3,3,3,3,3,1],[2]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[4,3,3,3,1],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[3,3,3,3,3,1],[1]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[4,4,3,3,1],[]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[3,3,3,3,3,1],[]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[4,4,4,3,1],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[4,4,4,4,1],[3]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[5,4,4,1],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[4,4,4,4,1],[2]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[5,5,4,1],[]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[4,4,4,4,1],[1]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[5,5,5,1],[]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[4,4,4,4,1],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2],[1,1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,2,2],[1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,2,2],[2,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[4,2,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[3,3,2,2,2,2],[1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2,2,2],[2,2,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[4,3,2,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[4,4,2,2,2],[3,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[5,2,2,2],[1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[4,4,2,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[3,3,3,2,2,2],[2,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[4,3,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[3,3,3,2,2,2],[1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[4,4,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3,2,2],[2,2,2,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[4,3,3,2,2],[2,2,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[4,4,3,2,2],[3,2,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[5,3,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[4,4,3,2,2],[2,2,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[4,4,4,2,2],[3,3,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[5,4,2,2],[3,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[5,5,2,2],[4,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[6,2,2],[1,1]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[5,5,2,2],[3,1,1]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[4,4,4,2,2],[3,2,1,1]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[5,4,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[4,4,4,2,2],[2,2,1,1]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[5,5,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[3,3,3,3,2,2],[2,2,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[4,3,3,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[4,4,3,2,2],[3,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[5,3,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[4,4,3,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[3,3,3,3,2,2],[2,1,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[4,3,3,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3,2,2],[1,1,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[4,4,3,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[4,4,4,2,2],[3,1,1,1]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[5,4,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[4,4,4,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[5,5,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[4,4,4,2,2],[1,1,1,1]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,2],[2,2,2,2,1]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[4,3,3,3,2],[2,2,2,1]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[4,4,3,3,2],[3,2,2,1]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[5,3,3,2],[2,2,1]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[4,4,3,3,2],[2,2,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[4,4,4,3,2],[3,3,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[5,4,3,2],[3,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[5,5,3,2],[4,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[6,3,2],[2,1]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[5,5,3,2],[3,2,1]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[4,4,4,3,2],[3,2,2,1]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[5,4,3,2],[2,2,1]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[4,4,4,3,2],[2,2,2,1]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[5,5,3,2],[2,2,1]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[4,4,4,4,2],[3,3,3,1]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[5,4,4,2],[3,3,1]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[5,5,4,2],[4,3,1]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[6,4,2],[3,1]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[5,5,4,2],[3,3,1]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[5,5,5,2],[4,4,1]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[6,5,2],[4,1]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[6,6,2],[5,1]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[7,2],[1]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[6,6,2],[4,1]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[5,5,5,2],[4,3,1]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[6,5,2],[3,1]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[5,5,5,2],[3,3,1]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[6,6,2],[3,1]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[4,4,4,4,2],[3,3,2,1]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[5,4,4,2],[3,2,1]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[5,5,4,2],[4,2,1]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[6,4,2],[2,1]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[5,5,4,2],[3,2,1]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[4,4,4,4,2],[3,2,2,1]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[5,4,4,2],[2,2,1]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[4,4,4,4,2],[2,2,2,1]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[5,5,4,2],[2,2,1]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[5,5,5,2],[4,2,1]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[6,5,2],[2,1]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[5,5,5,2],[3,2,1]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[6,6,2],[2,1]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[5,5,5,2],[2,2,1]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[3,3,3,3,3,2],[2,2,2,1,1]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[4,3,3,3,2],[2,2,1,1]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[4,4,3,3,2],[3,2,1,1]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[5,3,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3,2],[2,2,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[4,4,4,3,2],[3,3,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[5,4,3,2],[3,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[5,5,3,2],[4,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[6,3,2],[1,1]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[5,5,3,2],[3,1,1]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[4,4,4,3,2],[3,2,1,1]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[5,4,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3,2],[2,2,1,1]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[5,5,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[3,3,3,3,3,2],[2,2,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[4,3,3,3,2],[2,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[4,4,3,3,2],[3,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[5,3,3,2],[1,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3,2],[2,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[3,3,3,3,3,2],[2,1,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3,2],[1,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,2],[1,1,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3,2],[1,1,1,1]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[4,4,4,3,2],[3,1,1,1]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[5,4,3,2],[1,1,1]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3,2],[2,1,1,1]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[5,5,3,2],[1,1,1]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3,2],[1,1,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[4,4,4,4,2],[3,3,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[5,4,4,2],[3,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[5,5,4,2],[4,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[6,4,2],[1,1]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[5,5,4,2],[3,1,1]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[4,4,4,4,2],[3,2,1,1]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[5,4,4,2],[2,1,1]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4,2],[2,2,1,1]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[5,5,4,2],[2,1,1]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[5,5,5,2],[4,1,1]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[6,5,2],[1,1]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[5,5,5,2],[3,1,1]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[6,6,2],[1,1]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[5,5,5,2],[2,1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4,2],[3,1,1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[5,4,4,2],[1,1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4,2],[2,1,1,1]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[5,5,4,2],[1,1,1]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4,2],[1,1,1,1]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[5,5,5,2],[1,1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3],[2,2,2,2,2]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[4,3,3,3,3],[2,2,2,2]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[4,4,3,3,3],[3,2,2,2]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[5,3,3,3],[2,2,2]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[4,4,3,3,3],[2,2,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[4,4,4,3,3],[3,3,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[5,4,3,3],[3,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[5,5,3,3],[4,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[6,3,3],[2,2]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[5,5,3,3],[3,2,2]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[4,4,4,3,3],[3,2,2,2]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[5,4,3,3],[2,2,2]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[4,4,4,3,3],[2,2,2,2]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[5,5,3,3],[2,2,2]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[4,4,4,4,3],[3,3,3,2]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[5,4,4,3],[3,3,2]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[5,5,4,3],[4,3,2]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[6,4,3],[3,2]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[5,5,4,3],[3,3,2]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[5,5,5,3],[4,4,2]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[6,5,3],[4,2]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[6,6,3],[5,2]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[7,3],[2]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[6,6,3],[4,2]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[5,5,5,3],[4,3,2]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[6,5,3],[3,2]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[5,5,5,3],[3,3,2]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[6,6,3],[3,2]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[4,4,4,4,3],[3,3,2,2]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[5,4,4,3],[3,2,2]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[5,5,4,3],[4,2,2]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[6,4,3],[2,2]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[5,5,4,3],[3,2,2]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[4,4,4,4,3],[3,2,2,2]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[5,4,4,3],[2,2,2]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[4,4,4,4,3],[2,2,2,2]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[5,5,4,3],[2,2,2]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[5,5,5,3],[4,2,2]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[6,5,3],[2,2]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[5,5,5,3],[3,2,2]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[6,6,3],[2,2]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[5,5,5,3],[2,2,2]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[4,4,4,4,4],[3,3,3,3]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[5,4,4,4],[3,3,3]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[5,5,4,4],[4,3,3]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[6,4,4],[3,3]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[5,5,4,4],[3,3,3]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[5,5,5,4],[4,4,3]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[6,5,4],[4,3]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[6,6,4],[5,3]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[7,4],[3]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[6,6,4],[4,3]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[5,5,5,4],[4,3,3]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[6,5,4],[3,3]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[5,5,5,4],[3,3,3]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[6,6,4],[3,3]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[5,5,5,5],[4,4,4]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[6,5,5],[4,4]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[6,6,5],[5,4]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[7,5],[4]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[6,6,5],[4,4]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[6,6,6],[5,5]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[7,6],[5]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[7,7],[6]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[8],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[7,7],[5]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[6,6,6],[5,4]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[7,6],[4]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[6,6,6],[4,4]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[7,7],[4]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[5,5,5,5],[4,4,3]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[6,5,5],[4,3]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[6,6,5],[5,3]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[7,5],[3]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[6,6,5],[4,3]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[5,5,5,5],[4,3,3]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[6,5,5],[3,3]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[5,5,5,5],[3,3,3]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[6,6,5],[3,3]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[6,6,6],[5,3]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[7,6],[3]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[6,6,6],[4,3]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[7,7],[3]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[6,6,6],[3,3]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[4,4,4,4,4],[3,3,3,2]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[5,4,4,4],[3,3,2]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[5,5,4,4],[4,3,2]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[6,4,4],[3,2]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[5,5,4,4],[3,3,2]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[5,5,5,4],[4,4,2]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[6,5,4],[4,2]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[6,6,4],[5,2]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[7,4],[2]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[6,6,4],[4,2]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[5,5,5,4],[4,3,2]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[6,5,4],[3,2]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4],[3,3,2]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[6,6,4],[3,2]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[4,4,4,4,4],[3,3,2,2]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[5,4,4,4],[3,2,2]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[5,5,4,4],[4,2,2]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[6,4,4],[2,2]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[5,5,4,4],[3,2,2]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[4,4,4,4,4],[3,2,2,2]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[5,4,4,4],[2,2,2]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[4,4,4,4,4],[2,2,2,2]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[5,5,4,4],[2,2,2]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[5,5,5,4],[4,2,2]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[6,5,4],[2,2]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[5,5,5,4],[3,2,2]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[6,6,4],[2,2]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[5,5,5,4],[2,2,2]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[5,5,5,5],[4,4,2]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[6,5,5],[4,2]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[6,6,5],[5,2]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[7,5],[2]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[6,6,5],[4,2]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[5,5,5,5],[4,3,2]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[6,5,5],[3,2]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[5,5,5,5],[3,3,2]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[6,6,5],[3,2]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[6,6,6],[5,2]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[7,6],[2]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[6,6,6],[4,2]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[7,7],[2]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[6,6,6],[3,2]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[5,5,5,5],[4,2,2]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[6,5,5],[2,2]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[5,5,5,5],[3,2,2]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[6,6,5],[2,2]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[5,5,5,5],[2,2,2]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[6,6,6],[2,2]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3],[2,2,2,2,1]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[4,3,3,3,3],[2,2,2,1]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[4,4,3,3,3],[3,2,2,1]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[5,3,3,3],[2,2,1]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[4,4,3,3,3],[2,2,2,1]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[4,4,4,3,3],[3,3,2,1]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[5,4,3,3],[3,2,1]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[5,5,3,3],[4,2,1]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[6,3,3],[2,1]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[5,5,3,3],[3,2,1]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[4,4,4,3,3],[3,2,2,1]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[5,4,3,3],[2,2,1]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[4,4,4,3,3],[2,2,2,1]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[5,5,3,3],[2,2,1]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[4,4,4,4,3],[3,3,3,1]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[5,4,4,3],[3,3,1]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[5,5,4,3],[4,3,1]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[6,4,3],[3,1]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[5,5,4,3],[3,3,1]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[5,5,5,3],[4,4,1]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[6,5,3],[4,1]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[6,6,3],[5,1]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[7,3],[1]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[6,6,3],[4,1]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[5,5,5,3],[4,3,1]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[6,5,3],[3,1]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[5,5,5,3],[3,3,1]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[6,6,3],[3,1]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[4,4,4,4,3],[3,3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[5,4,4,3],[3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[5,5,4,3],[4,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[6,4,3],[2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[5,5,4,3],[3,2,1]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[4,4,4,4,3],[3,2,2,1]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[5,4,4,3],[2,2,1]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[4,4,4,4,3],[2,2,2,1]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[5,5,4,3],[2,2,1]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[5,5,5,3],[4,2,1]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[6,5,3],[2,1]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[5,5,5,3],[3,2,1]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[6,6,3],[2,1]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[5,5,5,3],[2,2,1]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3],[2,2,2,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[4,3,3,3,3],[2,2,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[4,4,3,3,3],[3,2,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[5,3,3,3],[2,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3,3],[2,2,1,1]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[4,4,4,3,3],[3,3,1,1]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[5,4,3,3],[3,1,1]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[5,5,3,3],[4,1,1]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[6,3,3],[1,1]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[5,5,3,3],[3,1,1]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[4,4,4,3,3],[3,2,1,1]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[5,4,3,3],[2,1,1]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3,3],[2,2,1,1]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[5,5,3,3],[2,1,1]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[3,3,3,3,3,3],[2,2,1,1,1]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[4,3,3,3,3],[2,1,1,1]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[4,4,3,3,3],[3,1,1,1]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[5,3,3,3],[1,1,1]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3,3],[2,1,1,1]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[3,3,3,3,3,3],[2,1,1,1,1]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3,3],[1,1,1,1]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3],[1,1,1,1,1]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3,3],[1,1,1,1]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[4,4,4,3,3],[3,1,1,1]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[5,4,3,3],[1,1,1]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3,3],[2,1,1,1]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[5,5,3,3],[1,1,1]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3,3],[1,1,1,1]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[4,4,4,4,3],[3,3,1,1]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[5,4,4,3],[3,1,1]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[5,5,4,3],[4,1,1]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[6,4,3],[1,1]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[5,5,4,3],[3,1,1]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[4,4,4,4,3],[3,2,1,1]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[5,4,4,3],[2,1,1]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4,3],[2,2,1,1]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[5,5,4,3],[2,1,1]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[5,5,5,3],[4,1,1]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[6,5,3],[1,1]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[5,5,5,3],[3,1,1]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[6,6,3],[1,1]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[5,5,5,3],[2,1,1]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4,3],[3,1,1,1]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[5,4,4,3],[1,1,1]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4,3],[2,1,1,1]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[5,5,4,3],[1,1,1]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4,3],[1,1,1,1]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[5,5,5,3],[1,1,1]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[4,4,4,4,4],[3,3,3,1]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[5,4,4,4],[3,3,1]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[5,5,4,4],[4,3,1]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[6,4,4],[3,1]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[5,5,4,4],[3,3,1]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[5,5,5,4],[4,4,1]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[6,5,4],[4,1]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[6,6,4],[5,1]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[7,4],[1]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[6,6,4],[4,1]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[5,5,5,4],[4,3,1]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[6,5,4],[3,1]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4],[3,3,1]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[6,6,4],[3,1]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[4,4,4,4,4],[3,3,2,1]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[5,4,4,4],[3,2,1]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[5,5,4,4],[4,2,1]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[6,4,4],[2,1]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[5,5,4,4],[3,2,1]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[4,4,4,4,4],[3,2,2,1]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[5,4,4,4],[2,2,1]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[4,4,4,4,4],[2,2,2,1]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[5,5,4,4],[2,2,1]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[5,5,5,4],[4,2,1]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[6,5,4],[2,1]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[5,5,5,4],[3,2,1]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[6,6,4],[2,1]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[5,5,5,4],[2,2,1]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[5,5,5,5],[4,4,1]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[6,5,5],[4,1]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[6,6,5],[5,1]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[7,5],[1]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[6,6,5],[4,1]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[5,5,5,5],[4,3,1]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[6,5,5],[3,1]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[5,5,5,5],[3,3,1]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[6,6,5],[3,1]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[6,6,6],[5,1]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[7,6],[1]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[6,6,6],[4,1]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[7,7],[1]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[6,6,6],[3,1]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[5,5,5,5],[4,2,1]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[6,5,5],[2,1]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[5,5,5,5],[3,2,1]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[6,6,5],[2,1]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[5,5,5,5],[2,2,1]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[6,6,6],[2,1]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[4,4,4,4,4],[3,3,1,1]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[5,4,4,4],[3,1,1]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[5,5,4,4],[4,1,1]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[6,4,4],[1,1]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[5,5,4,4],[3,1,1]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[4,4,4,4,4],[3,2,1,1]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[5,4,4,4],[2,1,1]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[4,4,4,4,4],[2,2,1,1]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[5,5,4,4],[2,1,1]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[5,5,5,4],[4,1,1]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[6,5,4],[1,1]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[5,5,5,4],[3,1,1]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[6,6,4],[1,1]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[5,5,5,4],[2,1,1]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[4,4,4,4,4],[3,1,1,1]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[5,4,4,4],[1,1,1]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[4,4,4,4,4],[2,1,1,1]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[5,5,4,4],[1,1,1]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[4,4,4,4,4],[1,1,1,1]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[5,5,5,4],[1,1,1]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[5,5,5,5],[4,1,1]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[6,5,5],[1,1]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[5,5,5,5],[3,1,1]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[6,6,5],[1,1]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[5,5,5,5],[2,1,1]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[6,6,6],[1,1]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5],[1,1,1]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2],[1,1,1,1,1]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,2,2],[1,1,1,1]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,2,2],[2,1,1,1]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[4,2,2,2,2],[1,1,1]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[3,3,2,2,2,2],[1,1,1,1]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2,2,2],[2,2,1,1]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[4,3,2,2,2],[2,1,1]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[4,4,2,2,2],[3,1,1]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[5,2,2,2],[1,1]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[4,4,2,2,2],[2,1,1]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[3,3,3,2,2,2],[2,1,1,1]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[4,3,2,2,2],[1,1,1]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[3,3,3,2,2,2],[1,1,1,1]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[4,4,2,2,2],[1,1,1]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3,2,2],[2,2,2,1]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[4,3,3,2,2],[2,2,1]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[4,4,3,2,2],[3,2,1]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[5,3,2,2],[2,1]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[4,4,3,2,2],[2,2,1]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[4,4,4,2,2],[3,3,1]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[5,4,2,2],[3,1]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[5,5,2,2],[4,1]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[6,2,2],[1]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[5,5,2,2],[3,1]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[4,4,4,2,2],[3,2,1]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[5,4,2,2],[2,1]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[4,4,4,2,2],[2,2,1]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[5,5,2,2],[2,1]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[3,3,3,3,2,2],[2,2,1,1]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[4,3,3,2,2],[2,1,1]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[4,4,3,2,2],[3,1,1]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[5,3,2,2],[1,1]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[4,4,3,2,2],[2,1,1]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[3,3,3,3,2,2],[2,1,1,1]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[4,3,3,2,2],[1,1,1]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3,2,2],[1,1,1,1]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[4,4,3,2,2],[1,1,1]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[4,4,4,2,2],[3,1,1]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[5,4,2,2],[1,1]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[4,4,4,2,2],[2,1,1]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[5,5,2,2],[1,1]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[4,4,4,2,2],[1,1,1]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,2],[2,2,2,2]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[4,3,3,3,2],[2,2,2]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[4,4,3,3,2],[3,2,2]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[5,3,3,2],[2,2]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[4,4,3,3,2],[2,2,2]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[4,4,4,3,2],[3,3,2]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[5,4,3,2],[3,2]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[5,5,3,2],[4,2]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[6,3,2],[2]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[5,5,3,2],[3,2]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[4,4,4,3,2],[3,2,2]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[5,4,3,2],[2,2]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[4,4,4,3,2],[2,2,2]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[5,5,3,2],[2,2]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[4,4,4,4,2],[3,3,3]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[5,4,4,2],[3,3]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[5,5,4,2],[4,3]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[6,4,2],[3]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[5,5,4,2],[3,3]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[5,5,5,2],[4,4]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[6,5,2],[4]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[6,6,2],[5]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7,2],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[6,6,2],[4]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[5,5,5,2],[4,3]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[6,5,2],[3]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[5,5,5,2],[3,3]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[6,6,2],[3]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[4,4,4,4,2],[3,3,2]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[5,4,4,2],[3,2]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[5,5,4,2],[4,2]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[6,4,2],[2]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[5,5,4,2],[3,2]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[4,4,4,4,2],[3,2,2]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[[5,4,4,2],[2,2]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[4,4,4,4,2],[2,2,2]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[5,5,4,2],[2,2]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[5,5,5,2],[4,2]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[6,5,2],[2]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[5,5,5,2],[3,2]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[6,6,2],[2]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[5,5,5,2],[2,2]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[3,3,3,3,3,2],[2,2,2,1]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[4,3,3,3,2],[2,2,1]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[4,4,3,3,2],[3,2,1]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[5,3,3,2],[2,1]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3,2],[2,2,1]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[4,4,4,3,2],[3,3,1]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[5,4,3,2],[3,1]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[5,5,3,2],[4,1]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[6,3,2],[1]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[5,5,3,2],[3,1]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[4,4,4,3,2],[3,2,1]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[5,4,3,2],[2,1]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3,2],[2,2,1]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[[5,5,3,2],[2,1]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[3,3,3,3,3,2],[2,2,1,1]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[4,3,3,3,2],[2,1,1]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[4,4,3,3,2],[3,1,1]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[[5,3,3,2],[1,1]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3,2],[2,1,1]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[3,3,3,3,3,2],[2,1,1,1]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3,2],[1,1,1]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,2],[1,1,1,1]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3,2],[1,1,1]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[4,4,4,3,2],[3,1,1]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[5,4,3,2],[1,1]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3,2],[2,1,1]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[5,5,3,2],[1,1]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3,2],[1,1,1]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[4,4,4,4,2],[3,3,1]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[5,4,4,2],[3,1]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[5,5,4,2],[4,1]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[6,4,2],[1]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[5,5,4,2],[3,1]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[4,4,4,4,2],[3,2,1]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[5,4,4,2],[2,1]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4,2],[2,2,1]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[[5,5,4,2],[2,1]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[5,5,5,2],[4,1]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[6,5,2],[1]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[5,5,5,2],[3,1]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[[6,6,2],[1]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[[5,5,5,2],[2,1]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4,2],[3,1,1]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[[5,4,4,2],[1,1]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4,2],[2,1,1]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[[5,5,4,2],[1,1]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4,2],[1,1,1]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[5,5,5,2],[1,1]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2],[1,1,1,1]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,2,2],[1,1,1]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,2,2],[2,1,1]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[4,2,2,2,2],[1,1]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[3,3,2,2,2,2],[1,1,1]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2,2,2],[2,2,1]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[4,3,2,2,2],[2,1]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[4,4,2,2,2],[3,1]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[5,2,2,2],[1]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[4,4,2,2,2],[2,1]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[3,3,3,2,2,2],[2,1,1]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[4,3,2,2,2],[1,1]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[3,3,3,2,2,2],[1,1,1]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[4,4,2,2,2],[1,1]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3,2,2],[2,2,2]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[4,3,3,2,2],[2,2]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[4,4,3,2,2],[3,2]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[5,3,2,2],[2]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[4,4,3,2,2],[2,2]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[4,4,4,2,2],[3,3]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[5,4,2,2],[3]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[5,5,2,2],[4]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[6,2,2],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[5,5,2,2],[3]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[4,4,4,2,2],[3,2]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[5,4,2,2],[2]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[4,4,4,2,2],[2,2]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[[5,5,2,2],[2]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[3,3,3,3,2,2],[2,2,1]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[4,3,3,2,2],[2,1]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[4,4,3,2,2],[3,1]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[5,3,2,2],[1]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[4,4,3,2,2],[2,1]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[3,3,3,3,2,2],[2,1,1]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[4,3,3,2,2],[1,1]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3,2,2],[1,1,1]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[4,4,3,2,2],[1,1]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[4,4,4,2,2],[3,1]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[5,4,2,2],[1]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[[4,4,4,2,2],[2,1]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[[5,5,2,2],[1]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[4,4,4,2,2],[1,1]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2],[1,1,1]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[3,2,2,2,2,2],[1,1]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[3,3,2,2,2,2],[2,1]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[4,2,2,2,2],[1]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[3,3,2,2,2,2],[1,1]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[3,3,3,2,2,2],[2,2]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[4,3,2,2,2],[2]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[4,4,2,2,2],[3]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[5,2,2,2],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[4,4,2,2,2],[2]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[3,3,3,2,2,2],[2,1]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[4,3,2,2,2],[1]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[[3,3,3,2,2,2],[1,1]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[4,4,2,2,2],[1]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[2,2,2,2,2,2,2],[1,1]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[3,2,2,2,2,2],[1]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[3,3,2,2,2,2],[2]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[4,2,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[3,3,2,2,2,2],[1]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[2,2,2,2,2,2,2],[1]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[3,3,2,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[3,3,3,2,2,2],[2]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[4,3,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[3,3,3,2,2,2],[1]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[4,4,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[3,3,3,2,2,2],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[3,3,3,3,2,2],[2,2]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[4,3,3,2,2],[2]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[4,4,3,2,2],[3]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[5,3,2,2],[]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[[4,4,3,2,2],[2]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[3,3,3,3,2,2],[2,1]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[4,3,3,2,2],[1]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[3,3,3,3,2,2],[1,1]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[4,4,3,2,2],[1]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[4,4,4,2,2],[3]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[5,4,2,2],[]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[[4,4,4,2,2],[2]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[5,5,2,2],[]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[4,4,4,2,2],[1]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[3,3,3,3,2,2],[2]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[4,3,3,2,2],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[[3,3,3,3,2,2],[1]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[[4,4,3,2,2],[]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[3,3,3,3,2,2],[]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[[4,4,4,2,2],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[3,3,3,3,3,2],[2,2,2]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[4,3,3,3,2],[2,2]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[4,4,3,3,2],[3,2]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[5,3,3,2],[2]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3,2],[2,2]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[4,4,4,3,2],[3,3]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[5,4,3,2],[3]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[5,5,3,2],[4]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[6,3,2],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[5,5,3,2],[3]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[4,4,4,3,2],[3,2]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[5,4,3,2],[2]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3,2],[2,2]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[[5,5,3,2],[2]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[3,3,3,3,3,2],[2,2,1]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[4,3,3,3,2],[2,1]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[4,4,3,3,2],[3,1]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[[5,3,3,2],[1]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3,2],[2,1]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[3,3,3,3,3,2],[2,1,1]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3,2],[1,1]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,2],[1,1,1]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3,2],[1,1]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[4,4,4,3,2],[3,1]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[5,4,3,2],[1]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3,2],[2,1]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[[5,5,3,2],[1]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3,2],[1,1]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[4,4,4,4,2],[3,3]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[5,4,4,2],[3]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[5,5,4,2],[4]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[6,4,2],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[[5,5,4,2],[3]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[4,4,4,4,2],[3,2]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[5,4,4,2],[2]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4,2],[2,2]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[5,5,4,2],[2]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[5,5,5,2],[4]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[6,5,2],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[[5,5,5,2],[3]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[6,6,2],[]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[5,5,5,2],[2]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4,2],[3,1]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[5,4,4,2],[1]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4,2],[2,1]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[5,5,4,2],[1]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4,2],[1,1]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[[5,5,5,2],[1]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[3,3,3,3,3,2],[2,2]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[4,3,3,3,2],[2]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[4,4,3,3,2],[3]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[5,3,3,2],[]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[[4,4,3,3,2],[2]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[3,3,3,3,3,2],[2,1]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[[4,3,3,3,2],[1]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[3,3,3,3,3,2],[1,1]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[4,4,3,3,2],[1]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[4,4,4,3,2],[3]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[5,4,3,2],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[4,4,4,3,2],[2]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[5,5,3,2],[]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[[4,4,4,3,2],[1]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[3,3,3,3,3,2],[2]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[4,3,3,3,2],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[3,3,3,3,3,2],[1]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[4,4,3,3,2],[]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[3,3,3,3,3,2],[]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[4,4,4,3,2],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[4,4,4,4,2],[3]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[5,4,4,2],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[4,4,4,4,2],[2]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[[5,5,4,2],[]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[4,4,4,4,2],[1]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[5,5,5,2],[]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[4,4,4,4,2],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3],[2,2,2,2]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[4,3,3,3,3],[2,2,2]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[4,4,3,3,3],[3,2,2]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[5,3,3,3],[2,2]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[4,4,3,3,3],[2,2,2]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[4,4,4,3,3],[3,3,2]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[5,4,3,3],[3,2]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[5,5,3,3],[4,2]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[6,3,3],[2]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[5,5,3,3],[3,2]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[4,4,4,3,3],[3,2,2]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[[5,4,3,3],[2,2]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[4,4,4,3,3],[2,2,2]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[5,5,3,3],[2,2]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[4,4,4,4,3],[3,3,3]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[5,4,4,3],[3,3]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[5,5,4,3],[4,3]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[6,4,3],[3]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[[5,5,4,3],[3,3]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[5,5,5,3],[4,4]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[6,5,3],[4]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[6,6,3],[5]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[7,3],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[[6,6,3],[4]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[5,5,5,3],[4,3]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[6,5,3],[3]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[5,5,5,3],[3,3]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[[6,6,3],[3]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[4,4,4,4,3],[3,3,2]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[5,4,4,3],[3,2]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[5,5,4,3],[4,2]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[6,4,3],[2]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[5,5,4,3],[3,2]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[4,4,4,4,3],[3,2,2]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[5,4,4,3],[2,2]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[[4,4,4,4,3],[2,2,2]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[5,5,4,3],[2,2]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[5,5,5,3],[4,2]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[6,5,3],[2]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[5,5,5,3],[3,2]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[6,6,3],[2]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[5,5,5,3],[2,2]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3],[2,2,2,1]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[4,3,3,3,3],[2,2,1]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[4,4,3,3,3],[3,2,1]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[5,3,3,3],[2,1]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3,3],[2,2,1]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[4,4,4,3,3],[3,3,1]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[5,4,3,3],[3,1]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[5,5,3,3],[4,1]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[[6,3,3],[1]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[5,5,3,3],[3,1]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[4,4,4,3,3],[3,2,1]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[5,4,3,3],[2,1]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3,3],[2,2,1]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[[5,5,3,3],[2,1]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[3,3,3,3,3,3],[2,2,1,1]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[4,3,3,3,3],[2,1,1]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[4,4,3,3,3],[3,1,1]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[[5,3,3,3],[1,1]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3,3],[2,1,1]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[3,3,3,3,3,3],[2,1,1,1]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3,3],[1,1,1]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3],[1,1,1,1]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3,3],[1,1,1]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[4,4,4,3,3],[3,1,1]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[5,4,3,3],[1,1]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3,3],[2,1,1]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[[5,5,3,3],[1,1]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3,3],[1,1,1]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[4,4,4,4,3],[3,3,1]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[5,4,4,3],[3,1]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[5,5,4,3],[4,1]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[[6,4,3],[1]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[5,5,4,3],[3,1]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[4,4,4,4,3],[3,2,1]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[5,4,4,3],[2,1]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4,3],[2,2,1]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[5,5,4,3],[2,1]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[5,5,5,3],[4,1]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[6,5,3],[1]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[5,5,5,3],[3,1]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[6,6,3],[1]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[5,5,5,3],[2,1]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4,3],[3,1,1]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[5,4,4,3],[1,1]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4,3],[2,1,1]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[[5,5,4,3],[1,1]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4,3],[1,1,1]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[[5,5,5,3],[1,1]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[4,4,4,4,4],[3,3,3]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[5,4,4,4],[3,3]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[5,5,4,4],[4,3]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[6,4,4],[3]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[5,5,4,4],[3,3]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[5,5,5,4],[4,4]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[6,5,4],[4]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[6,6,4],[5]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[7,4],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[[6,6,4],[4]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[5,5,5,4],[4,3]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[[6,5,4],[3]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4],[3,3]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[6,6,4],[3]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[4,4,4,4,4],[3,3,2]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[5,4,4,4],[3,2]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[5,5,4,4],[4,2]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[[6,4,4],[2]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[5,5,4,4],[3,2]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[4,4,4,4,4],[3,2,2]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[[5,4,4,4],[2,2]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[4,4,4,4,4],[2,2,2]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[[5,5,4,4],[2,2]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[5,5,5,4],[4,2]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[[6,5,4],[2]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[5,5,5,4],[3,2]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[6,6,4],[2]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[5,5,5,4],[2,2]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[5,5,5,5],[4,4]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[6,5,5],[4]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[6,6,5],[5]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[7,5],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[6,6,5],[4]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[5,5,5,5],[4,3]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[6,5,5],[3]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[5,5,5,5],[3,3]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[6,6,5],[3]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[6,6,6],[5]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[7,6],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[6,6,6],[4]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[7,7],[]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[6,6,6],[3]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[5,5,5,5],[4,2]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[6,5,5],[2]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[5,5,5,5],[3,2]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[6,6,5],[2]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[5,5,5,5],[2,2]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[6,6,6],[2]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[4,4,4,4,4],[3,3,1]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[5,4,4,4],[3,1]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[5,5,4,4],[4,1]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[6,4,4],[1]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[5,5,4,4],[3,1]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[4,4,4,4,4],[3,2,1]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[5,4,4,4],[2,1]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[4,4,4,4,4],[2,2,1]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[5,5,4,4],[2,1]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[5,5,5,4],[4,1]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[6,5,4],[1]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[5,5,5,4],[3,1]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[6,6,4],[1]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[5,5,5,4],[2,1]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[4,4,4,4,4],[3,1,1]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[5,4,4,4],[1,1]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[4,4,4,4,4],[2,1,1]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[5,5,4,4],[1,1]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[4,4,4,4,4],[1,1,1]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[5,5,5,4],[1,1]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[5,5,5,5],[4,1]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[6,5,5],[1]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[[5,5,5,5],[3,1]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[6,6,5],[1]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[[5,5,5,5],[2,1]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[6,6,6],[1]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5],[1,1]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3],[2,2,2]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[4,3,3,3,3],[2,2]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[4,4,3,3,3],[3,2]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[5,3,3,3],[2]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3,3],[2,2]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[4,4,4,3,3],[3,3]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[5,4,3,3],[3]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[5,5,3,3],[4]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[6,3,3],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[5,5,3,3],[3]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[4,4,4,3,3],[3,2]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[[5,4,3,3],[2]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3,3],[2,2]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[[5,5,3,3],[2]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[3,3,3,3,3,3],[2,2,1]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[4,3,3,3,3],[2,1]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[4,4,3,3,3],[3,1]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[5,3,3,3],[1]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3,3],[2,1]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[3,3,3,3,3,3],[2,1,1]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3,3],[1,1]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3],[1,1,1]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3,3],[1,1]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[4,4,4,3,3],[3,1]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[[5,4,3,3],[1]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3,3],[2,1]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[5,5,3,3],[1]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3,3],[1,1]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[4,4,4,4,3],[3,3]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[5,4,4,3],[3]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[5,5,4,3],[4]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[6,4,3],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[5,5,4,3],[3]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[4,4,4,4,3],[3,2]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[5,4,4,3],[2]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4,3],[2,2]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[5,5,4,3],[2]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[5,5,5,3],[4]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[6,5,3],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[5,5,5,3],[3]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[6,6,3],[]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[5,5,5,3],[2]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4,3],[3,1]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[5,4,4,3],[1]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4,3],[2,1]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[5,5,4,3],[1]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4,3],[1,1]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[[5,5,5,3],[1]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[3,3,3,3,3,3],[2,2]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[4,3,3,3,3],[2]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[4,4,3,3,3],[3]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[5,3,3,3],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[4,4,3,3,3],[2]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[3,3,3,3,3,3],[2,1]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[4,3,3,3,3],[1]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3],[1,1]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[4,4,3,3,3],[1]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[4,4,4,3,3],[3]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[5,4,3,3],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[4,4,4,3,3],[2]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[5,5,3,3],[]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[4,4,4,3,3],[1]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[3,3,3,3,3,3],[2]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[4,3,3,3,3],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[3,3,3,3,3,3],[1]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[4,4,3,3,3],[]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[3,3,3,3,3,3],[]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[4,4,4,3,3],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[4,4,4,4,3],[3]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[5,4,4,3],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[4,4,4,4,3],[2]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[5,5,4,3],[]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[4,4,4,4,3],[1]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[5,5,5,3],[]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[4,4,4,4,3],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[4,4,4,4,4],[3,3]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[5,4,4,4],[3]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[5,5,4,4],[4]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[6,4,4],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[5,5,4,4],[3]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[4,4,4,4,4],[3,2]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[5,4,4,4],[2]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[4,4,4,4,4],[2,2]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[5,5,4,4],[2]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[5,5,5,4],[4]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[6,5,4],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[[5,5,5,4],[3]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[6,6,4],[]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[5,5,5,4],[2]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[4,4,4,4,4],[3,1]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[5,4,4,4],[1]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[4,4,4,4,4],[2,1]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[5,5,4,4],[1]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[4,4,4,4,4],[1,1]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[5,5,5,4],[1]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[5,5,5,5],[4]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[6,5,5],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[5,5,5,5],[3]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[6,6,5],[]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[5,5,5,5],[2]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[6,6,6],[]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5],[1]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[4,4,4,4,4],[3]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[5,4,4,4],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[4,4,4,4,4],[2]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[5,5,4,4],[]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[4,4,4,4,4],[1]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[5,5,5,4],[]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[4,4,4,4,4],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[5,5,5,5],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[5,5,5,5,5],[4]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[5,5,5,5,1],[]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[4,4,4,4,4,4],[3]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[4,4,4,4,4,1],[]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[5,5,5,5,4],[4]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[5,5,5,5,5],[4,1]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[5,5,5,4,1],[]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5,1],[1]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[6,6,6,6],[5]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[[4,4,4,4,4,3],[3]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[4,4,4,4,4,1],[1]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[6,6,6,1],[]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[[5,5,5,5,4],[4,1]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[5,5,4,4,1],[]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[[4,4,4,4,3,3],[3]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[4,4,4,4,4,1],[2]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[4,4,4,4,4,1],[1,1]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[[5,5,4,4,4],[4]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[3,3,3,3,3,3,3],[2]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[5,5,5,5,5],[4,1,1,1]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[5,4,4,4,4],[3]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[5,4,4,4,1],[]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[3,3,3,3,3,3,1],[]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5,2],[1,1,1,1]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5,1],[1,1,1]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[4,4,4,4,4,4],[3,3]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[4,4,4,4,4,1],[3]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[[6,5,5,5],[4]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[6,6,6,2],[1,1,1]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[4,4,4,4,1,1],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[[5,4,4,4,4],[3,1]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[[5,4,4,4,3],[3]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[5,5,5,5,2],[2,1,1,1]]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[5,5,5,4,2],[1,1,1,1]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[6,6,6,6],[5,3]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[6,6,3,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[9],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[8,8],[6]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[8,7],[5]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[7,7,7],[5,5]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[8,8],[5]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[8,6],[4]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[7,7,6],[5,4]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[7,6,6],[4,4]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[6,6,6,6],[4,4,4]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[7,7,6],[4,4]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[8,7],[4]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[7,7,7],[5,4]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[8,8],[4]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[7,7,7],[4,4]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[8,5],[3]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[7,7,5],[4,3]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[5,5,5,5,5],[3,3,3,3]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[6,6,6,6],[4,4,3]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[7,7,7],[5,3]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[8,8],[3]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[6,6,6,6],[4,3,3]]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[7,7,7],[3,3]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[8,4],[2]]
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[6,6,6,4],[3,3,2]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[6,4,4,4],[2,2,2]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[4,4,4,4,4,4],[2,2,2,2,2]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[5,5,5,5,5],[3,3,3,2]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[6,6,6,6],[4,4,2]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[8,8],[2]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[5,5,5,5,5],[3,3,2,2]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[6,6,6,6],[2,2,2]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[8,3],[1]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[6,5,4,3],[3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[[6,6,4,3],[3,2,1]]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[6,6,6,3],[2,2,1]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[7,3,3],[1,1]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3,3,3],[1,1,1,1,1]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3,3],[1,1,1,1,1,1]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[8,4],[1]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[4,4,4,4,4,4],[2,2,2,2,1]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[5,5,5,5,5],[3,3,3,1]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[8,8],[1]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[[6,6,4,4],[3,1,1]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[4,4,4,4,4,4],[2,2,2,1,1]]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5,4],[1,1,1,1]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[7,7,7],[1,1]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[6,6,6,6],[2,1,1]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[6,5,5,5],[1,1,1]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[5,5,5,5,5],[2,1,1,1]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[6,6,6,5],[1,1,1]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[5,5,5,5,5],[1,1,1,1]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[6,6,6,6],[1,1,1]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[8,2],[]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5,2],[1,1,1]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7,2,2],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[6,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[5,5,2,2,2],[]]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[6,6,6,2],[3]]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3,3,2],[1,1]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[4,4,4,4,4,2],[2]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[5,5,5,5,2],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[8,3],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[7,3,3],[1]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3,3],[1,1,1,1,1]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[7,7,3],[1]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[8,4],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[4,4,4,4,4,4],[2,2,2,2]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[8,5],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[5,5,5,5,5],[3,3,3]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[8,6],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[7,7,6],[4]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[8,7],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[8,8],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[7,7,7],[4]]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[6,6,6,5],[3,1]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[6,6,5,5],[1,1]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[6,6,6,6],[1,1]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[[5,5,5,3,3],[2,2]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3,3],[1,1,1,1]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[[6,6,6,3],[4]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[[7,7,3],[]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[4,4,4,3,3,3],[]]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[[5,5,5,4,3],[1]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5,3],[1]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[[5,4,4,4,3],[]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[[4,4,4,4,4,3],[1]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[4,4,4,4,4,3],[]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[[5,5,5,5,3],[]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[[5,5,5,4,4],[2,2]]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[[6,6,6,4],[2]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[[4,4,4,4,4,4],[1,1,1]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[[6,6,6,4],[1]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[[6,6,6,5],[2]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[[7,6,6],[]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[6,6,6,6],[2]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[[6,5,5,5],[1]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[[6,6,6,5],[1]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[5,5,5,5,5],[1,1]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[6,6,6,6],[1]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[[5,4,4,4,4],[1]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[[5,5,5,4,4],[1]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[6,5,5,4],[]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[[5,5,5,5,4],[2]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[[6,6,6,4],[]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5,4],[1]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[[5,4,4,4,4],[]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[4,4,4,4,4,4],[]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[5,5,5,5,4],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[6,5,5,5],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[[5,5,5,5,5],[3]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[[6,6,5,5],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[[5,5,5,5,5],[2]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[6,6,6,5],[]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[5,5,5,5,5],[1]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[6,6,6,6],[]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[5,5,5,5,5],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[3,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[4,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[5,1,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[6,1,1,1],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7,1,1],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[8,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[2,2,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[3,2,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[4,2,1,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[5,2,1,1,1],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[6,2,1,1],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7,2,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[2,2,2,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[3,3,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[2,2,2,2,1,1,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[4,2,2,2,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[3,3,3,1,1,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,2,1,1],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,2,2,1],[]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[4,4,4,1,1,1],[]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[7,7,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[2,2,1,1,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[2,2,2,1,1,1,1,1],[1,1]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[3,2,1,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[2,2,2,1,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[2,2,2,2,1,1,1,1],[1,1,1]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[3,3,2,1,1,1,1],[2,1]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[3,2,2,1,1,1,1],[1]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,1,1,1],[1,1,1,1]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[4,3,2,1,1,1],[2,1]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,1,1],[1,1,1,1,1]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[4,3,2,2,1,1],[2,1]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,1],[1,1,1,1,1,1]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,2,2,1],[1,1,1,1,1]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,2,1],[2,2,2,2,1]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[5,4,3,2,1],[3,2,1]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[5,5,5,2,1],[1,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,1],[1,1,1,1,1]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[5,5,3,3,1],[2,2]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[5,4,4,4,1],[3]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,2,2,2],[1,1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,2,2,2],[2,1,1,1,1,1]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3,2],[2,2,2,2,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[5,5,4,3,2],[4,3,2,1]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[5,5,5,5,2],[4,1,1,1]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[5,4,3,2,2],[3,2,1]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[5,5,5,2,2],[1,1,1]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3,3],[2,2,2,2,2]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[5,5,5,3,3],[2,2,2]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3,3],[2,2,2,2]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[5,5,3,3,3],[2,2]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[4,4,4,4,4,4],[3,3,3]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[[5,5,4,4,4],[3,3]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3,3],[2,2,2,2,2,2]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[4,4,4,4,4,4],[3,3,3,3,3]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[5,5,5,5,5],[4,4,4,4]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[6,6,6,6],[5,5,5]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[7,7,7],[6,6]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[8,8],[7]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3,3],[2,2,2,2,2,1]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[4,4,4,4,4,4],[3,3,3,3,2]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[5,5,5,5,5],[4,4,4,3]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[6,6,6,6],[5,5,4]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[7,7,7],[6,5]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[4,2,2,2,2,2],[1,1,1,1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[5,3,3,3,3],[2,2,2,2]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[4,2,2,2,2,1],[1,1,1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[4,3,3,3,3,3],[2,2,2,2,2]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[2,2,2,2,2,2,2,2],[1]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[2,2,2,2,2,2,2,2],[1,1]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,2],[1,1,1]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,2],[1,1,1,1]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[[5,5,5,4,4],[4,4]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[[4,4,4,4,3,3],[3,3,3]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[4,4,4,4,4,3],[3,3,3,3]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3,2],[2,2,2,2,2]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[3,2,2,2,2,2,2],[1]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3,2],[1,1,1,1,1,1]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[3,3,3,3,3,3,3],[2,1,1,1,1,1]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[6,6,6,3],[2,2,2]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[4,4,4,2,2,2],[1,1,1]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[6,6,4,4],[3,3]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3,3,3],[2,2]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[4,4,4,4,4,1],[3,3,3,3]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,1,1],[2,2,2,2]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[6,5,5,5],[4,4,4]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[4,4,4,4,4,2],[3,3,3,3,1]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3,1],[1,1,1,1]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[7,7,2],[6]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[7,7,1],[5]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[8,7],[6]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[8,2],[1]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[7,7,6],[5,5]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[7,7,5],[4,4]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[7,7,4],[3,3]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[7,7,3],[2,2]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[7,7,2],[1,1]]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[6,6,6,2],[2,2,1]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[5,4,4,4,2],[3]]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3,2,2],[1,1,1,1]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[5,5,4,4,4],[3,3,1]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[6,6,3,3],[2,2]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[[6,4,4,4],[3]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[[4,4,4,3,3,3],[2,2,2]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4,2,2],[1,1,1,1]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[5,2,2,1,1],[1,1]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[[6,5,4,4],[4]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[5,5,5,5,2],[3,1,1,1]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[[4,4,3,3,3,3],[2,2,1]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[5,5,4,2,2],[1,1,1]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[4,4,1,1,1,1],[3]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[3,3,3,1,1,1,1],[2,2]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[6,2,2,2],[1,1,1]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[4,3,1,1,1,1],[2]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[7,7,6],[6,5]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[6,6,6,5],[5,5,4]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[5,5,5,5,4],[4,4,4,3]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[4,4,4,4,4,3],[3,3,3,3,2]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[5,5,4,3,3],[4,3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[5,5,4,4,3],[4,3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[5,5,5,4,3],[4,3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[6,5,4,3],[4,2,1]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[6,5,4,3],[4,3,1]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[6,5,4,3],[4,3,2]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[5,5,4,4,4],[4,3,2,1]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[5,5,5,5,3],[4,3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[5,5,5,4,3],[4,4,2,1]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[6,5,4,3],[3,3,1]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[6,5,4,3],[4,2,2]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[5,4,3,2,1],[3,2]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[7,4,4],[3,3]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[7,7,7],[6]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[3,3,3,2,2,2,2],[2]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[4,4,3,3,3,3],[3,2,2,2,2]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[5,5,5,1,1],[1,1]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[4,4,4,1,1,1],[1,1]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[4,4,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[3,3,1,1,1,1,1],[1]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[7,2,2],[1]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[7,3,3],[2]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[7,4,4],[3]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[7,5,5],[4]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[7,6,6],[5]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[4,4,4,4,4,4],[3,3,2,2,2]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[5,5,5,4,4],[4,4,3,3]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[5,5,5,5,5,5],[4]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[5,5,5,5,5,1],[]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[6,6,6,6,6],[5]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[6,6,6,6,1],[]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[[5,5,5,5,5,4],[4]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[5,5,5,5,5,1],[1]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[[4,4,4,4,4,4,4],[3]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[4,4,4,4,4,4,1],[]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[7,7,7,7],[6]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[7,7,7,1],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[6,5,5,5,5],[4]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[6,6,6,6,2],[1,1,1,1]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[[5,5,5,5,5,5],[4,4]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[5,5,5,5,5,1],[4]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[[5,4,4,4,4,4],[3]]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[5,5,5,5,5,2],[1,1,1,1,1]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[5,5,5,5,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[3,1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[4,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[5,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[6,1,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7,1,1,1],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[8,1,1],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[9,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[10],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[2,2,1,1,1,1,1,1,1],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[9,2],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[3,3,1,1,1,1,1,1],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[9,3],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[9,4],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[3,3,3,1,1,1,1,1],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[6,2,2,2,2],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[9,5],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[9,6],[]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[4,4,4,1,1,1,1],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[9,7],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,2,2,2,1],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2,2,2,2,2],[]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[8,8,1],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[9,8],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[2,2,1,1,1,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[2,2,2,1,1,1,1,1,1],[1,1]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[3,2,1,1,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[2,2,2,2,1,1,1,1,1],[1,1,1]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,1,1,1,1],[1,1,1,1]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[4,3,2,1,1,1,1],[2,1]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,1,1,1],[1,1,1,1,1]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[4,4,4,4,1,1,1],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,1,1],[1,1,1,1,1,1]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[5,4,3,2,1,1],[3,2,1]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,2,1],[1,1,1,1,1,1,1]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[5,5,4,3,2,1],[4,3,2,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[6,5,4,3,2],[4,3,2,1]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5,2,2],[1,1,1,1]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3,3,3],[2,2,2,2,2,2]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[6,6,6,3,3],[2,2,2]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3,3,3],[2,2,2,2,2]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[5,5,5,3,3,3],[2,2,2]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[4,4,4,4,4,4,4],[3,3,3,3]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[6,6,4,4,4],[3,3]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[[4,4,4,4,4,4,4],[3,3,3]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[[5,5,4,4,4,4],[3,3]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[4,4,4,4,4,4,4],[3,3,3,3,3,3]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[5,5,5,5,5,5],[4,4,4,4,4]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[6,6,6,6,6],[5,5,5,5]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[7,7,7,7],[6,6,6]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[8,8,8],[7,7]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[9,9],[8]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[4,4,4,3,3,3,3],[]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[4,4,4,4,4,4,4],[1,1,1,1]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[8,8,8],[5]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[8,8,3],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[9,9],[7]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6],[1]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[[6,6,6,6,5],[]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[[5,5,5,5,4,4],[]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[[5,5,5,5,5,5],[1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[4,2,2,2,2,2,2],[1,1,1,1,1,1]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6],[1,1,1,1]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[6,5,5,5,5],[]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[[7,6,6,6],[]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[5,5,5,5,5,5],[]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[[5,5,5,5,5,4],[]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6],[1,1]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[5,5,5,5,5,3],[]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6],[1,1,1]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[5,5,5,5,5,2],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3,3,3],[1,1,1,1,1,1,1]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[3,3,3,1,1,1,1,1],[2,2]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[4,4,1,1,1,1,1],[3]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[7,3,3,3],[1,1,1]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[8,4,4],[2,2]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[9,5],[3]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[3,3,3,3,3,3,3,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[9,9],[6]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[9,9],[5]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[9,9],[4]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[9,9],[3]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[9,9],[2]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[9,9],[1]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[9,9],[]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[[5,5,5,5,5,5],[3]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[[6,6,5,5,5],[]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[[5,5,5,5,5,5],[2]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[[6,6,6,5,5],[]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[[5,5,5,5,5,5],[1]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3,1,1],[2,2,2,2,2]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[4,4,4,4,4,4,1],[3,3,3,3,3]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[6,6,6,6,6],[4,4,4,4]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[7,6,6,6],[4,4,4]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[8,6,6],[4,4]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[9,6],[4]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[6,5,4,3,3],[4,3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[6,5,4,4,3],[4,3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[6,5,5,4,3],[4,3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[6,6,5,4,3],[4,3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[6,6,5,4,3],[5,3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[6,6,5,4,3],[5,4,2,1]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[6,6,5,4,3],[5,4,3,1]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[6,6,5,4,3],[5,4,3,2]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[7,7,7,7],[2,2,2]]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[7,7,7,7],[3,3,3]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[8,8,8],[4,4]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[8,8,8],[5,5]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[8,8,8],[6,6]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[7,7,7,7],[5,5,5]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[5,5,5,5,5,5],[3,3,3,3,3]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[4,4,4,4,4,4,4],[2,2,2,2,2,2]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,2,2,2,2],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[8,8,8],[6,5]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[7,7,7,7],[5,5,4]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[6,6,6,6,6],[4,4,4,3]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[5,5,5,5,5,5],[3,3,3,3,2]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[4,4,4,4,4,4,4],[2,2,2,2,2,1]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3,3,3],[1,1,1,1,1,1]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[[6,6,6,6,5],[1]]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[[6,6,6,6,5],[2]]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5,4,4],[1,1]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[[6,6,6,4,4],[2]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[[6,6,6,4,4],[2,2]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[[6,6,6,4,4],[3,3]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[5,5,5,5,3,1],[2,2,1,1]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[5,5,4,4,3,1],[1,1,1,1]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[7,7,5,1],[3,1]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[5,5,5,5,5,1],[3,2,2,1]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[5,5,5,4,4,1],[3,1,1,1]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[5,5,3,2,2,1],[1,1]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[5,5,5,2,2,1],[3,1]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4,2,1],[3,3]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4,4,1],[3,3,2]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[5,4,4,4,2,1],[1,1]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[5,4,3,3,2,1],[]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[7,6,4,1],[2]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[5,4,4,4,4,1],[2,1,1]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[5,4,4,3,3,1],[2]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[7,7,5,3],[3,3,2]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[7,7,7,3],[5,3,2]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4,4,3],[3,3,2,2,2]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[7,6,4,3],[2,2,2]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[7,6,6,3],[4,2,2]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[5,5,5,3,3,3],[3,3,2,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[5,4,4,3,3,3],[2,2,2,1,1]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[5,5,5,3,2,2],[3,3,2]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[5,4,4,3,2,2],[2,2,2]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[7,5,5,3],[4,1,1]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[7,5,5,5],[4,3,1]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[5,3,3,3,2,2],[2,1,1]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[7,5,4,2],[4]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[7,5,4,4],[4,2]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[5,5,5,5,5,3],[4,2,2,1,1]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[5,5,5,4,4,3],[4,1,1,1,1]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[7,7,7,5],[6,3,1]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[5,5,5,5,5,5],[4,3,2,2,1]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[5,5,5,5,4,4],[4,3,1,1,1]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[5,5,5,3,2,2],[4,1,1]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[5,5,5,5,2,2],[4,3,1]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[5,5,5,5,4,2],[4,3,3]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[5,5,5,5,4,4],[4,3,3,2]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[5,5,4,4,4,2],[4,1,1]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[5,5,4,3,3,2],[4]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[7,7,6,4],[6,2]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[5,5,4,4,4,4],[4,2,1,1]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[5,5,4,4,3,3],[4,2]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[2,2,2,2,2,2,2,2,2],[1]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[3,3,3,3,3,3,3,3],[2]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[8,8,8],[7]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[[6,6,6,6,4],[]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[7,7,7,7],[1,1,1]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[[6,5,5,5,5],[1]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[[6,5,5,5,4],[]]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[6,6,6,6,6],[2,1,1,1]]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[6,6,6,6,5],[1,1,1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[4,3,3,3,3,3,3],[2,2,2,2,2,2]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[6,6,6,6,6,6],[5]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[3,1,1,1,1,1,1,1,1],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[11],[]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[4,4,4,3,3,3,3,3],[]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[4,4,4,4,4,4,4,4],[1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1,1]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6,5],[]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6,6],[1]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[[7,6,6,6,6],[]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[[7,7,7,7,7],[]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[[6,5,5,5,5,5],[]]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6,6],[1,1,1,1,1]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[10,10],[8]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[9,9,9],[7,7]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[8,8,8,8],[6,6,6]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[7,7,7,7,7],[5,5,5,5]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[6,6,6,6,6,6],[4,4,4,4,4]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[5,5,5,5,5,5,5],[3,3,3,3,3,3]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[4,4,4,4,4,4,4,4],[2,2,2,2,2,2,2]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3,3,3,3,3],[1,1,1,1,1,1,1,1]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,2,2,2,2,2],[]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6,6],[]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6,2],[1,1,1,1,1]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[7,7,7,7,7],[1,1,1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2,2]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[6,5,5,5,5,5],[4]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[7,7,7,5,3,1],[2,2,1,1]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[7,7,7,7,3,1],[4,2,1,1]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[5,5,5,5,4,4,3,1],[2,2,1,1,1,1]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[[7,7,6,4,3,1],[1,1,1,1]]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[[7,7,6,6,3,1],[3,1,1,1]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[7,7,7,7,5,1],[4,4,3,1]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[7,7,6,6,5,1],[3,3,3,1]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[7,7,5,5,5,1],[3,2,2,1]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[7,7,5,4,4,1],[3,1,1,1]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[7,7,7,7,5,1],[5,2,2,1]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[[7,7,7,7,7,1],[5,4,2,1]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[5,5,5,5,5,4,4,1],[3,2,2,1,1,1]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[[7,7,7,6,4,1],[5,1,1,1]]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[7,7,7,6,6,1],[5,3,1,1]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[5,5,5,5,3,2,2,1],[2,2,1,1]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[5,5,4,4,3,2,2,1],[1,1,1,1]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[7,7,5,2,2,1],[3,1]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[5,5,5,5,5,2,2,1],[3,2,2,1]]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[5,5,5,4,4,2,2,1],[3,1,1,1]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[7,7,5,4,2,1],[3,3]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[7,7,7,4,2,1],[5,3]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[7,7,5,4,4,1],[3,3,2]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[7,7,7,4,4,1],[5,3,2]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4,4,4,2,1],[3,3,1,1]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4,3,3,2,1],[3,3]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[7,7,7,6,4,1],[5,5,2]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4,4,4,4,1],[3,3,2,1,1]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4,4,3,3,1],[3,3,2]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[7,6,6,4,2,1],[1,1]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[7,6,6,6,2,1],[3,1]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[5,4,4,4,3,3,2,1],[1,1]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[7,6,5,3,2,1],[]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[7,6,5,5,2,1],[2]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[7,6,6,6,4,1],[3,3,2]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[7,6,5,5,4,1],[2,2,2]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[7,6,4,4,4,1],[2,1,1]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[7,6,4,3,3,1],[2]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[7,6,6,6,4,1],[4,1,1]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[7,6,6,6,6,1],[4,3,1]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[5,4,4,4,4,3,3,1],[2,1,1]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[7,6,6,5,3,1],[4]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[7,6,6,5,5,1],[4,2]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[7,7,7,7,5,3],[4,4,3,3,2]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[7,7,6,6,5,3],[3,3,3,3,2]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[9,9,7,3],[5,3,2]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[7,7,7,7,7,3],[5,4,4,3,2]]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[7,7,7,6,6,3],[5,3,3,3,2]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[7,7,5,4,4,3],[3,3,2,2,2]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[7,7,7,4,4,3],[5,3,2,2,2]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[7,7,7,6,4,3],[5,5,2,2,2]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[7,7,7,6,6,3],[5,5,4,2,2]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[7,6,6,6,4,3],[3,3,2,2,2]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[7,6,5,5,4,3],[2,2,2,2,2]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[9,8,6,3],[4,2,2]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[7,6,6,6,6,3],[4,3,3,2,2]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[7,6,6,5,5,3],[4,2,2,2,2]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[7,7,5,3,3,3],[3,3,2,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[7,7,7,3,3,3],[5,3,2,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4,4,3,3,3],[3,3,2,2,2,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[7,6,4,3,3,3],[2,2,2,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[7,6,6,3,3,3],[4,2,2,1,1]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[7,7,5,3,2,2],[3,3,2]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[7,7,7,3,2,2],[5,3,2]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[5,5,5,4,4,3,2,2],[3,3,2,2,2]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[7,6,4,3,2,2],[2,2,2]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[7,6,6,3,2,2],[4,2,2]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[7,7,7,5,5,3],[5,5,4,1,1]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[7,6,6,5,5,3],[4,4,4,1,1]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[7,7,7,5,5,5],[5,5,4,3,1]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[7,6,6,5,5,5],[4,4,4,3,1]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[5,5,5,3,3,3,2,2],[3,3,2,1,1]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[5,4,4,3,3,3,2,2],[2,2,2,1,1]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[7,7,7,5,4,2],[5,5,4]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[7,6,6,5,4,2],[4,4,4]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[7,7,7,5,4,4],[5,5,4,2]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[7,6,6,5,4,4],[4,4,4,2]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[7,5,5,5,5,3],[4,2,2,1,1]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[7,5,5,4,4,3],[4,1,1,1,1]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[9,7,7,5],[6,3,1]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[7,5,5,5,5,5],[4,3,2,2,1]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[7,5,5,5,4,4],[4,3,1,1,1]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[7,5,5,3,2,2],[4,1,1]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[7,5,5,5,2,2],[4,3,1]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[7,5,5,5,4,2],[4,3,3]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[7,5,5,5,4,4],[4,3,3,2]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[7,5,4,4,4,2],[4,1,1]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[7,5,4,3,3,2],[4]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[9,7,6,4],[6,2]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[7,5,4,4,4,4],[4,2,1,1]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[7,5,4,4,3,3],[4,2]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[[7,7,7,7,5,3],[6,2,2,1,1]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[[7,7,7,7,7,3],[6,4,2,1,1]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[[5,5,5,5,5,4,4,3],[4,2,2,1,1,1,1]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[[7,7,7,6,4,3],[6,1,1,1,1]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[[7,7,7,6,6,3],[6,3,1,1,1]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[7,7,7,7,7,5],[6,4,4,3,1]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[7,7,7,6,6,5],[6,3,3,3,1]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[[7,7,7,5,5,5],[6,3,2,2,1]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[7,7,7,5,4,4],[6,3,1,1,1]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[[7,7,7,7,7,5],[6,5,2,2,1]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[[7,7,7,7,7,7],[6,5,4,2,1]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[5,5,5,5,5,5,4,4],[4,3,2,2,1,1,1]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[[7,7,7,7,6,4],[6,5,1,1,1]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[7,7,7,7,6,6],[6,5,3,1,1]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[5,5,5,5,5,3,2,2],[4,2,2,1,1]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[5,5,5,4,4,3,2,2],[4,1,1,1,1]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[7,7,7,5,2,2],[6,3,1]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[5,5,5,5,5,5,2,2],[4,3,2,2,1]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[5,5,5,5,4,4,2,2],[4,3,1,1,1]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[7,7,7,5,4,2],[6,3,3]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[7,7,7,7,4,2],[6,5,3]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[7,7,7,5,4,4],[6,3,3,2]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[7,7,7,7,4,4],[6,5,3,2]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[[5,5,5,5,4,4,4,2],[4,3,3,1,1]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[5,5,5,5,4,3,3,2],[4,3,3]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[7,7,7,7,6,4],[6,5,5,2]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[5,5,5,5,4,4,4,4],[4,3,3,2,1,1]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[5,5,5,5,4,4,3,3],[4,3,3,2]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[[7,7,6,6,4,2],[6,1,1]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[[7,7,6,6,6,2],[6,3,1]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[5,5,4,4,4,3,3,2],[4,1,1]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[[7,7,6,5,3,2],[6]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[7,7,6,5,5,2],[6,2]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[7,7,6,6,6,4],[6,3,3,2]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[7,7,6,5,5,4],[6,2,2,2]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[7,7,6,4,4,4],[6,2,1,1]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[7,7,6,4,3,3],[6,2]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[[7,7,6,6,6,4],[6,4,1,1]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[7,7,6,6,6,6],[6,4,3,1]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[5,5,4,4,4,4,3,3],[4,2,1,1]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[7,7,6,6,5,3],[6,4]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[7,7,6,6,5,5],[6,4,2]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[[7,6,6,6,6,6],[]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[7,7,7,7,7,7],[1,1,1,1,1]]
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Description
The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.
Properties
injective
Sage code
def mapping(D): p = ParallelogramPolyomino.from_dyck_word(D) return SkewPartitions(p.area()).from_row_and_column_length(p.widths()[::-1], p.heights())
Weight
40
Created
May 13, 2021 at 15:12 by Martin Rubey
Updated
May 13, 2021 at 15:12 by Martin Rubey
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