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Identifier
Mp00295: Standard tableaux valley compositionInteger compositions
Images
=>
Cc0007;cc-rep-0
[]=>[] [[1]]=>[1] [[1,2]]=>[2] [[1],[2]]=>[2] [[1,2,3]]=>[3] [[1,3],[2]]=>[2,1] [[1,2],[3]]=>[3] [[1],[2],[3]]=>[3] [[1,2,3,4]]=>[4] [[1,3,4],[2]]=>[2,2] [[1,2,4],[3]]=>[3,1] [[1,2,3],[4]]=>[4] [[1,3],[2,4]]=>[2,2] [[1,2],[3,4]]=>[3,1] [[1,4],[2],[3]]=>[3,1] [[1,3],[2],[4]]=>[2,2] [[1,2],[3],[4]]=>[4] [[1],[2],[3],[4]]=>[4] [[1,2,3,4,5]]=>[5] [[1,3,4,5],[2]]=>[2,3] [[1,2,4,5],[3]]=>[3,2] [[1,2,3,5],[4]]=>[4,1] [[1,2,3,4],[5]]=>[5] [[1,3,5],[2,4]]=>[2,2,1] [[1,2,5],[3,4]]=>[3,2] [[1,3,4],[2,5]]=>[2,3] [[1,2,4],[3,5]]=>[3,2] [[1,2,3],[4,5]]=>[4,1] [[1,4,5],[2],[3]]=>[3,2] [[1,3,5],[2],[4]]=>[2,2,1] [[1,2,5],[3],[4]]=>[4,1] [[1,3,4],[2],[5]]=>[2,3] [[1,2,4],[3],[5]]=>[3,2] [[1,2,3],[4],[5]]=>[5] [[1,4],[2,5],[3]]=>[3,2] [[1,3],[2,5],[4]]=>[2,2,1] [[1,2],[3,5],[4]]=>[4,1] [[1,3],[2,4],[5]]=>[2,3] [[1,2],[3,4],[5]]=>[3,2] [[1,5],[2],[3],[4]]=>[4,1] [[1,4],[2],[3],[5]]=>[3,2] [[1,3],[2],[4],[5]]=>[2,3] [[1,2],[3],[4],[5]]=>[5] [[1],[2],[3],[4],[5]]=>[5] [[1,2,3,4,5,6]]=>[6] [[1,3,4,5,6],[2]]=>[2,4] [[1,2,4,5,6],[3]]=>[3,3] [[1,2,3,5,6],[4]]=>[4,2] [[1,2,3,4,6],[5]]=>[5,1] [[1,2,3,4,5],[6]]=>[6] [[1,3,5,6],[2,4]]=>[2,2,2] [[1,2,5,6],[3,4]]=>[3,3] [[1,3,4,6],[2,5]]=>[2,3,1] [[1,2,4,6],[3,5]]=>[3,2,1] [[1,2,3,6],[4,5]]=>[4,2] [[1,3,4,5],[2,6]]=>[2,4] [[1,2,4,5],[3,6]]=>[3,3] [[1,2,3,5],[4,6]]=>[4,2] [[1,2,3,4],[5,6]]=>[5,1] [[1,4,5,6],[2],[3]]=>[3,3] [[1,3,5,6],[2],[4]]=>[2,2,2] [[1,2,5,6],[3],[4]]=>[4,2] [[1,3,4,6],[2],[5]]=>[2,3,1] [[1,2,4,6],[3],[5]]=>[3,2,1] [[1,2,3,6],[4],[5]]=>[5,1] [[1,3,4,5],[2],[6]]=>[2,4] [[1,2,4,5],[3],[6]]=>[3,3] [[1,2,3,5],[4],[6]]=>[4,2] [[1,2,3,4],[5],[6]]=>[6] [[1,3,5],[2,4,6]]=>[2,2,2] [[1,2,5],[3,4,6]]=>[3,3] [[1,3,4],[2,5,6]]=>[2,3,1] [[1,2,4],[3,5,6]]=>[3,2,1] [[1,2,3],[4,5,6]]=>[4,2] [[1,4,6],[2,5],[3]]=>[3,2,1] [[1,3,6],[2,5],[4]]=>[2,2,2] [[1,2,6],[3,5],[4]]=>[4,2] [[1,3,6],[2,4],[5]]=>[2,3,1] [[1,2,6],[3,4],[5]]=>[3,2,1] [[1,4,5],[2,6],[3]]=>[3,3] [[1,3,5],[2,6],[4]]=>[2,2,2] [[1,2,5],[3,6],[4]]=>[4,2] [[1,3,4],[2,6],[5]]=>[2,3,1] [[1,2,4],[3,6],[5]]=>[3,2,1] [[1,2,3],[4,6],[5]]=>[5,1] [[1,3,5],[2,4],[6]]=>[2,2,2] [[1,2,5],[3,4],[6]]=>[3,3] [[1,3,4],[2,5],[6]]=>[2,4] [[1,2,4],[3,5],[6]]=>[3,3] [[1,2,3],[4,5],[6]]=>[4,2] [[1,5,6],[2],[3],[4]]=>[4,2] [[1,4,6],[2],[3],[5]]=>[3,2,1] [[1,3,6],[2],[4],[5]]=>[2,3,1] [[1,2,6],[3],[4],[5]]=>[5,1] [[1,4,5],[2],[3],[6]]=>[3,3] [[1,3,5],[2],[4],[6]]=>[2,2,2] [[1,2,5],[3],[4],[6]]=>[4,2] [[1,3,4],[2],[5],[6]]=>[2,4] [[1,2,4],[3],[5],[6]]=>[3,3] [[1,2,3],[4],[5],[6]]=>[6] [[1,4],[2,5],[3,6]]=>[3,3] [[1,3],[2,5],[4,6]]=>[2,2,2] [[1,2],[3,5],[4,6]]=>[4,2] [[1,3],[2,4],[5,6]]=>[2,3,1] [[1,2],[3,4],[5,6]]=>[3,2,1] [[1,5],[2,6],[3],[4]]=>[4,2] [[1,4],[2,6],[3],[5]]=>[3,2,1] [[1,3],[2,6],[4],[5]]=>[2,3,1] [[1,2],[3,6],[4],[5]]=>[5,1] [[1,4],[2,5],[3],[6]]=>[3,3] [[1,3],[2,5],[4],[6]]=>[2,2,2] [[1,2],[3,5],[4],[6]]=>[4,2] [[1,3],[2,4],[5],[6]]=>[2,4] [[1,2],[3,4],[5],[6]]=>[3,3] [[1,6],[2],[3],[4],[5]]=>[5,1] [[1,5],[2],[3],[4],[6]]=>[4,2] [[1,4],[2],[3],[5],[6]]=>[3,3] [[1,3],[2],[4],[5],[6]]=>[2,4] [[1,2],[3],[4],[5],[6]]=>[6] [[1],[2],[3],[4],[5],[6]]=>[6] [[1,2,3,4,5,6,7]]=>[7] [[1,3,4,5,6,7],[2]]=>[2,5] [[1,2,4,5,6,7],[3]]=>[3,4] [[1,2,3,5,6,7],[4]]=>[4,3] [[1,2,3,4,6,7],[5]]=>[5,2] [[1,2,3,4,5,7],[6]]=>[6,1] [[1,2,3,4,5,6],[7]]=>[7] [[1,3,5,6,7],[2,4]]=>[2,2,3] [[1,2,5,6,7],[3,4]]=>[3,4] [[1,3,4,6,7],[2,5]]=>[2,3,2] [[1,2,4,6,7],[3,5]]=>[3,2,2] [[1,2,3,6,7],[4,5]]=>[4,3] [[1,3,4,5,7],[2,6]]=>[2,4,1] [[1,2,4,5,7],[3,6]]=>[3,3,1] [[1,2,3,5,7],[4,6]]=>[4,2,1] [[1,2,3,4,7],[5,6]]=>[5,2] [[1,3,4,5,6],[2,7]]=>[2,5] [[1,2,4,5,6],[3,7]]=>[3,4] [[1,2,3,5,6],[4,7]]=>[4,3] [[1,2,3,4,6],[5,7]]=>[5,2] [[1,2,3,4,5],[6,7]]=>[6,1] [[1,4,5,6,7],[2],[3]]=>[3,4] [[1,3,5,6,7],[2],[4]]=>[2,2,3] [[1,2,5,6,7],[3],[4]]=>[4,3] [[1,3,4,6,7],[2],[5]]=>[2,3,2] [[1,2,4,6,7],[3],[5]]=>[3,2,2] [[1,2,3,6,7],[4],[5]]=>[5,2] [[1,3,4,5,7],[2],[6]]=>[2,4,1] [[1,2,4,5,7],[3],[6]]=>[3,3,1] [[1,2,3,5,7],[4],[6]]=>[4,2,1] [[1,2,3,4,7],[5],[6]]=>[6,1] [[1,3,4,5,6],[2],[7]]=>[2,5] [[1,2,4,5,6],[3],[7]]=>[3,4] [[1,2,3,5,6],[4],[7]]=>[4,3] [[1,2,3,4,6],[5],[7]]=>[5,2] [[1,2,3,4,5],[6],[7]]=>[7] [[1,3,5,7],[2,4,6]]=>[2,2,2,1] [[1,2,5,7],[3,4,6]]=>[3,3,1] [[1,3,4,7],[2,5,6]]=>[2,3,2] [[1,2,4,7],[3,5,6]]=>[3,2,2] [[1,2,3,7],[4,5,6]]=>[4,3] [[1,3,5,6],[2,4,7]]=>[2,2,3] [[1,2,5,6],[3,4,7]]=>[3,4] [[1,3,4,6],[2,5,7]]=>[2,3,2] [[1,2,4,6],[3,5,7]]=>[3,2,2] [[1,2,3,6],[4,5,7]]=>[4,3] [[1,3,4,5],[2,6,7]]=>[2,4,1] [[1,2,4,5],[3,6,7]]=>[3,3,1] [[1,2,3,5],[4,6,7]]=>[4,2,1] [[1,2,3,4],[5,6,7]]=>[5,2] [[1,4,6,7],[2,5],[3]]=>[3,2,2] [[1,3,6,7],[2,5],[4]]=>[2,2,3] [[1,2,6,7],[3,5],[4]]=>[4,3] [[1,3,6,7],[2,4],[5]]=>[2,3,2] [[1,2,6,7],[3,4],[5]]=>[3,2,2] [[1,4,5,7],[2,6],[3]]=>[3,3,1] [[1,3,5,7],[2,6],[4]]=>[2,2,2,1] [[1,2,5,7],[3,6],[4]]=>[4,2,1] [[1,3,4,7],[2,6],[5]]=>[2,3,2] [[1,2,4,7],[3,6],[5]]=>[3,2,2] [[1,2,3,7],[4,6],[5]]=>[5,2] [[1,3,5,7],[2,4],[6]]=>[2,2,2,1] [[1,2,5,7],[3,4],[6]]=>[3,3,1] [[1,3,4,7],[2,5],[6]]=>[2,4,1] [[1,2,4,7],[3,5],[6]]=>[3,3,1] [[1,2,3,7],[4,5],[6]]=>[4,2,1] [[1,4,5,6],[2,7],[3]]=>[3,4] [[1,3,5,6],[2,7],[4]]=>[2,2,3] [[1,2,5,6],[3,7],[4]]=>[4,3] [[1,3,4,6],[2,7],[5]]=>[2,3,2] [[1,2,4,6],[3,7],[5]]=>[3,2,2] [[1,2,3,6],[4,7],[5]]=>[5,2] [[1,3,4,5],[2,7],[6]]=>[2,4,1] [[1,2,4,5],[3,7],[6]]=>[3,3,1] [[1,2,3,5],[4,7],[6]]=>[4,2,1] [[1,2,3,4],[5,7],[6]]=>[6,1] [[1,3,5,6],[2,4],[7]]=>[2,2,3] [[1,2,5,6],[3,4],[7]]=>[3,4] [[1,3,4,6],[2,5],[7]]=>[2,3,2] [[1,2,4,6],[3,5],[7]]=>[3,2,2] [[1,2,3,6],[4,5],[7]]=>[4,3] [[1,3,4,5],[2,6],[7]]=>[2,5] [[1,2,4,5],[3,6],[7]]=>[3,4] [[1,2,3,5],[4,6],[7]]=>[4,3] [[1,2,3,4],[5,6],[7]]=>[5,2] [[1,5,6,7],[2],[3],[4]]=>[4,3] [[1,4,6,7],[2],[3],[5]]=>[3,2,2] [[1,3,6,7],[2],[4],[5]]=>[2,3,2] [[1,2,6,7],[3],[4],[5]]=>[5,2] [[1,4,5,7],[2],[3],[6]]=>[3,3,1] [[1,3,5,7],[2],[4],[6]]=>[2,2,2,1] [[1,2,5,7],[3],[4],[6]]=>[4,2,1] [[1,3,4,7],[2],[5],[6]]=>[2,4,1] [[1,2,4,7],[3],[5],[6]]=>[3,3,1] [[1,2,3,7],[4],[5],[6]]=>[6,1] [[1,4,5,6],[2],[3],[7]]=>[3,4] [[1,3,5,6],[2],[4],[7]]=>[2,2,3] [[1,2,5,6],[3],[4],[7]]=>[4,3] [[1,3,4,6],[2],[5],[7]]=>[2,3,2] [[1,2,4,6],[3],[5],[7]]=>[3,2,2] [[1,2,3,6],[4],[5],[7]]=>[5,2] [[1,3,4,5],[2],[6],[7]]=>[2,5] [[1,2,4,5],[3],[6],[7]]=>[3,4] [[1,2,3,5],[4],[6],[7]]=>[4,3] [[1,2,3,4],[5],[6],[7]]=>[7] [[1,4,6],[2,5,7],[3]]=>[3,2,2] [[1,3,6],[2,5,7],[4]]=>[2,2,3] [[1,2,6],[3,5,7],[4]]=>[4,3] [[1,3,6],[2,4,7],[5]]=>[2,3,2] [[1,2,6],[3,4,7],[5]]=>[3,2,2] [[1,4,5],[2,6,7],[3]]=>[3,3,1] [[1,3,5],[2,6,7],[4]]=>[2,2,2,1] [[1,2,5],[3,6,7],[4]]=>[4,2,1] [[1,3,4],[2,6,7],[5]]=>[2,3,2] [[1,2,4],[3,6,7],[5]]=>[3,2,2] [[1,2,3],[4,6,7],[5]]=>[5,2] [[1,3,5],[2,4,7],[6]]=>[2,2,2,1] [[1,2,5],[3,4,7],[6]]=>[3,3,1] [[1,3,4],[2,5,7],[6]]=>[2,4,1] [[1,2,4],[3,5,7],[6]]=>[3,3,1] [[1,2,3],[4,5,7],[6]]=>[4,2,1] [[1,3,5],[2,4,6],[7]]=>[2,2,3] [[1,2,5],[3,4,6],[7]]=>[3,4] [[1,3,4],[2,5,6],[7]]=>[2,3,2] [[1,2,4],[3,5,6],[7]]=>[3,2,2] [[1,2,3],[4,5,6],[7]]=>[4,3] [[1,4,7],[2,5],[3,6]]=>[3,3,1] [[1,3,7],[2,5],[4,6]]=>[2,2,2,1] [[1,2,7],[3,5],[4,6]]=>[4,2,1] [[1,3,7],[2,4],[5,6]]=>[2,3,2] [[1,2,7],[3,4],[5,6]]=>[3,2,2] [[1,4,6],[2,5],[3,7]]=>[3,2,2] [[1,3,6],[2,5],[4,7]]=>[2,2,3] [[1,2,6],[3,5],[4,7]]=>[4,3] [[1,3,6],[2,4],[5,7]]=>[2,3,2] [[1,2,6],[3,4],[5,7]]=>[3,2,2] [[1,4,5],[2,6],[3,7]]=>[3,4] [[1,3,5],[2,6],[4,7]]=>[2,2,3] [[1,2,5],[3,6],[4,7]]=>[4,3] [[1,3,4],[2,6],[5,7]]=>[2,3,2] [[1,2,4],[3,6],[5,7]]=>[3,2,2] [[1,2,3],[4,6],[5,7]]=>[5,2] [[1,3,5],[2,4],[6,7]]=>[2,2,2,1] [[1,2,5],[3,4],[6,7]]=>[3,3,1] [[1,3,4],[2,5],[6,7]]=>[2,4,1] [[1,2,4],[3,5],[6,7]]=>[3,3,1] [[1,2,3],[4,5],[6,7]]=>[4,2,1] [[1,5,7],[2,6],[3],[4]]=>[4,2,1] [[1,4,7],[2,6],[3],[5]]=>[3,2,2] [[1,3,7],[2,6],[4],[5]]=>[2,3,2] [[1,2,7],[3,6],[4],[5]]=>[5,2] [[1,4,7],[2,5],[3],[6]]=>[3,3,1] [[1,3,7],[2,5],[4],[6]]=>[2,2,2,1] [[1,2,7],[3,5],[4],[6]]=>[4,2,1] [[1,3,7],[2,4],[5],[6]]=>[2,4,1] [[1,2,7],[3,4],[5],[6]]=>[3,3,1] [[1,5,6],[2,7],[3],[4]]=>[4,3] [[1,4,6],[2,7],[3],[5]]=>[3,2,2] [[1,3,6],[2,7],[4],[5]]=>[2,3,2] [[1,2,6],[3,7],[4],[5]]=>[5,2] [[1,4,5],[2,7],[3],[6]]=>[3,3,1] [[1,3,5],[2,7],[4],[6]]=>[2,2,2,1] [[1,2,5],[3,7],[4],[6]]=>[4,2,1] [[1,3,4],[2,7],[5],[6]]=>[2,4,1] [[1,2,4],[3,7],[5],[6]]=>[3,3,1] [[1,2,3],[4,7],[5],[6]]=>[6,1] [[1,4,6],[2,5],[3],[7]]=>[3,2,2] [[1,3,6],[2,5],[4],[7]]=>[2,2,3] [[1,2,6],[3,5],[4],[7]]=>[4,3] [[1,3,6],[2,4],[5],[7]]=>[2,3,2] [[1,2,6],[3,4],[5],[7]]=>[3,2,2] [[1,4,5],[2,6],[3],[7]]=>[3,4] [[1,3,5],[2,6],[4],[7]]=>[2,2,3] [[1,2,5],[3,6],[4],[7]]=>[4,3] [[1,3,4],[2,6],[5],[7]]=>[2,3,2] [[1,2,4],[3,6],[5],[7]]=>[3,2,2] [[1,2,3],[4,6],[5],[7]]=>[5,2] [[1,3,5],[2,4],[6],[7]]=>[2,2,3] [[1,2,5],[3,4],[6],[7]]=>[3,4] [[1,3,4],[2,5],[6],[7]]=>[2,5] [[1,2,4],[3,5],[6],[7]]=>[3,4] [[1,2,3],[4,5],[6],[7]]=>[4,3] [[1,6,7],[2],[3],[4],[5]]=>[5,2] [[1,5,7],[2],[3],[4],[6]]=>[4,2,1] [[1,4,7],[2],[3],[5],[6]]=>[3,3,1] [[1,3,7],[2],[4],[5],[6]]=>[2,4,1] [[1,2,7],[3],[4],[5],[6]]=>[6,1] [[1,5,6],[2],[3],[4],[7]]=>[4,3] [[1,4,6],[2],[3],[5],[7]]=>[3,2,2] [[1,3,6],[2],[4],[5],[7]]=>[2,3,2] [[1,2,6],[3],[4],[5],[7]]=>[5,2] [[1,4,5],[2],[3],[6],[7]]=>[3,4] [[1,3,5],[2],[4],[6],[7]]=>[2,2,3] [[1,2,5],[3],[4],[6],[7]]=>[4,3] [[1,3,4],[2],[5],[6],[7]]=>[2,5] [[1,2,4],[3],[5],[6],[7]]=>[3,4] [[1,2,3],[4],[5],[6],[7]]=>[7] [[1,5],[2,6],[3,7],[4]]=>[4,3] [[1,4],[2,6],[3,7],[5]]=>[3,2,2] [[1,3],[2,6],[4,7],[5]]=>[2,3,2] [[1,2],[3,6],[4,7],[5]]=>[5,2] [[1,4],[2,5],[3,7],[6]]=>[3,3,1] [[1,3],[2,5],[4,7],[6]]=>[2,2,2,1] [[1,2],[3,5],[4,7],[6]]=>[4,2,1] [[1,3],[2,4],[5,7],[6]]=>[2,4,1] [[1,2],[3,4],[5,7],[6]]=>[3,3,1] [[1,4],[2,5],[3,6],[7]]=>[3,4] [[1,3],[2,5],[4,6],[7]]=>[2,2,3] [[1,2],[3,5],[4,6],[7]]=>[4,3] [[1,3],[2,4],[5,6],[7]]=>[2,3,2] [[1,2],[3,4],[5,6],[7]]=>[3,2,2] [[1,6],[2,7],[3],[4],[5]]=>[5,2] [[1,5],[2,7],[3],[4],[6]]=>[4,2,1] [[1,4],[2,7],[3],[5],[6]]=>[3,3,1] [[1,3],[2,7],[4],[5],[6]]=>[2,4,1] [[1,2],[3,7],[4],[5],[6]]=>[6,1] [[1,5],[2,6],[3],[4],[7]]=>[4,3] [[1,4],[2,6],[3],[5],[7]]=>[3,2,2] [[1,3],[2,6],[4],[5],[7]]=>[2,3,2] [[1,2],[3,6],[4],[5],[7]]=>[5,2] [[1,4],[2,5],[3],[6],[7]]=>[3,4] [[1,3],[2,5],[4],[6],[7]]=>[2,2,3] [[1,2],[3,5],[4],[6],[7]]=>[4,3] [[1,3],[2,4],[5],[6],[7]]=>[2,5] [[1,2],[3,4],[5],[6],[7]]=>[3,4] [[1,7],[2],[3],[4],[5],[6]]=>[6,1] [[1,6],[2],[3],[4],[5],[7]]=>[5,2] [[1,5],[2],[3],[4],[6],[7]]=>[4,3] [[1,4],[2],[3],[5],[6],[7]]=>[3,4] [[1,3],[2],[4],[5],[6],[7]]=>[2,5] [[1,2],[3],[4],[5],[6],[7]]=>[7] [[1],[2],[3],[4],[5],[6],[7]]=>[7] [[1,2,3,4,5,6,7,8]]=>[8] [[1,3,4,5,6,7,8],[2]]=>[2,6] [[1,2,4,5,6,7,8],[3]]=>[3,5] [[1,2,3,5,6,7,8],[4]]=>[4,4] [[1,2,3,4,6,7,8],[5]]=>[5,3] [[1,2,3,4,5,7,8],[6]]=>[6,2] [[1,2,3,4,5,6,8],[7]]=>[7,1] [[1,2,3,4,5,6,7],[8]]=>[8] [[1,3,5,6,7,8],[2,4]]=>[2,2,4] [[1,2,5,6,7,8],[3,4]]=>[3,5] [[1,3,4,6,7,8],[2,5]]=>[2,3,3] [[1,2,4,6,7,8],[3,5]]=>[3,2,3] [[1,2,3,6,7,8],[4,5]]=>[4,4] [[1,3,4,5,7,8],[2,6]]=>[2,4,2] [[1,2,4,5,7,8],[3,6]]=>[3,3,2] [[1,2,3,5,7,8],[4,6]]=>[4,2,2] [[1,2,3,4,7,8],[5,6]]=>[5,3] [[1,3,4,5,6,8],[2,7]]=>[2,5,1] [[1,2,4,5,6,8],[3,7]]=>[3,4,1] [[1,2,3,5,6,8],[4,7]]=>[4,3,1] [[1,2,3,4,6,8],[5,7]]=>[5,2,1] [[1,2,3,4,5,8],[6,7]]=>[6,2] [[1,3,4,5,6,7],[2,8]]=>[2,6] [[1,2,4,5,6,7],[3,8]]=>[3,5] [[1,2,3,5,6,7],[4,8]]=>[4,4] [[1,2,3,4,6,7],[5,8]]=>[5,3] [[1,2,3,4,5,7],[6,8]]=>[6,2] [[1,2,3,4,5,6],[7,8]]=>[7,1] [[1,4,5,6,7,8],[2],[3]]=>[3,5] [[1,3,5,6,7,8],[2],[4]]=>[2,2,4] [[1,2,5,6,7,8],[3],[4]]=>[4,4] [[1,3,4,6,7,8],[2],[5]]=>[2,3,3] [[1,2,4,6,7,8],[3],[5]]=>[3,2,3] [[1,2,3,6,7,8],[4],[5]]=>[5,3] [[1,3,4,5,7,8],[2],[6]]=>[2,4,2] [[1,2,4,5,7,8],[3],[6]]=>[3,3,2] [[1,2,3,5,7,8],[4],[6]]=>[4,2,2] [[1,2,3,4,7,8],[5],[6]]=>[6,2] [[1,3,4,5,6,8],[2],[7]]=>[2,5,1] [[1,2,4,5,6,8],[3],[7]]=>[3,4,1] [[1,2,3,5,6,8],[4],[7]]=>[4,3,1] [[1,2,3,4,6,8],[5],[7]]=>[5,2,1] [[1,2,3,4,5,8],[6],[7]]=>[7,1] [[1,3,4,5,6,7],[2],[8]]=>[2,6] [[1,2,4,5,6,7],[3],[8]]=>[3,5] [[1,2,3,5,6,7],[4],[8]]=>[4,4] [[1,2,3,4,6,7],[5],[8]]=>[5,3] [[1,2,3,4,5,7],[6],[8]]=>[6,2] [[1,2,3,4,5,6],[7],[8]]=>[8] [[1,3,5,7,8],[2,4,6]]=>[2,2,2,2] [[1,2,5,7,8],[3,4,6]]=>[3,3,2] [[1,3,4,7,8],[2,5,6]]=>[2,3,3] [[1,2,4,7,8],[3,5,6]]=>[3,2,3] [[1,2,3,7,8],[4,5,6]]=>[4,4] [[1,3,5,6,8],[2,4,7]]=>[2,2,3,1] [[1,2,5,6,8],[3,4,7]]=>[3,4,1] [[1,3,4,6,8],[2,5,7]]=>[2,3,2,1] [[1,2,4,6,8],[3,5,7]]=>[3,2,2,1] [[1,2,3,6,8],[4,5,7]]=>[4,3,1] [[1,3,4,5,8],[2,6,7]]=>[2,4,2] [[1,2,4,5,8],[3,6,7]]=>[3,3,2] [[1,2,3,5,8],[4,6,7]]=>[4,2,2] [[1,2,3,4,8],[5,6,7]]=>[5,3] [[1,3,5,6,7],[2,4,8]]=>[2,2,4] [[1,2,5,6,7],[3,4,8]]=>[3,5] [[1,3,4,6,7],[2,5,8]]=>[2,3,3] [[1,2,4,6,7],[3,5,8]]=>[3,2,3] [[1,2,3,6,7],[4,5,8]]=>[4,4] [[1,3,4,5,7],[2,6,8]]=>[2,4,2] [[1,2,4,5,7],[3,6,8]]=>[3,3,2] [[1,2,3,5,7],[4,6,8]]=>[4,2,2] [[1,2,3,4,7],[5,6,8]]=>[5,3] [[1,3,4,5,6],[2,7,8]]=>[2,5,1] [[1,2,4,5,6],[3,7,8]]=>[3,4,1] [[1,2,3,5,6],[4,7,8]]=>[4,3,1] [[1,2,3,4,6],[5,7,8]]=>[5,2,1] [[1,2,3,4,5],[6,7,8]]=>[6,2] [[1,4,6,7,8],[2,5],[3]]=>[3,2,3] [[1,3,6,7,8],[2,5],[4]]=>[2,2,4] [[1,2,6,7,8],[3,5],[4]]=>[4,4] [[1,3,6,7,8],[2,4],[5]]=>[2,3,3] [[1,2,6,7,8],[3,4],[5]]=>[3,2,3] [[1,4,5,7,8],[2,6],[3]]=>[3,3,2] [[1,3,5,7,8],[2,6],[4]]=>[2,2,2,2] [[1,2,5,7,8],[3,6],[4]]=>[4,2,2] [[1,3,4,7,8],[2,6],[5]]=>[2,3,3] [[1,2,4,7,8],[3,6],[5]]=>[3,2,3] [[1,2,3,7,8],[4,6],[5]]=>[5,3] [[1,3,5,7,8],[2,4],[6]]=>[2,2,2,2] [[1,2,5,7,8],[3,4],[6]]=>[3,3,2] [[1,3,4,7,8],[2,5],[6]]=>[2,4,2] [[1,2,4,7,8],[3,5],[6]]=>[3,3,2] [[1,2,3,7,8],[4,5],[6]]=>[4,2,2] [[1,4,5,6,8],[2,7],[3]]=>[3,4,1] [[1,3,5,6,8],[2,7],[4]]=>[2,2,3,1] [[1,2,5,6,8],[3,7],[4]]=>[4,3,1] [[1,3,4,6,8],[2,7],[5]]=>[2,3,2,1] [[1,2,4,6,8],[3,7],[5]]=>[3,2,2,1] [[1,2,3,6,8],[4,7],[5]]=>[5,2,1] [[1,3,4,5,8],[2,7],[6]]=>[2,4,2] [[1,2,4,5,8],[3,7],[6]]=>[3,3,2] [[1,2,3,5,8],[4,7],[6]]=>[4,2,2] [[1,2,3,4,8],[5,7],[6]]=>[6,2] [[1,3,5,6,8],[2,4],[7]]=>[2,2,3,1] [[1,2,5,6,8],[3,4],[7]]=>[3,4,1] [[1,3,4,6,8],[2,5],[7]]=>[2,3,2,1] [[1,2,4,6,8],[3,5],[7]]=>[3,2,2,1] [[1,2,3,6,8],[4,5],[7]]=>[4,3,1] [[1,3,4,5,8],[2,6],[7]]=>[2,5,1] [[1,2,4,5,8],[3,6],[7]]=>[3,4,1] [[1,2,3,5,8],[4,6],[7]]=>[4,3,1] [[1,2,3,4,8],[5,6],[7]]=>[5,2,1] [[1,4,5,6,7],[2,8],[3]]=>[3,5] [[1,3,5,6,7],[2,8],[4]]=>[2,2,4] [[1,2,5,6,7],[3,8],[4]]=>[4,4] [[1,3,4,6,7],[2,8],[5]]=>[2,3,3] [[1,2,4,6,7],[3,8],[5]]=>[3,2,3] [[1,2,3,6,7],[4,8],[5]]=>[5,3] [[1,3,4,5,7],[2,8],[6]]=>[2,4,2] [[1,2,4,5,7],[3,8],[6]]=>[3,3,2] [[1,2,3,5,7],[4,8],[6]]=>[4,2,2] [[1,2,3,4,7],[5,8],[6]]=>[6,2] [[1,3,4,5,6],[2,8],[7]]=>[2,5,1] [[1,2,4,5,6],[3,8],[7]]=>[3,4,1] [[1,2,3,5,6],[4,8],[7]]=>[4,3,1] [[1,2,3,4,6],[5,8],[7]]=>[5,2,1] [[1,2,3,4,5],[6,8],[7]]=>[7,1] [[1,3,5,6,7],[2,4],[8]]=>[2,2,4] [[1,2,5,6,7],[3,4],[8]]=>[3,5] [[1,3,4,6,7],[2,5],[8]]=>[2,3,3] [[1,2,4,6,7],[3,5],[8]]=>[3,2,3] [[1,2,3,6,7],[4,5],[8]]=>[4,4] [[1,3,4,5,7],[2,6],[8]]=>[2,4,2] [[1,2,4,5,7],[3,6],[8]]=>[3,3,2] [[1,2,3,5,7],[4,6],[8]]=>[4,2,2] [[1,2,3,4,7],[5,6],[8]]=>[5,3] [[1,3,4,5,6],[2,7],[8]]=>[2,6] [[1,2,4,5,6],[3,7],[8]]=>[3,5] [[1,2,3,5,6],[4,7],[8]]=>[4,4] [[1,2,3,4,6],[5,7],[8]]=>[5,3] [[1,2,3,4,5],[6,7],[8]]=>[6,2] [[1,5,6,7,8],[2],[3],[4]]=>[4,4] [[1,4,6,7,8],[2],[3],[5]]=>[3,2,3] [[1,3,6,7,8],[2],[4],[5]]=>[2,3,3] [[1,2,6,7,8],[3],[4],[5]]=>[5,3] [[1,4,5,7,8],[2],[3],[6]]=>[3,3,2] [[1,3,5,7,8],[2],[4],[6]]=>[2,2,2,2] [[1,2,5,7,8],[3],[4],[6]]=>[4,2,2] [[1,3,4,7,8],[2],[5],[6]]=>[2,4,2] [[1,2,4,7,8],[3],[5],[6]]=>[3,3,2] [[1,2,3,7,8],[4],[5],[6]]=>[6,2] [[1,4,5,6,8],[2],[3],[7]]=>[3,4,1] [[1,3,5,6,8],[2],[4],[7]]=>[2,2,3,1] [[1,2,5,6,8],[3],[4],[7]]=>[4,3,1] [[1,3,4,6,8],[2],[5],[7]]=>[2,3,2,1] [[1,2,4,6,8],[3],[5],[7]]=>[3,2,2,1] [[1,2,3,6,8],[4],[5],[7]]=>[5,2,1] [[1,3,4,5,8],[2],[6],[7]]=>[2,5,1] [[1,2,4,5,8],[3],[6],[7]]=>[3,4,1] [[1,2,3,5,8],[4],[6],[7]]=>[4,3,1] [[1,2,3,4,8],[5],[6],[7]]=>[7,1] [[1,4,5,6,7],[2],[3],[8]]=>[3,5] [[1,3,5,6,7],[2],[4],[8]]=>[2,2,4] [[1,2,5,6,7],[3],[4],[8]]=>[4,4] [[1,3,4,6,7],[2],[5],[8]]=>[2,3,3] [[1,2,4,6,7],[3],[5],[8]]=>[3,2,3] [[1,2,3,6,7],[4],[5],[8]]=>[5,3] [[1,3,4,5,7],[2],[6],[8]]=>[2,4,2] [[1,2,4,5,7],[3],[6],[8]]=>[3,3,2] [[1,2,3,5,7],[4],[6],[8]]=>[4,2,2] [[1,2,3,4,7],[5],[6],[8]]=>[6,2] [[1,3,4,5,6],[2],[7],[8]]=>[2,6] [[1,2,4,5,6],[3],[7],[8]]=>[3,5] [[1,2,3,5,6],[4],[7],[8]]=>[4,4] [[1,2,3,4,6],[5],[7],[8]]=>[5,3] [[1,2,3,4,5],[6],[7],[8]]=>[8] [[1,3,5,7],[2,4,6,8]]=>[2,2,2,2] [[1,2,5,7],[3,4,6,8]]=>[3,3,2] [[1,3,4,7],[2,5,6,8]]=>[2,3,3] [[1,2,4,7],[3,5,6,8]]=>[3,2,3] [[1,2,3,7],[4,5,6,8]]=>[4,4] [[1,3,5,6],[2,4,7,8]]=>[2,2,3,1] [[1,2,5,6],[3,4,7,8]]=>[3,4,1] [[1,3,4,6],[2,5,7,8]]=>[2,3,2,1] [[1,2,4,6],[3,5,7,8]]=>[3,2,2,1] [[1,2,3,6],[4,5,7,8]]=>[4,3,1] [[1,3,4,5],[2,6,7,8]]=>[2,4,2] [[1,2,4,5],[3,6,7,8]]=>[3,3,2] [[1,2,3,5],[4,6,7,8]]=>[4,2,2] [[1,2,3,4],[5,6,7,8]]=>[5,3] [[1,4,6,8],[2,5,7],[3]]=>[3,2,2,1] [[1,3,6,8],[2,5,7],[4]]=>[2,2,3,1] [[1,2,6,8],[3,5,7],[4]]=>[4,3,1] [[1,3,6,8],[2,4,7],[5]]=>[2,3,2,1] [[1,2,6,8],[3,4,7],[5]]=>[3,2,2,1] [[1,4,5,8],[2,6,7],[3]]=>[3,3,2] [[1,3,5,8],[2,6,7],[4]]=>[2,2,2,2] [[1,2,5,8],[3,6,7],[4]]=>[4,2,2] [[1,3,4,8],[2,6,7],[5]]=>[2,3,3] [[1,2,4,8],[3,6,7],[5]]=>[3,2,3] [[1,2,3,8],[4,6,7],[5]]=>[5,3] [[1,3,5,8],[2,4,7],[6]]=>[2,2,2,2] [[1,2,5,8],[3,4,7],[6]]=>[3,3,2] [[1,3,4,8],[2,5,7],[6]]=>[2,4,2] [[1,2,4,8],[3,5,7],[6]]=>[3,3,2] [[1,2,3,8],[4,5,7],[6]]=>[4,2,2] [[1,3,5,8],[2,4,6],[7]]=>[2,2,3,1] [[1,2,5,8],[3,4,6],[7]]=>[3,4,1] [[1,3,4,8],[2,5,6],[7]]=>[2,3,2,1] [[1,2,4,8],[3,5,6],[7]]=>[3,2,2,1] [[1,2,3,8],[4,5,6],[7]]=>[4,3,1] [[1,4,6,7],[2,5,8],[3]]=>[3,2,3] [[1,3,6,7],[2,5,8],[4]]=>[2,2,4] [[1,2,6,7],[3,5,8],[4]]=>[4,4] [[1,3,6,7],[2,4,8],[5]]=>[2,3,3] [[1,2,6,7],[3,4,8],[5]]=>[3,2,3] [[1,4,5,7],[2,6,8],[3]]=>[3,3,2] [[1,3,5,7],[2,6,8],[4]]=>[2,2,2,2] [[1,2,5,7],[3,6,8],[4]]=>[4,2,2] [[1,3,4,7],[2,6,8],[5]]=>[2,3,3] [[1,2,4,7],[3,6,8],[5]]=>[3,2,3] [[1,2,3,7],[4,6,8],[5]]=>[5,3] [[1,3,5,7],[2,4,8],[6]]=>[2,2,2,2] [[1,2,5,7],[3,4,8],[6]]=>[3,3,2] [[1,3,4,7],[2,5,8],[6]]=>[2,4,2] [[1,2,4,7],[3,5,8],[6]]=>[3,3,2] [[1,2,3,7],[4,5,8],[6]]=>[4,2,2] [[1,4,5,6],[2,7,8],[3]]=>[3,4,1] [[1,3,5,6],[2,7,8],[4]]=>[2,2,3,1] [[1,2,5,6],[3,7,8],[4]]=>[4,3,1] [[1,3,4,6],[2,7,8],[5]]=>[2,3,2,1] [[1,2,4,6],[3,7,8],[5]]=>[3,2,2,1] [[1,2,3,6],[4,7,8],[5]]=>[5,2,1] [[1,3,4,5],[2,7,8],[6]]=>[2,4,2] [[1,2,4,5],[3,7,8],[6]]=>[3,3,2] [[1,2,3,5],[4,7,8],[6]]=>[4,2,2] [[1,2,3,4],[5,7,8],[6]]=>[6,2] [[1,3,5,6],[2,4,8],[7]]=>[2,2,3,1] [[1,2,5,6],[3,4,8],[7]]=>[3,4,1] [[1,3,4,6],[2,5,8],[7]]=>[2,3,2,1] [[1,2,4,6],[3,5,8],[7]]=>[3,2,2,1] [[1,2,3,6],[4,5,8],[7]]=>[4,3,1] [[1,3,4,5],[2,6,8],[7]]=>[2,5,1] [[1,2,4,5],[3,6,8],[7]]=>[3,4,1] [[1,2,3,5],[4,6,8],[7]]=>[4,3,1] [[1,2,3,4],[5,6,8],[7]]=>[5,2,1] [[1,3,5,7],[2,4,6],[8]]=>[2,2,2,2] [[1,2,5,7],[3,4,6],[8]]=>[3,3,2] [[1,3,4,7],[2,5,6],[8]]=>[2,3,3] [[1,2,4,7],[3,5,6],[8]]=>[3,2,3] [[1,2,3,7],[4,5,6],[8]]=>[4,4] [[1,3,5,6],[2,4,7],[8]]=>[2,2,4] [[1,2,5,6],[3,4,7],[8]]=>[3,5] [[1,3,4,6],[2,5,7],[8]]=>[2,3,3] [[1,2,4,6],[3,5,7],[8]]=>[3,2,3] [[1,2,3,6],[4,5,7],[8]]=>[4,4] [[1,3,4,5],[2,6,7],[8]]=>[2,4,2] [[1,2,4,5],[3,6,7],[8]]=>[3,3,2] [[1,2,3,5],[4,6,7],[8]]=>[4,2,2] [[1,2,3,4],[5,6,7],[8]]=>[5,3] [[1,4,7,8],[2,5],[3,6]]=>[3,3,2] [[1,3,7,8],[2,5],[4,6]]=>[2,2,2,2] [[1,2,7,8],[3,5],[4,6]]=>[4,2,2] [[1,3,7,8],[2,4],[5,6]]=>[2,3,3] [[1,2,7,8],[3,4],[5,6]]=>[3,2,3] [[1,4,6,8],[2,5],[3,7]]=>[3,2,2,1] [[1,3,6,8],[2,5],[4,7]]=>[2,2,3,1] [[1,2,6,8],[3,5],[4,7]]=>[4,3,1] [[1,3,6,8],[2,4],[5,7]]=>[2,3,2,1] [[1,2,6,8],[3,4],[5,7]]=>[3,2,2,1] [[1,4,5,8],[2,6],[3,7]]=>[3,4,1] [[1,3,5,8],[2,6],[4,7]]=>[2,2,3,1] [[1,2,5,8],[3,6],[4,7]]=>[4,3,1] [[1,3,4,8],[2,6],[5,7]]=>[2,3,2,1] [[1,2,4,8],[3,6],[5,7]]=>[3,2,2,1] [[1,2,3,8],[4,6],[5,7]]=>[5,2,1] [[1,3,5,8],[2,4],[6,7]]=>[2,2,2,2] [[1,2,5,8],[3,4],[6,7]]=>[3,3,2] [[1,3,4,8],[2,5],[6,7]]=>[2,4,2] [[1,2,4,8],[3,5],[6,7]]=>[3,3,2] [[1,2,3,8],[4,5],[6,7]]=>[4,2,2] [[1,4,6,7],[2,5],[3,8]]=>[3,2,3] [[1,3,6,7],[2,5],[4,8]]=>[2,2,4] [[1,2,6,7],[3,5],[4,8]]=>[4,4] [[1,3,6,7],[2,4],[5,8]]=>[2,3,3] [[1,2,6,7],[3,4],[5,8]]=>[3,2,3] [[1,4,5,7],[2,6],[3,8]]=>[3,3,2] [[1,3,5,7],[2,6],[4,8]]=>[2,2,2,2] [[1,2,5,7],[3,6],[4,8]]=>[4,2,2] [[1,3,4,7],[2,6],[5,8]]=>[2,3,3] [[1,2,4,7],[3,6],[5,8]]=>[3,2,3] [[1,2,3,7],[4,6],[5,8]]=>[5,3] [[1,3,5,7],[2,4],[6,8]]=>[2,2,2,2] [[1,2,5,7],[3,4],[6,8]]=>[3,3,2] [[1,3,4,7],[2,5],[6,8]]=>[2,4,2] [[1,2,4,7],[3,5],[6,8]]=>[3,3,2] [[1,2,3,7],[4,5],[6,8]]=>[4,2,2] [[1,4,5,6],[2,7],[3,8]]=>[3,5] [[1,3,5,6],[2,7],[4,8]]=>[2,2,4] [[1,2,5,6],[3,7],[4,8]]=>[4,4] [[1,3,4,6],[2,7],[5,8]]=>[2,3,3] [[1,2,4,6],[3,7],[5,8]]=>[3,2,3] [[1,2,3,6],[4,7],[5,8]]=>[5,3] [[1,3,4,5],[2,7],[6,8]]=>[2,4,2] [[1,2,4,5],[3,7],[6,8]]=>[3,3,2] [[1,2,3,5],[4,7],[6,8]]=>[4,2,2] [[1,2,3,4],[5,7],[6,8]]=>[6,2] [[1,3,5,6],[2,4],[7,8]]=>[2,2,3,1] [[1,2,5,6],[3,4],[7,8]]=>[3,4,1] [[1,3,4,6],[2,5],[7,8]]=>[2,3,2,1] [[1,2,4,6],[3,5],[7,8]]=>[3,2,2,1] [[1,2,3,6],[4,5],[7,8]]=>[4,3,1] [[1,3,4,5],[2,6],[7,8]]=>[2,5,1] [[1,2,4,5],[3,6],[7,8]]=>[3,4,1] [[1,2,3,5],[4,6],[7,8]]=>[4,3,1] [[1,2,3,4],[5,6],[7,8]]=>[5,2,1] [[1,5,7,8],[2,6],[3],[4]]=>[4,2,2] [[1,4,7,8],[2,6],[3],[5]]=>[3,2,3] [[1,3,7,8],[2,6],[4],[5]]=>[2,3,3] [[1,2,7,8],[3,6],[4],[5]]=>[5,3] [[1,4,7,8],[2,5],[3],[6]]=>[3,3,2] [[1,3,7,8],[2,5],[4],[6]]=>[2,2,2,2] [[1,2,7,8],[3,5],[4],[6]]=>[4,2,2] [[1,3,7,8],[2,4],[5],[6]]=>[2,4,2] [[1,2,7,8],[3,4],[5],[6]]=>[3,3,2] [[1,5,6,8],[2,7],[3],[4]]=>[4,3,1] [[1,4,6,8],[2,7],[3],[5]]=>[3,2,2,1] [[1,3,6,8],[2,7],[4],[5]]=>[2,3,2,1] [[1,2,6,8],[3,7],[4],[5]]=>[5,2,1] [[1,4,5,8],[2,7],[3],[6]]=>[3,3,2] [[1,3,5,8],[2,7],[4],[6]]=>[2,2,2,2] [[1,2,5,8],[3,7],[4],[6]]=>[4,2,2] [[1,3,4,8],[2,7],[5],[6]]=>[2,4,2] [[1,2,4,8],[3,7],[5],[6]]=>[3,3,2] [[1,2,3,8],[4,7],[5],[6]]=>[6,2] [[1,4,6,8],[2,5],[3],[7]]=>[3,2,2,1] [[1,3,6,8],[2,5],[4],[7]]=>[2,2,3,1] [[1,2,6,8],[3,5],[4],[7]]=>[4,3,1] [[1,3,6,8],[2,4],[5],[7]]=>[2,3,2,1] [[1,2,6,8],[3,4],[5],[7]]=>[3,2,2,1] [[1,4,5,8],[2,6],[3],[7]]=>[3,4,1] [[1,3,5,8],[2,6],[4],[7]]=>[2,2,3,1] [[1,2,5,8],[3,6],[4],[7]]=>[4,3,1] [[1,3,4,8],[2,6],[5],[7]]=>[2,3,2,1] [[1,2,4,8],[3,6],[5],[7]]=>[3,2,2,1] [[1,2,3,8],[4,6],[5],[7]]=>[5,2,1] [[1,3,5,8],[2,4],[6],[7]]=>[2,2,3,1] [[1,2,5,8],[3,4],[6],[7]]=>[3,4,1] [[1,3,4,8],[2,5],[6],[7]]=>[2,5,1] [[1,2,4,8],[3,5],[6],[7]]=>[3,4,1] [[1,2,3,8],[4,5],[6],[7]]=>[4,3,1] [[1,5,6,7],[2,8],[3],[4]]=>[4,4] [[1,4,6,7],[2,8],[3],[5]]=>[3,2,3] [[1,3,6,7],[2,8],[4],[5]]=>[2,3,3] [[1,2,6,7],[3,8],[4],[5]]=>[5,3] [[1,4,5,7],[2,8],[3],[6]]=>[3,3,2] [[1,3,5,7],[2,8],[4],[6]]=>[2,2,2,2] [[1,2,5,7],[3,8],[4],[6]]=>[4,2,2] [[1,3,4,7],[2,8],[5],[6]]=>[2,4,2] [[1,2,4,7],[3,8],[5],[6]]=>[3,3,2] [[1,2,3,7],[4,8],[5],[6]]=>[6,2] [[1,4,5,6],[2,8],[3],[7]]=>[3,4,1] [[1,3,5,6],[2,8],[4],[7]]=>[2,2,3,1] [[1,2,5,6],[3,8],[4],[7]]=>[4,3,1] [[1,3,4,6],[2,8],[5],[7]]=>[2,3,2,1] [[1,2,4,6],[3,8],[5],[7]]=>[3,2,2,1] [[1,2,3,6],[4,8],[5],[7]]=>[5,2,1] [[1,3,4,5],[2,8],[6],[7]]=>[2,5,1] [[1,2,4,5],[3,8],[6],[7]]=>[3,4,1] [[1,2,3,5],[4,8],[6],[7]]=>[4,3,1] [[1,2,3,4],[5,8],[6],[7]]=>[7,1] [[1,4,6,7],[2,5],[3],[8]]=>[3,2,3] [[1,3,6,7],[2,5],[4],[8]]=>[2,2,4] [[1,2,6,7],[3,5],[4],[8]]=>[4,4] [[1,3,6,7],[2,4],[5],[8]]=>[2,3,3] [[1,2,6,7],[3,4],[5],[8]]=>[3,2,3] [[1,4,5,7],[2,6],[3],[8]]=>[3,3,2] [[1,3,5,7],[2,6],[4],[8]]=>[2,2,2,2] [[1,2,5,7],[3,6],[4],[8]]=>[4,2,2] [[1,3,4,7],[2,6],[5],[8]]=>[2,3,3] [[1,2,4,7],[3,6],[5],[8]]=>[3,2,3] [[1,2,3,7],[4,6],[5],[8]]=>[5,3] [[1,3,5,7],[2,4],[6],[8]]=>[2,2,2,2] [[1,2,5,7],[3,4],[6],[8]]=>[3,3,2] [[1,3,4,7],[2,5],[6],[8]]=>[2,4,2] [[1,2,4,7],[3,5],[6],[8]]=>[3,3,2] [[1,2,3,7],[4,5],[6],[8]]=>[4,2,2] [[1,4,5,6],[2,7],[3],[8]]=>[3,5] [[1,3,5,6],[2,7],[4],[8]]=>[2,2,4] [[1,2,5,6],[3,7],[4],[8]]=>[4,4] [[1,3,4,6],[2,7],[5],[8]]=>[2,3,3] [[1,2,4,6],[3,7],[5],[8]]=>[3,2,3] [[1,2,3,6],[4,7],[5],[8]]=>[5,3] [[1,3,4,5],[2,7],[6],[8]]=>[2,4,2] [[1,2,4,5],[3,7],[6],[8]]=>[3,3,2] [[1,2,3,5],[4,7],[6],[8]]=>[4,2,2] [[1,2,3,4],[5,7],[6],[8]]=>[6,2] [[1,3,5,6],[2,4],[7],[8]]=>[2,2,4] [[1,2,5,6],[3,4],[7],[8]]=>[3,5] [[1,3,4,6],[2,5],[7],[8]]=>[2,3,3] [[1,2,4,6],[3,5],[7],[8]]=>[3,2,3] [[1,2,3,6],[4,5],[7],[8]]=>[4,4] [[1,3,4,5],[2,6],[7],[8]]=>[2,6] [[1,2,4,5],[3,6],[7],[8]]=>[3,5] [[1,2,3,5],[4,6],[7],[8]]=>[4,4] [[1,2,3,4],[5,6],[7],[8]]=>[5,3] [[1,6,7,8],[2],[3],[4],[5]]=>[5,3] [[1,5,7,8],[2],[3],[4],[6]]=>[4,2,2] [[1,4,7,8],[2],[3],[5],[6]]=>[3,3,2] [[1,3,7,8],[2],[4],[5],[6]]=>[2,4,2] [[1,2,7,8],[3],[4],[5],[6]]=>[6,2] [[1,5,6,8],[2],[3],[4],[7]]=>[4,3,1] [[1,4,6,8],[2],[3],[5],[7]]=>[3,2,2,1] [[1,3,6,8],[2],[4],[5],[7]]=>[2,3,2,1] [[1,2,6,8],[3],[4],[5],[7]]=>[5,2,1] [[1,4,5,8],[2],[3],[6],[7]]=>[3,4,1] [[1,3,5,8],[2],[4],[6],[7]]=>[2,2,3,1] [[1,2,5,8],[3],[4],[6],[7]]=>[4,3,1] [[1,3,4,8],[2],[5],[6],[7]]=>[2,5,1] [[1,2,4,8],[3],[5],[6],[7]]=>[3,4,1] [[1,2,3,8],[4],[5],[6],[7]]=>[7,1] [[1,5,6,7],[2],[3],[4],[8]]=>[4,4] [[1,4,6,7],[2],[3],[5],[8]]=>[3,2,3] [[1,3,6,7],[2],[4],[5],[8]]=>[2,3,3] [[1,2,6,7],[3],[4],[5],[8]]=>[5,3] [[1,4,5,7],[2],[3],[6],[8]]=>[3,3,2] [[1,3,5,7],[2],[4],[6],[8]]=>[2,2,2,2] [[1,2,5,7],[3],[4],[6],[8]]=>[4,2,2] [[1,3,4,7],[2],[5],[6],[8]]=>[2,4,2] [[1,2,4,7],[3],[5],[6],[8]]=>[3,3,2] [[1,2,3,7],[4],[5],[6],[8]]=>[6,2] [[1,4,5,6],[2],[3],[7],[8]]=>[3,5] [[1,3,5,6],[2],[4],[7],[8]]=>[2,2,4] [[1,2,5,6],[3],[4],[7],[8]]=>[4,4] [[1,3,4,6],[2],[5],[7],[8]]=>[2,3,3] [[1,2,4,6],[3],[5],[7],[8]]=>[3,2,3] [[1,2,3,6],[4],[5],[7],[8]]=>[5,3] [[1,3,4,5],[2],[6],[7],[8]]=>[2,6] [[1,2,4,5],[3],[6],[7],[8]]=>[3,5] [[1,2,3,5],[4],[6],[7],[8]]=>[4,4] [[1,2,3,4],[5],[6],[7],[8]]=>[8] [[1,4,7],[2,5,8],[3,6]]=>[3,3,2] [[1,3,7],[2,5,8],[4,6]]=>[2,2,2,2] [[1,2,7],[3,5,8],[4,6]]=>[4,2,2] [[1,3,7],[2,4,8],[5,6]]=>[2,3,3] [[1,2,7],[3,4,8],[5,6]]=>[3,2,3] [[1,4,6],[2,5,8],[3,7]]=>[3,2,2,1] [[1,3,6],[2,5,8],[4,7]]=>[2,2,3,1] [[1,2,6],[3,5,8],[4,7]]=>[4,3,1] [[1,3,6],[2,4,8],[5,7]]=>[2,3,2,1] [[1,2,6],[3,4,8],[5,7]]=>[3,2,2,1] [[1,4,5],[2,6,8],[3,7]]=>[3,4,1] [[1,3,5],[2,6,8],[4,7]]=>[2,2,3,1] [[1,2,5],[3,6,8],[4,7]]=>[4,3,1] [[1,3,4],[2,6,8],[5,7]]=>[2,3,2,1] [[1,2,4],[3,6,8],[5,7]]=>[3,2,2,1] [[1,2,3],[4,6,8],[5,7]]=>[5,2,1] [[1,3,5],[2,4,8],[6,7]]=>[2,2,2,2] [[1,2,5],[3,4,8],[6,7]]=>[3,3,2] [[1,3,4],[2,5,8],[6,7]]=>[2,4,2] [[1,2,4],[3,5,8],[6,7]]=>[3,3,2] [[1,2,3],[4,5,8],[6,7]]=>[4,2,2] [[1,4,6],[2,5,7],[3,8]]=>[3,2,3] [[1,3,6],[2,5,7],[4,8]]=>[2,2,4] [[1,2,6],[3,5,7],[4,8]]=>[4,4] [[1,3,6],[2,4,7],[5,8]]=>[2,3,3] [[1,2,6],[3,4,7],[5,8]]=>[3,2,3] [[1,4,5],[2,6,7],[3,8]]=>[3,3,2] [[1,3,5],[2,6,7],[4,8]]=>[2,2,2,2] [[1,2,5],[3,6,7],[4,8]]=>[4,2,2] [[1,3,4],[2,6,7],[5,8]]=>[2,3,3] [[1,2,4],[3,6,7],[5,8]]=>[3,2,3] [[1,2,3],[4,6,7],[5,8]]=>[5,3] [[1,3,5],[2,4,7],[6,8]]=>[2,2,2,2] [[1,2,5],[3,4,7],[6,8]]=>[3,3,2] [[1,3,4],[2,5,7],[6,8]]=>[2,4,2] [[1,2,4],[3,5,7],[6,8]]=>[3,3,2] [[1,2,3],[4,5,7],[6,8]]=>[4,2,2] [[1,3,5],[2,4,6],[7,8]]=>[2,2,3,1] [[1,2,5],[3,4,6],[7,8]]=>[3,4,1] [[1,3,4],[2,5,6],[7,8]]=>[2,3,2,1] [[1,2,4],[3,5,6],[7,8]]=>[3,2,2,1] [[1,2,3],[4,5,6],[7,8]]=>[4,3,1] [[1,5,7],[2,6,8],[3],[4]]=>[4,2,2] [[1,4,7],[2,6,8],[3],[5]]=>[3,2,3] [[1,3,7],[2,6,8],[4],[5]]=>[2,3,3] [[1,2,7],[3,6,8],[4],[5]]=>[5,3] [[1,4,7],[2,5,8],[3],[6]]=>[3,3,2] [[1,3,7],[2,5,8],[4],[6]]=>[2,2,2,2] [[1,2,7],[3,5,8],[4],[6]]=>[4,2,2] [[1,3,7],[2,4,8],[5],[6]]=>[2,4,2] [[1,2,7],[3,4,8],[5],[6]]=>[3,3,2] [[1,5,6],[2,7,8],[3],[4]]=>[4,3,1] [[1,4,6],[2,7,8],[3],[5]]=>[3,2,2,1] [[1,3,6],[2,7,8],[4],[5]]=>[2,3,2,1] [[1,2,6],[3,7,8],[4],[5]]=>[5,2,1] [[1,4,5],[2,7,8],[3],[6]]=>[3,3,2] [[1,3,5],[2,7,8],[4],[6]]=>[2,2,2,2] [[1,2,5],[3,7,8],[4],[6]]=>[4,2,2] [[1,3,4],[2,7,8],[5],[6]]=>[2,4,2] [[1,2,4],[3,7,8],[5],[6]]=>[3,3,2] [[1,2,3],[4,7,8],[5],[6]]=>[6,2] [[1,4,6],[2,5,8],[3],[7]]=>[3,2,2,1] [[1,3,6],[2,5,8],[4],[7]]=>[2,2,3,1] [[1,2,6],[3,5,8],[4],[7]]=>[4,3,1] [[1,3,6],[2,4,8],[5],[7]]=>[2,3,2,1] [[1,2,6],[3,4,8],[5],[7]]=>[3,2,2,1] [[1,4,5],[2,6,8],[3],[7]]=>[3,4,1] [[1,3,5],[2,6,8],[4],[7]]=>[2,2,3,1] [[1,2,5],[3,6,8],[4],[7]]=>[4,3,1] [[1,3,4],[2,6,8],[5],[7]]=>[2,3,2,1] [[1,2,4],[3,6,8],[5],[7]]=>[3,2,2,1] [[1,2,3],[4,6,8],[5],[7]]=>[5,2,1] [[1,3,5],[2,4,8],[6],[7]]=>[2,2,3,1] [[1,2,5],[3,4,8],[6],[7]]=>[3,4,1] [[1,3,4],[2,5,8],[6],[7]]=>[2,5,1] [[1,2,4],[3,5,8],[6],[7]]=>[3,4,1] [[1,2,3],[4,5,8],[6],[7]]=>[4,3,1] [[1,4,6],[2,5,7],[3],[8]]=>[3,2,3] [[1,3,6],[2,5,7],[4],[8]]=>[2,2,4] [[1,2,6],[3,5,7],[4],[8]]=>[4,4] [[1,3,6],[2,4,7],[5],[8]]=>[2,3,3] [[1,2,6],[3,4,7],[5],[8]]=>[3,2,3] [[1,4,5],[2,6,7],[3],[8]]=>[3,3,2] [[1,3,5],[2,6,7],[4],[8]]=>[2,2,2,2] [[1,2,5],[3,6,7],[4],[8]]=>[4,2,2] [[1,3,4],[2,6,7],[5],[8]]=>[2,3,3] [[1,2,4],[3,6,7],[5],[8]]=>[3,2,3] [[1,2,3],[4,6,7],[5],[8]]=>[5,3] [[1,3,5],[2,4,7],[6],[8]]=>[2,2,2,2] [[1,2,5],[3,4,7],[6],[8]]=>[3,3,2] [[1,3,4],[2,5,7],[6],[8]]=>[2,4,2] [[1,2,4],[3,5,7],[6],[8]]=>[3,3,2] [[1,2,3],[4,5,7],[6],[8]]=>[4,2,2] [[1,3,5],[2,4,6],[7],[8]]=>[2,2,4] [[1,2,5],[3,4,6],[7],[8]]=>[3,5] [[1,3,4],[2,5,6],[7],[8]]=>[2,3,3] [[1,2,4],[3,5,6],[7],[8]]=>[3,2,3] [[1,2,3],[4,5,6],[7],[8]]=>[4,4] [[1,5,8],[2,6],[3,7],[4]]=>[4,3,1] [[1,4,8],[2,6],[3,7],[5]]=>[3,2,2,1] [[1,3,8],[2,6],[4,7],[5]]=>[2,3,2,1] [[1,2,8],[3,6],[4,7],[5]]=>[5,2,1] [[1,4,8],[2,5],[3,7],[6]]=>[3,3,2] [[1,3,8],[2,5],[4,7],[6]]=>[2,2,2,2] [[1,2,8],[3,5],[4,7],[6]]=>[4,2,2] [[1,3,8],[2,4],[5,7],[6]]=>[2,4,2] [[1,2,8],[3,4],[5,7],[6]]=>[3,3,2] [[1,4,8],[2,5],[3,6],[7]]=>[3,4,1] [[1,3,8],[2,5],[4,6],[7]]=>[2,2,3,1] [[1,2,8],[3,5],[4,6],[7]]=>[4,3,1] [[1,3,8],[2,4],[5,6],[7]]=>[2,3,2,1] [[1,2,8],[3,4],[5,6],[7]]=>[3,2,2,1] [[1,5,7],[2,6],[3,8],[4]]=>[4,2,2] [[1,4,7],[2,6],[3,8],[5]]=>[3,2,3] [[1,3,7],[2,6],[4,8],[5]]=>[2,3,3] [[1,2,7],[3,6],[4,8],[5]]=>[5,3] [[1,4,7],[2,5],[3,8],[6]]=>[3,3,2] [[1,3,7],[2,5],[4,8],[6]]=>[2,2,2,2] [[1,2,7],[3,5],[4,8],[6]]=>[4,2,2] [[1,3,7],[2,4],[5,8],[6]]=>[2,4,2] [[1,2,7],[3,4],[5,8],[6]]=>[3,3,2] [[1,5,6],[2,7],[3,8],[4]]=>[4,4] [[1,4,6],[2,7],[3,8],[5]]=>[3,2,3] [[1,3,6],[2,7],[4,8],[5]]=>[2,3,3] [[1,2,6],[3,7],[4,8],[5]]=>[5,3] [[1,4,5],[2,7],[3,8],[6]]=>[3,3,2] [[1,3,5],[2,7],[4,8],[6]]=>[2,2,2,2] [[1,2,5],[3,7],[4,8],[6]]=>[4,2,2] [[1,3,4],[2,7],[5,8],[6]]=>[2,4,2] [[1,2,4],[3,7],[5,8],[6]]=>[3,3,2] [[1,2,3],[4,7],[5,8],[6]]=>[6,2] [[1,4,6],[2,5],[3,8],[7]]=>[3,2,2,1] [[1,3,6],[2,5],[4,8],[7]]=>[2,2,3,1] [[1,2,6],[3,5],[4,8],[7]]=>[4,3,1] [[1,3,6],[2,4],[5,8],[7]]=>[2,3,2,1] [[1,2,6],[3,4],[5,8],[7]]=>[3,2,2,1] [[1,4,5],[2,6],[3,8],[7]]=>[3,4,1] [[1,3,5],[2,6],[4,8],[7]]=>[2,2,3,1] [[1,2,5],[3,6],[4,8],[7]]=>[4,3,1] [[1,3,4],[2,6],[5,8],[7]]=>[2,3,2,1] [[1,2,4],[3,6],[5,8],[7]]=>[3,2,2,1] [[1,2,3],[4,6],[5,8],[7]]=>[5,2,1] [[1,3,5],[2,4],[6,8],[7]]=>[2,2,3,1] [[1,2,5],[3,4],[6,8],[7]]=>[3,4,1] [[1,3,4],[2,5],[6,8],[7]]=>[2,5,1] [[1,2,4],[3,5],[6,8],[7]]=>[3,4,1] [[1,2,3],[4,5],[6,8],[7]]=>[4,3,1] [[1,4,7],[2,5],[3,6],[8]]=>[3,3,2] [[1,3,7],[2,5],[4,6],[8]]=>[2,2,2,2] [[1,2,7],[3,5],[4,6],[8]]=>[4,2,2] [[1,3,7],[2,4],[5,6],[8]]=>[2,3,3] [[1,2,7],[3,4],[5,6],[8]]=>[3,2,3] [[1,4,6],[2,5],[3,7],[8]]=>[3,2,3] [[1,3,6],[2,5],[4,7],[8]]=>[2,2,4] [[1,2,6],[3,5],[4,7],[8]]=>[4,4] [[1,3,6],[2,4],[5,7],[8]]=>[2,3,3] [[1,2,6],[3,4],[5,7],[8]]=>[3,2,3] [[1,4,5],[2,6],[3,7],[8]]=>[3,5] [[1,3,5],[2,6],[4,7],[8]]=>[2,2,4] [[1,2,5],[3,6],[4,7],[8]]=>[4,4] [[1,3,4],[2,6],[5,7],[8]]=>[2,3,3] [[1,2,4],[3,6],[5,7],[8]]=>[3,2,3] [[1,2,3],[4,6],[5,7],[8]]=>[5,3] [[1,3,5],[2,4],[6,7],[8]]=>[2,2,2,2] [[1,2,5],[3,4],[6,7],[8]]=>[3,3,2] [[1,3,4],[2,5],[6,7],[8]]=>[2,4,2] [[1,2,4],[3,5],[6,7],[8]]=>[3,3,2] [[1,2,3],[4,5],[6,7],[8]]=>[4,2,2] [[1,6,8],[2,7],[3],[4],[5]]=>[5,2,1] [[1,5,8],[2,7],[3],[4],[6]]=>[4,2,2] [[1,4,8],[2,7],[3],[5],[6]]=>[3,3,2] [[1,3,8],[2,7],[4],[5],[6]]=>[2,4,2] [[1,2,8],[3,7],[4],[5],[6]]=>[6,2] [[1,5,8],[2,6],[3],[4],[7]]=>[4,3,1] [[1,4,8],[2,6],[3],[5],[7]]=>[3,2,2,1] [[1,3,8],[2,6],[4],[5],[7]]=>[2,3,2,1] [[1,2,8],[3,6],[4],[5],[7]]=>[5,2,1] [[1,4,8],[2,5],[3],[6],[7]]=>[3,4,1] [[1,3,8],[2,5],[4],[6],[7]]=>[2,2,3,1] [[1,2,8],[3,5],[4],[6],[7]]=>[4,3,1] [[1,3,8],[2,4],[5],[6],[7]]=>[2,5,1] [[1,2,8],[3,4],[5],[6],[7]]=>[3,4,1] [[1,6,7],[2,8],[3],[4],[5]]=>[5,3] [[1,5,7],[2,8],[3],[4],[6]]=>[4,2,2] [[1,4,7],[2,8],[3],[5],[6]]=>[3,3,2] [[1,3,7],[2,8],[4],[5],[6]]=>[2,4,2] [[1,2,7],[3,8],[4],[5],[6]]=>[6,2] [[1,5,6],[2,8],[3],[4],[7]]=>[4,3,1] [[1,4,6],[2,8],[3],[5],[7]]=>[3,2,2,1] [[1,3,6],[2,8],[4],[5],[7]]=>[2,3,2,1] [[1,2,6],[3,8],[4],[5],[7]]=>[5,2,1] [[1,4,5],[2,8],[3],[6],[7]]=>[3,4,1] [[1,3,5],[2,8],[4],[6],[7]]=>[2,2,3,1] [[1,2,5],[3,8],[4],[6],[7]]=>[4,3,1] [[1,3,4],[2,8],[5],[6],[7]]=>[2,5,1] [[1,2,4],[3,8],[5],[6],[7]]=>[3,4,1] [[1,2,3],[4,8],[5],[6],[7]]=>[7,1] [[1,5,7],[2,6],[3],[4],[8]]=>[4,2,2] [[1,4,7],[2,6],[3],[5],[8]]=>[3,2,3] [[1,3,7],[2,6],[4],[5],[8]]=>[2,3,3] [[1,2,7],[3,6],[4],[5],[8]]=>[5,3] [[1,4,7],[2,5],[3],[6],[8]]=>[3,3,2] [[1,3,7],[2,5],[4],[6],[8]]=>[2,2,2,2] [[1,2,7],[3,5],[4],[6],[8]]=>[4,2,2] [[1,3,7],[2,4],[5],[6],[8]]=>[2,4,2] [[1,2,7],[3,4],[5],[6],[8]]=>[3,3,2] [[1,5,6],[2,7],[3],[4],[8]]=>[4,4] [[1,4,6],[2,7],[3],[5],[8]]=>[3,2,3] [[1,3,6],[2,7],[4],[5],[8]]=>[2,3,3] [[1,2,6],[3,7],[4],[5],[8]]=>[5,3] [[1,4,5],[2,7],[3],[6],[8]]=>[3,3,2] [[1,3,5],[2,7],[4],[6],[8]]=>[2,2,2,2] [[1,2,5],[3,7],[4],[6],[8]]=>[4,2,2] [[1,3,4],[2,7],[5],[6],[8]]=>[2,4,2] [[1,2,4],[3,7],[5],[6],[8]]=>[3,3,2] [[1,2,3],[4,7],[5],[6],[8]]=>[6,2] [[1,4,6],[2,5],[3],[7],[8]]=>[3,2,3] [[1,3,6],[2,5],[4],[7],[8]]=>[2,2,4] [[1,2,6],[3,5],[4],[7],[8]]=>[4,4] [[1,3,6],[2,4],[5],[7],[8]]=>[2,3,3] [[1,2,6],[3,4],[5],[7],[8]]=>[3,2,3] [[1,4,5],[2,6],[3],[7],[8]]=>[3,5] [[1,3,5],[2,6],[4],[7],[8]]=>[2,2,4] [[1,2,5],[3,6],[4],[7],[8]]=>[4,4] [[1,3,4],[2,6],[5],[7],[8]]=>[2,3,3] [[1,2,4],[3,6],[5],[7],[8]]=>[3,2,3] [[1,2,3],[4,6],[5],[7],[8]]=>[5,3] [[1,3,5],[2,4],[6],[7],[8]]=>[2,2,4] [[1,2,5],[3,4],[6],[7],[8]]=>[3,5] [[1,3,4],[2,5],[6],[7],[8]]=>[2,6] [[1,2,4],[3,5],[6],[7],[8]]=>[3,5] [[1,2,3],[4,5],[6],[7],[8]]=>[4,4] [[1,7,8],[2],[3],[4],[5],[6]]=>[6,2] [[1,6,8],[2],[3],[4],[5],[7]]=>[5,2,1] [[1,5,8],[2],[3],[4],[6],[7]]=>[4,3,1] [[1,4,8],[2],[3],[5],[6],[7]]=>[3,4,1] [[1,3,8],[2],[4],[5],[6],[7]]=>[2,5,1] [[1,2,8],[3],[4],[5],[6],[7]]=>[7,1] [[1,6,7],[2],[3],[4],[5],[8]]=>[5,3] [[1,5,7],[2],[3],[4],[6],[8]]=>[4,2,2] [[1,4,7],[2],[3],[5],[6],[8]]=>[3,3,2] [[1,3,7],[2],[4],[5],[6],[8]]=>[2,4,2] [[1,2,7],[3],[4],[5],[6],[8]]=>[6,2] [[1,5,6],[2],[3],[4],[7],[8]]=>[4,4] [[1,4,6],[2],[3],[5],[7],[8]]=>[3,2,3] [[1,3,6],[2],[4],[5],[7],[8]]=>[2,3,3] [[1,2,6],[3],[4],[5],[7],[8]]=>[5,3] [[1,4,5],[2],[3],[6],[7],[8]]=>[3,5] [[1,3,5],[2],[4],[6],[7],[8]]=>[2,2,4] [[1,2,5],[3],[4],[6],[7],[8]]=>[4,4] [[1,3,4],[2],[5],[6],[7],[8]]=>[2,6] [[1,2,4],[3],[5],[6],[7],[8]]=>[3,5] [[1,2,3],[4],[5],[6],[7],[8]]=>[8] [[1,5],[2,6],[3,7],[4,8]]=>[4,4] [[1,4],[2,6],[3,7],[5,8]]=>[3,2,3] [[1,3],[2,6],[4,7],[5,8]]=>[2,3,3] [[1,2],[3,6],[4,7],[5,8]]=>[5,3] [[1,4],[2,5],[3,7],[6,8]]=>[3,3,2] [[1,3],[2,5],[4,7],[6,8]]=>[2,2,2,2] [[1,2],[3,5],[4,7],[6,8]]=>[4,2,2] [[1,3],[2,4],[5,7],[6,8]]=>[2,4,2] [[1,2],[3,4],[5,7],[6,8]]=>[3,3,2] [[1,4],[2,5],[3,6],[7,8]]=>[3,4,1] [[1,3],[2,5],[4,6],[7,8]]=>[2,2,3,1] [[1,2],[3,5],[4,6],[7,8]]=>[4,3,1] [[1,3],[2,4],[5,6],[7,8]]=>[2,3,2,1] [[1,2],[3,4],[5,6],[7,8]]=>[3,2,2,1] [[1,6],[2,7],[3,8],[4],[5]]=>[5,3] [[1,5],[2,7],[3,8],[4],[6]]=>[4,2,2] [[1,4],[2,7],[3,8],[5],[6]]=>[3,3,2] [[1,3],[2,7],[4,8],[5],[6]]=>[2,4,2] [[1,2],[3,7],[4,8],[5],[6]]=>[6,2] [[1,5],[2,6],[3,8],[4],[7]]=>[4,3,1] [[1,4],[2,6],[3,8],[5],[7]]=>[3,2,2,1] [[1,3],[2,6],[4,8],[5],[7]]=>[2,3,2,1] [[1,2],[3,6],[4,8],[5],[7]]=>[5,2,1] [[1,4],[2,5],[3,8],[6],[7]]=>[3,4,1] [[1,3],[2,5],[4,8],[6],[7]]=>[2,2,3,1] [[1,2],[3,5],[4,8],[6],[7]]=>[4,3,1] [[1,3],[2,4],[5,8],[6],[7]]=>[2,5,1] [[1,2],[3,4],[5,8],[6],[7]]=>[3,4,1] [[1,5],[2,6],[3,7],[4],[8]]=>[4,4] [[1,4],[2,6],[3,7],[5],[8]]=>[3,2,3] [[1,3],[2,6],[4,7],[5],[8]]=>[2,3,3] [[1,2],[3,6],[4,7],[5],[8]]=>[5,3] [[1,4],[2,5],[3,7],[6],[8]]=>[3,3,2] [[1,3],[2,5],[4,7],[6],[8]]=>[2,2,2,2] [[1,2],[3,5],[4,7],[6],[8]]=>[4,2,2] [[1,3],[2,4],[5,7],[6],[8]]=>[2,4,2] [[1,2],[3,4],[5,7],[6],[8]]=>[3,3,2] [[1,4],[2,5],[3,6],[7],[8]]=>[3,5] [[1,3],[2,5],[4,6],[7],[8]]=>[2,2,4] [[1,2],[3,5],[4,6],[7],[8]]=>[4,4] [[1,3],[2,4],[5,6],[7],[8]]=>[2,3,3] [[1,2],[3,4],[5,6],[7],[8]]=>[3,2,3] [[1,7],[2,8],[3],[4],[5],[6]]=>[6,2] [[1,6],[2,8],[3],[4],[5],[7]]=>[5,2,1] [[1,5],[2,8],[3],[4],[6],[7]]=>[4,3,1] [[1,4],[2,8],[3],[5],[6],[7]]=>[3,4,1] [[1,3],[2,8],[4],[5],[6],[7]]=>[2,5,1] [[1,2],[3,8],[4],[5],[6],[7]]=>[7,1] [[1,6],[2,7],[3],[4],[5],[8]]=>[5,3] [[1,5],[2,7],[3],[4],[6],[8]]=>[4,2,2] [[1,4],[2,7],[3],[5],[6],[8]]=>[3,3,2] [[1,3],[2,7],[4],[5],[6],[8]]=>[2,4,2] [[1,2],[3,7],[4],[5],[6],[8]]=>[6,2] [[1,5],[2,6],[3],[4],[7],[8]]=>[4,4] [[1,4],[2,6],[3],[5],[7],[8]]=>[3,2,3] [[1,3],[2,6],[4],[5],[7],[8]]=>[2,3,3] [[1,2],[3,6],[4],[5],[7],[8]]=>[5,3] [[1,4],[2,5],[3],[6],[7],[8]]=>[3,5] [[1,3],[2,5],[4],[6],[7],[8]]=>[2,2,4] [[1,2],[3,5],[4],[6],[7],[8]]=>[4,4] [[1,3],[2,4],[5],[6],[7],[8]]=>[2,6] [[1,2],[3,4],[5],[6],[7],[8]]=>[3,5] [[1,8],[2],[3],[4],[5],[6],[7]]=>[7,1] [[1,7],[2],[3],[4],[5],[6],[8]]=>[6,2] [[1,6],[2],[3],[4],[5],[7],[8]]=>[5,3] [[1,5],[2],[3],[4],[6],[7],[8]]=>[4,4] [[1,4],[2],[3],[5],[6],[7],[8]]=>[3,5] [[1,3],[2],[4],[5],[6],[7],[8]]=>[2,6] [[1,2],[3],[4],[5],[6],[7],[8]]=>[8] [[1],[2],[3],[4],[5],[6],[7],[8]]=>[8] [[1,2,3,4,5,6,7,8,9]]=>[9] [[1,2,3,4,5,6,7,8],[9]]=>[9] [[1,2,3,4,5,6,7],[8,9]]=>[8,1] [[1,2,3,4,5,6,7],[8],[9]]=>[9] [[1,2,3,4,5,6],[7,8,9]]=>[7,2] [[1,2,3,4,5,6],[7,8],[9]]=>[7,2] [[1,2,3,4,5,6],[7],[8],[9]]=>[9] [[1,2,3,4,5],[6,7,8,9]]=>[6,3] [[1,2,3,4,5],[6,7,8],[9]]=>[6,3] [[1,2,3,4,5],[6,7],[8,9]]=>[6,2,1] [[1,2,3,4,5],[6,7],[8],[9]]=>[6,3] [[1,2,3,4,5],[6],[7],[8],[9]]=>[9] [[1,2,3,4],[5,6,7,8],[9]]=>[5,4] [[1,2,3,4],[5,6,7],[8,9]]=>[5,3,1] [[1,2,3,4],[5,6,7],[8],[9]]=>[5,4] [[1,2,3,4],[5,6],[7,8],[9]]=>[5,2,2] [[1,2,3,4],[5,6],[7],[8],[9]]=>[5,4] [[1,2,3,4],[5],[6],[7],[8],[9]]=>[9] [[1,2,3],[4,5,6],[7,8,9]]=>[4,3,2] [[1,2,3],[4,5,6],[7,8],[9]]=>[4,3,2] [[1,2,3],[4,5,6],[7],[8],[9]]=>[4,5] [[1,2,3],[4,5],[6,7],[8,9]]=>[4,2,2,1] [[1,2,3],[4,5],[6,7],[8],[9]]=>[4,2,3] [[1,2,3],[4,5],[6],[7],[8],[9]]=>[4,5] [[1,2,3],[4],[5],[6],[7],[8],[9]]=>[9] [[1,2],[3,4],[5,6],[7,8],[9]]=>[3,2,2,2] [[1,2],[3,4],[5,6],[7],[8],[9]]=>[3,2,4] [[1,2],[3,4],[5],[6],[7],[8],[9]]=>[3,6] [[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[9] [[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9] [[1,3,4,5,6,7,8,9],[2]]=>[2,7] [[1,2,5,6,7,8,9],[3,4]]=>[3,6] [[1,4,5,6,7,8,9],[2],[3]]=>[3,6] [[1,2,3,7,8,9],[4,5,6]]=>[4,5] [[1,3,6,7,8,9],[2,5],[4]]=>[2,2,5] [[1,5,6,7,8,9],[2],[3],[4]]=>[4,5] [[1,2,3,4,9],[5,6,7,8]]=>[5,4] [[1,3,4,8,9],[2,6,7],[5]]=>[2,3,4] [[1,2,7,8,9],[3,4],[5,6]]=>[3,2,4] [[1,4,7,8,9],[2,6],[3],[5]]=>[3,2,4] [[1,6,7,8,9],[2],[3],[4],[5]]=>[5,4] [[1,3,4,5],[2,7,8,9],[6]]=>[2,4,3] [[1,2,5,9],[3,4,8],[6,7]]=>[3,3,3] [[1,4,5,9],[2,7,8],[3],[6]]=>[3,3,3] [[1,3,8,9],[2,5],[4,7],[6]]=>[2,2,2,3] [[1,5,8,9],[2,7],[3],[4],[6]]=>[4,2,3] [[1,7,8,9],[2],[3],[4],[5],[6]]=>[6,3] [[1,3,6],[2,5,9],[4,8],[7]]=>[2,2,3,2] [[1,5,6],[2,8,9],[3],[4],[7]]=>[4,3,2] [[1,2,9],[3,4],[5,6],[7,8]]=>[3,2,2,2] [[1,4,9],[2,6],[3,8],[5],[7]]=>[3,2,2,2] [[1,6,9],[2,8],[3],[4],[5],[7]]=>[5,2,2] [[1,8,9],[2],[3],[4],[5],[6],[7]]=>[7,2] [[1,3],[2,5],[4,7],[6,9],[8]]=>[2,2,2,2,1] [[1,5],[2,7],[3,9],[4],[6],[8]]=>[4,2,2,1] [[1,7],[2,9],[3],[4],[5],[6],[8]]=>[6,2,1] [[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[8,1] [[1,4,7],[2,5,8],[3,6,9]]=>[3,3,3] [[1,2,3,4,5,6,7,9],[8]]=>[8,1] [[1,2,3,4,5,6,9],[7,8]]=>[7,2] [[1,2,3,4,5,6,9],[7],[8]]=>[8,1] [[1,2,3,4,5,9],[6,7,8]]=>[6,3] [[1,2,3,4,5,9],[6,7],[8]]=>[6,2,1] [[1,2,3,4,5,9],[6],[7],[8]]=>[8,1] [[1,2,3,4,9],[5,6,7],[8]]=>[5,3,1] [[1,2,3,4,9],[5,6],[7,8]]=>[5,2,2] [[1,2,3,4,9],[5,6],[7],[8]]=>[5,3,1] [[1,2,3,4,9],[5],[6],[7],[8]]=>[8,1] [[1,2,3,7],[4,5,6,9],[8]]=>[4,4,1] [[1,2,3,9],[4,5,6],[7,8]]=>[4,3,2] [[1,2,3,9],[4,5,6],[7],[8]]=>[4,4,1] [[1,2,3,9],[4,5],[6,7],[8]]=>[4,2,2,1] [[1,2,3,9],[4,5],[6],[7],[8]]=>[4,4,1] [[1,2,3,9],[4],[5],[6],[7],[8]]=>[8,1] [[1,2,5],[3,4,8],[6,7,9]]=>[3,3,3] [[1,2,5],[3,4,9],[6,7],[8]]=>[3,3,2,1] [[1,2,5],[3,4,9],[6],[7],[8]]=>[3,5,1] [[1,2,9],[3,4],[5,6],[7],[8]]=>[3,2,3,1] [[1,2,9],[3,4],[5],[6],[7],[8]]=>[3,5,1] [[1,2,9],[3],[4],[5],[6],[7],[8]]=>[8,1] [[1,3],[2,5],[4,9],[6],[7],[8]]=>[2,2,4,1] [[1,3],[2,9],[4],[5],[6],[7],[8]]=>[2,6,1] [[1,2,4,5,6,7,8,9],[3]]=>[3,6] [[1,3,4,6,7,8,9],[2,5]]=>[2,3,4] [[1,3,5,6,7,8,9],[2],[4]]=>[2,2,5] [[1,3,5,6,8,9],[2,4,7]]=>[2,2,3,2] [[1,2,4,7,8,9],[3,5],[6]]=>[3,3,3] [[1,4,6,7,8,9],[2],[3],[5]]=>[3,2,4] [[1,3,5,7,8],[2,4,6,9]]=>[2,2,2,3] [[1,2,5,7,9],[3,6,8],[4]]=>[4,2,2,1] [[1,4,6,8,9],[2,5],[3,7]]=>[3,2,2,2] [[1,3,5,8,9],[2,6],[4],[7]]=>[2,2,3,2] [[1,5,7,8,9],[2],[3],[4],[6]]=>[4,2,3] [[1,2,5,6],[3,7,8,9],[4]]=>[4,3,2] [[1,3,4,7],[2,6,8],[5,9]]=>[2,3,4] [[1,3,6,8],[2,7,9],[4],[5]]=>[2,3,2,2] [[1,2,6,9],[3,4],[5,7],[8]]=>[3,2,3,1] [[1,4,6,9],[2,7],[3],[5],[8]]=>[3,2,3,1] [[1,6,8,9],[2],[3],[4],[5],[7]]=>[5,2,2] [[1,2,4],[3,5,7],[6,8],[9]]=>[3,3,3] [[1,4,7],[2,8,9],[3],[5],[6]]=>[3,3,2,1] [[1,5,8],[2,6],[3,7],[4,9]]=>[4,3,2] [[1,3,7],[2,5],[4,8],[6],[9]]=>[2,2,2,3] [[1,5,7],[2,8],[3],[4],[6],[9]]=>[4,2,3] [[1,7,9],[2],[3],[4],[5],[6],[8]]=>[6,2,1] [[1,4],[2,6],[3,8],[5],[7],[9]]=>[3,2,2,2] [[1,6],[2,8],[3],[4],[5],[7],[9]]=>[5,2,2] [[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[7,2] [[1,3,4,5,6,7,8],[2,9]]=>[2,7] [[1,3,4,5,6,7,8],[2],[9]]=>[2,7] [[1,3,4,5,6,7],[2,8,9]]=>[2,6,1] [[1,3,4,5,6,7],[2,9],[8]]=>[2,6,1] [[1,3,4,5,6,7],[2],[8],[9]]=>[2,7] [[1,3,4,5,6],[2,7,8,9]]=>[2,5,2] [[1,3,4,5,6],[2,8,9],[7]]=>[2,5,2] [[1,3,4,5,6],[2,8],[7,9]]=>[2,5,2] [[1,3,4,5,6],[2,8],[7],[9]]=>[2,5,2] [[1,3,4,5,6],[2],[7],[8],[9]]=>[2,7] [[1,3,4,5],[2,7,8],[6,9]]=>[2,4,3] [[1,3,4,5],[2,7,8],[6],[9]]=>[2,4,3] [[1,3,4,5],[2,7],[6,9],[8]]=>[2,4,2,1] [[1,3,4,5],[2,7],[6],[8],[9]]=>[2,4,3] [[1,3,4,5],[2],[6],[7],[8],[9]]=>[2,7] [[1,3,4],[2,6,7],[5,8,9]]=>[2,3,3,1] [[1,3,4],[2,6,7],[5,9],[8]]=>[2,3,3,1] [[1,3,4],[2,6,7],[5],[8],[9]]=>[2,3,4] [[1,3,4],[2,6],[5,8],[7,9]]=>[2,3,2,2] [[1,3,4],[2,6],[5,8],[7],[9]]=>[2,3,2,2] [[1,3,4],[2,6],[5],[7],[8],[9]]=>[2,3,4] [[1,3,4],[2],[5],[6],[7],[8],[9]]=>[2,7] [[1,3],[2,5],[4,7],[6],[8],[9]]=>[2,2,2,3] [[1,3],[2,5],[4],[6],[7],[8],[9]]=>[2,2,5] [[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[2,7] [[1,2,5,6,7,8],[3,4,9]]=>[3,6] [[1,2,5,6,7,8],[3,4],[9]]=>[3,6] [[1,4,5,6,7,8],[2],[3],[9]]=>[3,6] [[1,2,3,7,8],[4,5,6,9]]=>[4,5] [[1,2,3,7,8],[4,5,6],[9]]=>[4,5] [[1,3,6,7,8],[2,5],[4,9]]=>[2,2,5] [[1,3,6,7,8],[2,5],[4],[9]]=>[2,2,5] [[1,5,6,7,8],[2],[3],[4],[9]]=>[4,5] [[1,3,4,8],[2,6,7],[5,9]]=>[2,3,4] [[1,3,4,8],[2,6,7],[5],[9]]=>[2,3,4] [[1,2,7,8],[3,4],[5,6],[9]]=>[3,2,4] [[1,4,7,8],[2,6],[3],[5],[9]]=>[3,2,4] [[1,6,7,8],[2],[3],[4],[5],[9]]=>[5,4] [[1,2,5],[3,4,8],[6,7],[9]]=>[3,3,3] [[1,4,5],[2,7,8],[3],[6],[9]]=>[3,3,3] [[1,3,8],[2,5],[4,7],[6,9]]=>[2,2,2,3] [[1,3,8],[2,5],[4,7],[6],[9]]=>[2,2,2,3] [[1,5,8],[2,7],[3],[4],[6],[9]]=>[4,2,3] [[1,7,8],[2],[3],[4],[5],[6],[9]]=>[6,3] [[1,2,3,6,7,8,9],[4,5]]=>[4,5] [[1,2,5,6,7,8,9],[3],[4]]=>[4,5] [[1,2,3,4,8,9],[5,6,7]]=>[5,4] [[1,2,4,7,8,9],[3,6],[5]]=>[3,2,4] [[1,2,6,7,8,9],[3],[4],[5]]=>[5,4] [[1,2,4,5,9],[3,7,8],[6]]=>[3,3,3] [[1,2,3,8,9],[4,5],[6,7]]=>[4,2,3] [[1,2,5,8,9],[3,7],[4],[6]]=>[4,2,3] [[1,2,7,8,9],[3],[4],[5],[6]]=>[6,3] [[1,2,5,6],[3,4,8,9],[7]]=>[3,4,2] [[1,2,3,6],[4,5,9],[7,8]]=>[4,3,2] [[1,2,5,6],[3,8,9],[4],[7]]=>[4,3,2] [[1,2,4,9],[3,6],[5,8],[7]]=>[3,2,2,2] [[1,2,6,9],[3,8],[4],[5],[7]]=>[5,2,2] [[1,2,8,9],[3],[4],[5],[6],[7]]=>[7,2] [[1,2,4],[3,6,7],[5,9],[8]]=>[3,2,3,1] [[1,2,7],[3,6,9],[4],[5],[8]]=>[5,3,1] [[1,2,5],[3,7],[4,9],[6],[8]]=>[4,2,2,1] [[1,2,7],[3,9],[4],[5],[6],[8]]=>[6,2,1] [[1,2],[3,6],[4,8],[5],[7],[9]]=>[5,2,2] [[1,2],[3,8],[4],[5],[6],[7],[9]]=>[7,2] [[1,2,3,4,7,8,9],[5,6]]=>[5,4] [[1,2,4,5,8,9],[3,7],[6]]=>[3,3,3] [[1,2,4,5,6,7],[3,9],[8]]=>[3,5,1] [[1,2,5,6,9],[3,8],[4],[7]]=>[4,3,2] [[1,2,3,4,7,8],[5,6],[9]]=>[5,4] [[1,2,5,6,7,8],[3],[4],[9]]=>[4,5] [[1,2,4,5],[3,7],[6,9],[8]]=>[3,3,2,1] [[1,2,6,7],[3,9],[4],[5],[8]]=>[5,3,1] [[1,2,5,6],[3,8],[4],[7],[9]]=>[4,3,2] [[1,2,7,8],[3],[4],[5],[6],[9]]=>[6,3] [[1,3,5,7,9],[2,4,6,8,10]]=>[2,2,2,2,2] [[1,3,5,7,8],[2,4,6,9,10]]=>[2,2,2,3,1] [[1,3,5,6,9],[2,4,7,8,10]]=>[2,2,3,3] [[1,3,5,6,8],[2,4,7,9,10]]=>[2,2,3,2,1] [[1,3,5,6,7],[2,4,8,9,10]]=>[2,2,4,2] [[1,3,4,7,9],[2,5,6,8,10]]=>[2,3,3,2] [[1,3,4,7,8],[2,5,6,9,10]]=>[2,3,4,1] [[1,3,4,6,9],[2,5,7,8,10]]=>[2,3,2,3] [[1,3,4,6,8],[2,5,7,9,10]]=>[2,3,2,2,1] [[1,3,4,6,7],[2,5,8,9,10]]=>[2,3,3,2] [[1,3,4,5,9],[2,6,7,8,10]]=>[2,4,4] [[1,3,4,5,8],[2,6,7,9,10]]=>[2,4,3,1] [[1,3,4,5,7],[2,6,8,9,10]]=>[2,4,2,2] [[1,3,4,5,6],[2,7,8,9,10]]=>[2,5,3] [[1,2,5,7,9],[3,4,6,8,10]]=>[3,3,2,2] [[1,2,5,7,8],[3,4,6,9,10]]=>[3,3,3,1] [[1,2,5,6,9],[3,4,7,8,10]]=>[3,4,3] [[1,2,5,6,8],[3,4,7,9,10]]=>[3,4,2,1] [[1,2,5,6,7],[3,4,8,9,10]]=>[3,5,2] [[1,2,4,7,9],[3,5,6,8,10]]=>[3,2,3,2] [[1,2,4,7,8],[3,5,6,9,10]]=>[3,2,4,1] [[1,2,4,6,9],[3,5,7,8,10]]=>[3,2,2,3] [[1,2,4,6,8],[3,5,7,9,10]]=>[3,2,2,2,1] [[1,2,4,6,7],[3,5,8,9,10]]=>[3,2,3,2] [[1,2,4,5,9],[3,6,7,8,10]]=>[3,3,4] [[1,2,4,5,8],[3,6,7,9,10]]=>[3,3,3,1] [[1,2,4,5,7],[3,6,8,9,10]]=>[3,3,2,2] [[1,2,4,5,6],[3,7,8,9,10]]=>[3,4,3] [[1,2,3,7,9],[4,5,6,8,10]]=>[4,4,2] [[1,2,3,7,8],[4,5,6,9,10]]=>[4,5,1] [[1,2,3,6,9],[4,5,7,8,10]]=>[4,3,3] [[1,2,3,6,8],[4,5,7,9,10]]=>[4,3,2,1] [[1,2,3,6,7],[4,5,8,9,10]]=>[4,4,2] [[1,2,3,5,9],[4,6,7,8,10]]=>[4,2,4] [[1,2,3,5,8],[4,6,7,9,10]]=>[4,2,3,1] [[1,2,3,5,7],[4,6,8,9,10]]=>[4,2,2,2] [[1,2,3,5,6],[4,7,8,9,10]]=>[4,3,3] [[1,2,3,4,9],[5,6,7,8,10]]=>[5,5] [[1,2,3,4,8],[5,6,7,9,10]]=>[5,4,1] [[1,2,3,4,7],[5,6,8,9,10]]=>[5,3,2] [[1,2,3,4,6],[5,7,8,9,10]]=>[5,2,3] [[1,2,3,4,5],[6,7,8,9,10]]=>[6,4] [[1,2,3,4,5,6,7,8,9,10]]=>[10] [[1,2,3,4,5,6,7,8,9],[10]]=>[10] [[1,2,3,4,5,6,7,8],[9,10]]=>[9,1] [[1,2,3,4,5,6,7,8],[9],[10]]=>[10] [[1,2,3,4,5,6,7],[8,9,10]]=>[8,2] [[1,2,3,4,5,6,7],[8,9],[10]]=>[8,2] [[1,2,3,4,5,6,7],[8],[9],[10]]=>[10] [[1,2,3,4,5,6],[7,8,9,10]]=>[7,3] [[1,2,3,4,5,6],[7,8,9],[10]]=>[7,3] [[1,2,3,4,5,6],[7,8],[9,10]]=>[7,2,1] [[1,2,3,4,5,6],[7,8],[9],[10]]=>[7,3] [[1,2,3,4,5,6],[7],[8],[9],[10]]=>[10] [[1,2,3,4,5],[6,7,8,9],[10]]=>[6,4] [[1,2,3,4,5],[6,7,8],[9,10]]=>[6,3,1] [[1,2,3,4,5],[6,7,8],[9],[10]]=>[6,4] [[1,2,3,4,5],[6,7],[8,9],[10]]=>[6,2,2] [[1,2,3,4,5],[6,7],[8],[9],[10]]=>[6,4] [[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[10] [[1,2,3,4],[5,6,7,8],[9,10]]=>[5,4,1] [[1,2,3,4],[5,6,7,8],[9],[10]]=>[5,5] [[1,2,3,4],[5,6,7],[8,9,10]]=>[5,3,2] [[1,2,3,4],[5,6,7],[8,9],[10]]=>[5,3,2] [[1,2,3,4],[5,6,7],[8],[9],[10]]=>[5,5] [[1,2,3,4],[5,6],[7,8],[9,10]]=>[5,2,2,1] [[1,2,3,4],[5,6],[7,8],[9],[10]]=>[5,2,3] [[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[5,5] [[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[10] [[1,2,3],[4,5,6],[7,8,9],[10]]=>[4,3,3] [[1,2,3],[4,5,6],[7,8],[9,10]]=>[4,3,2,1] [[1,2,3],[4,5,6],[7,8],[9],[10]]=>[4,3,3] [[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[4,6] [[1,2,3],[4,5],[6,7],[8,9],[10]]=>[4,2,2,2] [[1,2,3],[4,5],[6,7],[8],[9],[10]]=>[4,2,4] [[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[4,6] [[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[10] [[1,2],[3,4],[5,6],[7,8],[9,10]]=>[3,2,2,2,1] [[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[3,2,2,3] [[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>[3,2,5] [[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[3,7] [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10] [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10] [[1,3,4,5,6,7,8,9,10],[2]]=>[2,8] [[1,2,5,6,7,8,9,10],[3,4]]=>[3,7] [[1,4,5,6,7,8,9,10],[2],[3]]=>[3,7] [[1,2,3,7,8,9,10],[4,5,6]]=>[4,6] [[1,3,6,7,8,9,10],[2,5],[4]]=>[2,2,6] [[1,5,6,7,8,9,10],[2],[3],[4]]=>[4,6] [[1,2,3,4,9,10],[5,6,7,8]]=>[5,5] [[1,3,4,8,9,10],[2,6,7],[5]]=>[2,3,5] [[1,2,7,8,9,10],[3,4],[5,6]]=>[3,2,5] [[1,4,7,8,9,10],[2,6],[3],[5]]=>[3,2,5] [[1,6,7,8,9,10],[2],[3],[4],[5]]=>[5,5] [[1,3,4,5,10],[2,7,8,9],[6]]=>[2,4,4] [[1,2,5,9,10],[3,4,8],[6,7]]=>[3,3,4] [[1,4,5,9,10],[2,7,8],[3],[6]]=>[3,3,4] [[1,3,8,9,10],[2,5],[4,7],[6]]=>[2,2,2,4] [[1,5,8,9,10],[2,7],[3],[4],[6]]=>[4,2,4] [[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[6,4] [[1,2,5,6],[3,4,9,10],[7,8]]=>[3,4,3] [[1,4,5,6],[2,8,9,10],[3],[7]]=>[3,4,3] [[1,2,3,10],[4,5,6],[7,8,9]]=>[4,3,3] [[1,3,6,10],[2,5,9],[4,8],[7]]=>[2,2,3,3] [[1,5,6,10],[2,8,9],[3],[4],[7]]=>[4,3,3] [[1,2,9,10],[3,4],[5,6],[7,8]]=>[3,2,2,3] [[1,4,9,10],[2,6],[3,8],[5],[7]]=>[3,2,2,3] [[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[5,2,3] [[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[7,3] [[1,3,4],[2,6,7],[5,9,10],[8]]=>[2,3,3,2] [[1,2,7],[3,4,10],[5,6],[8,9]]=>[3,2,3,2] [[1,4,7],[2,6,10],[3,9],[5],[8]]=>[3,2,3,2] [[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[5,3,2] [[1,3,10],[2,5],[4,7],[6,9],[8]]=>[2,2,2,2,2] [[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[4,2,2,2] [[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>[6,2,2] [[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[8,2] [[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[3,2,2,2,1] [[1,6],[2,8],[3,10],[4],[5],[7],[9]]=>[5,2,2,1] [[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[7,2,1] [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,1] [[1,6],[2,7],[3,8],[4,9],[5,10]]=>[5,5] [[1,2,4,7],[3,5,8],[6,9],[10]]=>[3,3,4] [[1,3],[2,5],[4,7],[6,9],[8,10]]=>[2,2,2,2,2] [[1,2,3,4,5,6,7,8,10],[9]]=>[9,1] [[1,2,3,4,5,6,7,10],[8,9]]=>[8,2] [[1,2,3,4,5,6,7,10],[8],[9]]=>[9,1] [[1,2,3,4,5,6,10],[7,8,9]]=>[7,3] [[1,2,3,4,5,6,10],[7,8],[9]]=>[7,2,1] [[1,2,3,4,5,6,10],[7],[8],[9]]=>[9,1] [[1,2,3,4,5,10],[6,7,8,9]]=>[6,4] [[1,2,3,4,5,10],[6,7,8],[9]]=>[6,3,1] [[1,2,3,4,5,10],[6,7],[8,9]]=>[6,2,2] [[1,2,3,4,5,10],[6,7],[8],[9]]=>[6,3,1] [[1,2,3,4,5,10],[6],[7],[8],[9]]=>[9,1] [[1,2,3,4,10],[5,6,7,8],[9]]=>[5,4,1] [[1,2,3,4,10],[5,6,7],[8,9]]=>[5,3,2] [[1,2,3,4,10],[5,6,7],[8],[9]]=>[5,4,1] [[1,2,3,4,10],[5,6],[7,8],[9]]=>[5,2,2,1] [[1,2,3,4,10],[5,6],[7],[8],[9]]=>[5,4,1] [[1,2,3,4,10],[5],[6],[7],[8],[9]]=>[9,1] [[1,2,3,7],[4,5,6,10],[8,9]]=>[4,4,2] [[1,2,3,7],[4,5,6,10],[8],[9]]=>[4,5,1] [[1,2,3,10],[4,5,6],[7,8],[9]]=>[4,3,2,1] [[1,2,3,10],[4,5,6],[7],[8],[9]]=>[4,5,1] [[1,2,3,10],[4,5],[6,7],[8,9]]=>[4,2,2,2] [[1,2,3,10],[4,5],[6,7],[8],[9]]=>[4,2,3,1] [[1,2,3,10],[4,5],[6],[7],[8],[9]]=>[4,5,1] [[1,2,3,10],[4],[5],[6],[7],[8],[9]]=>[9,1] [[1,2,5],[3,4,8],[6,7,10],[9]]=>[3,3,3,1] [[1,2,5],[3,4,10],[6,7],[8,9]]=>[3,3,2,2] [[1,2,5],[3,4,10],[6,7],[8],[9]]=>[3,3,3,1] [[1,2,5],[3,4,10],[6],[7],[8],[9]]=>[3,6,1] [[1,2,10],[3,4],[5,6],[7,8],[9]]=>[3,2,2,2,1] [[1,2,10],[3,4],[5,6],[7],[8],[9]]=>[3,2,4,1] [[1,2,10],[3,4],[5],[6],[7],[8],[9]]=>[3,6,1] [[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[9,1] [[1,3],[2,5],[4,7],[6,10],[8],[9]]=>[2,2,2,3,1] [[1,3],[2,5],[4,10],[6],[7],[8],[9]]=>[2,2,5,1] [[1,3],[2,10],[4],[5],[6],[7],[8],[9]]=>[2,7,1] [[1,2,4,5,6,7,8,9,10],[3]]=>[3,7] [[1,3,4,6,7,8,9,10],[2,5]]=>[2,3,5] [[1,3,5,6,7,8,9,10],[2],[4]]=>[2,2,6] [[1,3,5,6,8,9,10],[2,4,7]]=>[2,2,3,3] [[1,2,4,7,8,9,10],[3,5],[6]]=>[3,3,4] [[1,4,6,7,8,9,10],[2],[3],[5]]=>[3,2,5] [[1,3,5,7,8,10],[2,4,6,9]]=>[2,2,2,3,1] [[1,2,5,7,9,10],[3,6,8],[4]]=>[4,2,2,2] [[1,4,6,8,9,10],[2,5],[3,7]]=>[3,2,2,3] [[1,3,5,8,9,10],[2,6],[4],[7]]=>[2,2,3,3] [[1,5,7,8,9,10],[2],[3],[4],[6]]=>[4,2,4] [[1,2,5,6,9],[3,7,8,10],[4]]=>[4,3,3] [[1,3,4,7,10],[2,6,8],[5,9]]=>[2,3,4,1] [[1,3,6,8,10],[2,7,9],[4],[5]]=>[2,3,2,2,1] [[1,2,6,9,10],[3,4],[5,7],[8]]=>[3,2,3,2] [[1,4,6,9,10],[2,7],[3],[5],[8]]=>[3,2,3,2] [[1,6,8,9,10],[2],[3],[4],[5],[7]]=>[5,2,3] [[1,3,4,8],[2,6,9,10],[5,7]]=>[2,3,2,2,1] [[1,3,6,7],[2,8,9,10],[4],[5]]=>[2,3,3,2] [[1,4,7,9],[2,5,8],[3,6,10]]=>[3,3,2,2] [[1,4,7,9],[2,8,10],[3],[5],[6]]=>[3,3,2,2] [[1,5,8,10],[2,6],[3,7],[4,9]]=>[4,3,2,1] [[1,3,7,10],[2,5],[4,8],[6],[9]]=>[2,2,2,3,1] [[1,5,7,10],[2,8],[3],[4],[6],[9]]=>[4,2,3,1] [[1,7,9,10],[2],[3],[4],[5],[6],[8]]=>[6,2,2] [[1,2,5],[3,7,8],[4,9,10],[6]]=>[4,2,3,1] [[1,4,6],[2,5,9],[3,8],[7,10]]=>[3,2,2,3] [[1,3,5],[2,6,8],[4,9],[7],[10]]=>[2,2,3,3] [[1,5,8],[2,9,10],[3],[4],[6],[7]]=>[4,3,2,1] [[1,2,8],[3,4],[5,6],[7,9],[10]]=>[3,2,2,3] [[1,4,8],[2,6],[3,9],[5],[7],[10]]=>[3,2,2,3] [[1,6,8],[2,9],[3],[4],[5],[7],[10]]=>[5,2,3] [[1,8,10],[2],[3],[4],[5],[6],[7],[9]]=>[7,2,1] [[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[2,2,2,2,2] [[1,5],[2,7],[3,9],[4],[6],[8],[10]]=>[4,2,2,2] [[1,7],[2,9],[3],[4],[5],[6],[8],[10]]=>[6,2,2] [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[8,2] [[1,3,4,5,6,7,8,9],[2,10]]=>[2,8] [[1,3,4,5,6,7,8,9],[2],[10]]=>[2,8] [[1,3,4,5,6,7,8],[2,9,10]]=>[2,7,1] [[1,3,4,5,6,7,8],[2,10],[9]]=>[2,7,1] [[1,3,4,5,6,7,8],[2],[9],[10]]=>[2,8] [[1,3,4,5,6,7],[2,8,9,10]]=>[2,6,2] [[1,3,4,5,6,7],[2,9,10],[8]]=>[2,6,2] [[1,3,4,5,6,7],[2,9],[8,10]]=>[2,6,2] [[1,3,4,5,6,7],[2,9],[8],[10]]=>[2,6,2] [[1,3,4,5,6,7],[2],[8],[9],[10]]=>[2,8] [[1,3,4,5,6],[2,8,9,10],[7]]=>[2,5,3] [[1,3,4,5,6],[2,8,9],[7,10]]=>[2,5,3] [[1,3,4,5,6],[2,8,9],[7],[10]]=>[2,5,3] [[1,3,4,5,6],[2,8],[7,10],[9]]=>[2,5,2,1] [[1,3,4,5,6],[2,8],[7],[9],[10]]=>[2,5,3] [[1,3,4,5,6],[2],[7],[8],[9],[10]]=>[2,8] [[1,3,4,5],[2,7,8,9],[6,10]]=>[2,4,4] [[1,3,4,5],[2,7,8,9],[6],[10]]=>[2,4,4] [[1,3,4,5],[2,7,8],[6,9,10]]=>[2,4,3,1] [[1,3,4,5],[2,7,8],[6,10],[9]]=>[2,4,3,1] [[1,3,4,5],[2,7,8],[6],[9],[10]]=>[2,4,4] [[1,3,4,5],[2,7],[6,9],[8,10]]=>[2,4,2,2] [[1,3,4,5],[2,7],[6,9],[8],[10]]=>[2,4,2,2] [[1,3,4,5],[2,7],[6],[8],[9],[10]]=>[2,4,4] [[1,3,4,5],[2],[6],[7],[8],[9],[10]]=>[2,8] [[1,3,4],[2,6,7],[5,9],[8,10]]=>[2,3,3,2] [[1,3,4],[2,6,7],[5,9],[8],[10]]=>[2,3,3,2] [[1,3,4],[2,6,7],[5],[8],[9],[10]]=>[2,3,5] [[1,3,4],[2,6],[5,8],[7,10],[9]]=>[2,3,2,2,1] [[1,3,4],[2,6],[5,8],[7],[9],[10]]=>[2,3,2,3] [[1,3,4],[2,6],[5],[7],[8],[9],[10]]=>[2,3,5] [[1,3,4],[2],[5],[6],[7],[8],[9],[10]]=>[2,8] [[1,3],[2,5],[4,7],[6],[8],[9],[10]]=>[2,2,2,4] [[1,3],[2,5],[4],[6],[7],[8],[9],[10]]=>[2,2,6] [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[2,8] [[1,2,4,6,8,10],[3,5,7,9]]=>[3,2,2,2,1] [[1,2,4,6,8,9,10],[3,5,7]]=>[3,2,2,3] [[1,2,4,6,7,8,10],[3,5,9]]=>[3,2,4,1] [[1,2,4,6,7,9,10],[3,5,8]]=>[3,2,3,2] [[1,2,4,6,7,8,9,10],[3,5]]=>[3,2,5] [[1,2,4,5,6,8,10],[3,7,9]]=>[3,4,2,1] [[1,2,4,5,6,9,10],[3,7,8]]=>[3,4,3] [[1,2,4,5,7,8,10],[3,6,9]]=>[3,3,3,1] [[1,2,4,5,7,9,10],[3,6,8]]=>[3,3,2,2] [[1,2,4,5,7,8,9,10],[3,6]]=>[3,3,4] [[1,2,4,5,6,7,8,10],[3,9]]=>[3,6,1] [[1,2,4,5,6,7,9,10],[3,8]]=>[3,5,2] [[1,2,4,5,6,8,9,10],[3,7]]=>[3,4,3] [[1,2,3,4,6,8,10],[5,7,9]]=>[5,2,2,1] [[1,2,3,4,6,9,10],[5,7,8]]=>[5,2,3] [[1,2,3,4,7,8,10],[5,6,9]]=>[5,4,1] [[1,2,3,4,7,9,10],[5,6,8]]=>[5,3,2] [[1,2,3,4,7,8,9,10],[5,6]]=>[5,5] [[1,2,3,5,6,8,10],[4,7,9]]=>[4,3,2,1] [[1,2,3,5,6,9,10],[4,7,8]]=>[4,3,3] [[1,2,3,5,7,8,10],[4,6,9]]=>[4,2,3,1] [[1,2,3,5,7,9,10],[4,6,8]]=>[4,2,2,2] [[1,2,3,5,7,8,9,10],[4,6]]=>[4,2,4] [[1,2,3,5,6,7,8,10],[4,9]]=>[4,5,1] [[1,2,3,5,6,7,9,10],[4,8]]=>[4,4,2] [[1,2,3,5,6,8,9,10],[4,7]]=>[4,3,3] [[1,2,3,5,6,7,8,9,10],[4]]=>[4,6] [[1,2,3,4,5,6,8,10],[7,9]]=>[7,2,1] [[1,2,3,4,5,6,9,10],[7,8]]=>[7,3] [[1,2,3,4,5,7,8,10],[6,9]]=>[6,3,1] [[1,2,3,4,5,7,9,10],[6,8]]=>[6,2,2] [[1,2,3,4,5,8,9,10],[6,7]]=>[6,4] [[1,2,3,4,6,7,8,10],[5,9]]=>[5,4,1] [[1,2,3,4,6,7,9,10],[5,8]]=>[5,3,2] [[1,2,3,4,6,8,9,10],[5,7]]=>[5,2,3] [[1,2,3,4,6,7,8,9,10],[5]]=>[5,5] [[1,2,3,4,5,6,7,9,10],[8]]=>[8,2] [[1,2,3,4,5,6,8,9,10],[7]]=>[7,3] [[1,2,3,4,5,7,8,9,10],[6]]=>[6,4] [[1,2,5,6,7,8,9],[3,4,10]]=>[3,7] [[1,2,5,6,7,8,9],[3,4],[10]]=>[3,7] [[1,4,5,6,7,8,9],[2],[3],[10]]=>[3,7] [[1,2,3,7,8,9],[4,5,6,10]]=>[4,6] [[1,2,3,7,8,9],[4,5,6],[10]]=>[4,6] [[1,3,6,7,8,9],[2,5],[4,10]]=>[2,2,6] [[1,3,6,7,8,9],[2,5],[4],[10]]=>[2,2,6] [[1,5,6,7,8,9],[2],[3],[4],[10]]=>[4,6] [[1,2,3,4,9],[5,6,7,8],[10]]=>[5,5] [[1,3,4,8,9],[2,6,7],[5,10]]=>[2,3,5] [[1,3,4,8,9],[2,6,7],[5],[10]]=>[2,3,5] [[1,2,7,8,9],[3,4],[5,6],[10]]=>[3,2,5] [[1,4,7,8,9],[2,6],[3],[5],[10]]=>[3,2,5] [[1,6,7,8,9],[2],[3],[4],[5],[10]]=>[5,5] [[1,2,5,9],[3,4,8],[6,7,10]]=>[3,3,4] [[1,2,5,9],[3,4,8],[6,7],[10]]=>[3,3,4] [[1,4,5,9],[2,7,8],[3],[6],[10]]=>[3,3,4] [[1,3,8,9],[2,5],[4,7],[6,10]]=>[2,2,2,4] [[1,3,8,9],[2,5],[4,7],[6],[10]]=>[2,2,2,4] [[1,5,8,9],[2,7],[3],[4],[6],[10]]=>[4,2,4] [[1,7,8,9],[2],[3],[4],[5],[6],[10]]=>[6,4] [[1,3,6],[2,5,9],[4,8],[7,10]]=>[2,2,3,3] [[1,3,6],[2,5,9],[4,8],[7],[10]]=>[2,2,3,3] [[1,5,6],[2,8,9],[3],[4],[7],[10]]=>[4,3,3] [[1,2,9],[3,4],[5,6],[7,8],[10]]=>[3,2,2,3] [[1,4,9],[2,6],[3,8],[5],[7],[10]]=>[3,2,2,3] [[1,6,9],[2,8],[3],[4],[5],[7],[10]]=>[5,2,3] [[1,8,9],[2],[3],[4],[5],[6],[7],[10]]=>[7,3] [[1,2,3,6,7,8,9,10],[4,5]]=>[4,6] [[1,2,5,6,7,8,9,10],[3],[4]]=>[4,6] [[1,2,3,4,8,9,10],[5,6,7]]=>[5,5] [[1,2,4,7,8,9,10],[3,6],[5]]=>[3,2,5] [[1,2,6,7,8,9,10],[3],[4],[5]]=>[5,5] [[1,2,4,5,9,10],[3,7,8],[6]]=>[3,3,4] [[1,2,3,8,9,10],[4,5],[6,7]]=>[4,2,4] [[1,2,5,8,9,10],[3,7],[4],[6]]=>[4,2,4] [[1,2,7,8,9,10],[3],[4],[5],[6]]=>[6,4] [[1,2,4,5,6],[3,8,9,10],[7]]=>[3,4,3] [[1,2,3,6,10],[4,5,9],[7,8]]=>[4,3,3] [[1,2,5,6,10],[3,8,9],[4],[7]]=>[4,3,3] [[1,2,4,9,10],[3,6],[5,8],[7]]=>[3,2,2,3] [[1,2,6,9,10],[3,8],[4],[5],[7]]=>[5,2,3] [[1,2,8,9,10],[3],[4],[5],[6],[7]]=>[7,3] [[1,2,6,7],[3,5,9,10],[4],[8]]=>[4,4,2] [[1,2,4,7],[3,6,10],[5,9],[8]]=>[3,2,3,2] [[1,2,6,7],[3,9,10],[4],[5],[8]]=>[5,3,2] [[1,2,5,10],[3,7],[4,9],[6],[8]]=>[4,2,2,2] [[1,2,7,10],[3,9],[4],[5],[6],[8]]=>[6,2,2] [[1,2,9,10],[3],[4],[5],[6],[7],[8]]=>[8,2] [[1,2,3],[4,5,8],[6,7],[9,10]]=>[4,2,3,1] [[1,2,5],[3,7,8],[4,10],[6],[9]]=>[4,2,3,1] [[1,2,8],[3,7,10],[4],[5],[6],[9]]=>[6,3,1] [[1,2,4],[3,6],[5,8],[7,10],[9]]=>[3,2,2,2,1] [[1,2,6],[3,8],[4,10],[5],[7],[9]]=>[5,2,2,1] [[1,2,8],[3,10],[4],[5],[6],[7],[9]]=>[7,2,1] [[1,2],[3,5],[4,7],[6,9],[8],[10]]=>[4,2,2,2] [[1,2],[3,7],[4,9],[5],[6],[8],[10]]=>[6,2,2] [[1,2],[3,9],[4],[5],[6],[7],[8],[10]]=>[8,2] [[1,2,4,5,8,9,10],[3,7],[6]]=>[3,3,4] [[1,2,4,5,6,7],[3,9,10],[8]]=>[3,5,2] [[1,2,3,4,9,10],[5,6],[7,8]]=>[5,2,3] [[1,2,5,6,9,10],[3,8],[4],[7]]=>[4,3,3] [[1,2,4,5,6,7,8,9],[3],[10]]=>[3,7] [[1,2,3,4,7,8],[5,6],[9,10]]=>[5,4,1] [[1,2,5,6,7,8],[3,10],[4],[9]]=>[4,5,1] [[1,2,4,5,10],[3,7],[6,9],[8]]=>[3,3,2,2] [[1,2,6,7,10],[3,9],[4],[5],[8]]=>[5,3,2] [[1,2,4,5,8,9],[3,7],[6],[10]]=>[3,3,4] [[1,2,6,7,8,9],[3],[4],[5],[10]]=>[5,5] [[1,2,5,6],[3,8],[4,10],[7],[9]]=>[4,3,2,1] [[1,2,7,8],[3,10],[4],[5],[6],[9]]=>[6,3,1] [[1,2,4,5],[3,7],[6,9],[8],[10]]=>[3,3,2,2] [[1,2,6,7],[3,9],[4],[5],[8],[10]]=>[5,3,2] [[1,2,8,9],[3],[4],[5],[6],[7],[10]]=>[7,3] [[1,2,3,4,5],[6,7,8,9],[10,11]]=>[6,4,1] [[1,2,3,4,5],[6,7,8,9],[10],[11]]=>[6,5] [[1,2,3,4,5],[6,7,8],[9,10,11]]=>[6,3,2] [[1,2,3,4,5],[6,7,8],[9,10],[11]]=>[6,3,2] [[1,2,3,4,5],[6,7,8],[9],[10],[11]]=>[6,5] [[1,2,3,4,5],[6,7],[8,9],[10,11]]=>[6,2,2,1] [[1,2,3,4,5],[6,7],[8,9],[10],[11]]=>[6,2,3] [[1,2,3,4],[5,6,7,8],[9,10,11]]=>[5,4,2] [[1,2,3,4],[5,6,7,8],[9,10],[11]]=>[5,4,2] [[1,2,3,4],[5,6,7,8],[9],[10],[11]]=>[5,6] [[1,2,3,4],[5,6,7],[8,9,10],[11]]=>[5,3,3] [[1,2,3,4],[5,6,7],[8,9],[10,11]]=>[5,3,2,1] [[1,2,3,4],[5,6,7],[8,9],[10],[11]]=>[5,3,3] [[1,2,3,4],[5,6],[7,8],[9,10],[11]]=>[5,2,2,2] [[1,2,3],[4,5,6],[7,8,9],[10,11]]=>[4,3,3,1] [[1,2,3],[4,5,6],[7,8,9],[10],[11]]=>[4,3,4] [[1,2,3],[4,5,6],[7,8],[9,10],[11]]=>[4,3,2,2] [[1,2,5,6,11],[3,4,9,10],[7,8]]=>[3,4,4] [[1,4,5,6,11],[2,8,9,10],[3],[7]]=>[3,4,4] [[1,2,3,10,11],[4,5,6],[7,8,9]]=>[4,3,4] [[1,3,6,10,11],[2,5,9],[4,8],[7]]=>[2,2,3,4] [[1,5,6,10,11],[2,8,9],[3],[4],[7]]=>[4,3,4] [[1,2,9,10,11],[3,4],[5,6],[7,8]]=>[3,2,2,4] [[1,4,9,10,11],[2,6],[3,8],[5],[7]]=>[3,2,2,4] [[1,2,3,7],[4,5,6,11],[8,9,10]]=>[4,4,3] [[1,3,6,7],[2,5,10,11],[4,9],[8]]=>[2,2,4,3] [[1,5,6,7],[2,9,10,11],[3],[4],[8]]=>[4,4,3] [[1,3,4,11],[2,6,7],[5,9,10],[8]]=>[2,3,3,3] [[1,2,7,11],[3,4,10],[5,6],[8,9]]=>[3,2,3,3] [[1,4,7,11],[2,6,10],[3,9],[5],[8]]=>[3,2,3,3] [[1,3,10,11],[2,5],[4,7],[6,9],[8]]=>[2,2,2,2,3] [[1,2,5],[3,4,8],[6,7,11],[9,10]]=>[3,3,3,2] [[1,4,5],[2,7,8],[3,10,11],[6],[9]]=>[3,3,3,2] [[1,3,8],[2,5,11],[4,7],[6,10],[9]]=>[2,2,2,3,2] [[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[2,2,2,2,2,2] [[1,3,5,7,9,10],[2,4,6,8,11,12]]=>[2,2,2,2,3,1] [[1,3,5,7,8,11],[2,4,6,9,10,12]]=>[2,2,2,3,3] [[1,3,5,7,8,10],[2,4,6,9,11,12]]=>[2,2,2,3,2,1] [[1,3,5,7,8,9],[2,4,6,10,11,12]]=>[2,2,2,4,2] [[1,3,5,6,9,11],[2,4,7,8,10,12]]=>[2,2,3,3,2] [[1,3,5,6,9,10],[2,4,7,8,11,12]]=>[2,2,3,4,1] [[1,3,5,6,8,11],[2,4,7,9,10,12]]=>[2,2,3,2,3] [[1,3,5,6,8,10],[2,4,7,9,11,12]]=>[2,2,3,2,2,1] [[1,3,5,6,8,9],[2,4,7,10,11,12]]=>[2,2,3,3,2] [[1,3,5,6,7,11],[2,4,8,9,10,12]]=>[2,2,4,4] [[1,3,5,6,7,10],[2,4,8,9,11,12]]=>[2,2,4,3,1] [[1,3,5,6,7,9],[2,4,8,10,11,12]]=>[2,2,4,2,2] [[1,3,5,6,7,8],[2,4,9,10,11,12]]=>[2,2,5,3] [[1,3,4,7,9,11],[2,5,6,8,10,12]]=>[2,3,3,2,2] [[1,3,4,7,9,10],[2,5,6,8,11,12]]=>[2,3,3,3,1] [[1,3,4,7,8,11],[2,5,6,9,10,12]]=>[2,3,4,3] [[1,3,4,7,8,10],[2,5,6,9,11,12]]=>[2,3,4,2,1] [[1,3,4,7,8,9],[2,5,6,10,11,12]]=>[2,3,5,2] [[1,3,4,6,9,11],[2,5,7,8,10,12]]=>[2,3,2,3,2] [[1,3,4,6,9,10],[2,5,7,8,11,12]]=>[2,3,2,4,1] [[1,3,4,6,8,11],[2,5,7,9,10,12]]=>[2,3,2,2,3] [[1,3,4,6,8,10],[2,5,7,9,11,12]]=>[2,3,2,2,2,1] [[1,3,4,6,8,9],[2,5,7,10,11,12]]=>[2,3,2,3,2] [[1,3,4,6,7,11],[2,5,8,9,10,12]]=>[2,3,3,4] [[1,3,4,6,7,10],[2,5,8,9,11,12]]=>[2,3,3,3,1] [[1,3,4,6,7,9],[2,5,8,10,11,12]]=>[2,3,3,2,2] [[1,3,4,6,7,8],[2,5,9,10,11,12]]=>[2,3,4,3] [[1,3,4,5,9,11],[2,6,7,8,10,12]]=>[2,4,4,2] [[1,3,4,5,9,10],[2,6,7,8,11,12]]=>[2,4,5,1] [[1,3,4,5,8,11],[2,6,7,9,10,12]]=>[2,4,3,3] [[1,3,4,5,8,10],[2,6,7,9,11,12]]=>[2,4,3,2,1] [[1,3,4,5,8,9],[2,6,7,10,11,12]]=>[2,4,4,2] [[1,3,4,5,7,11],[2,6,8,9,10,12]]=>[2,4,2,4] [[1,3,4,5,7,10],[2,6,8,9,11,12]]=>[2,4,2,3,1] [[1,3,4,5,7,9],[2,6,8,10,11,12]]=>[2,4,2,2,2] [[1,3,4,5,7,8],[2,6,9,10,11,12]]=>[2,4,3,3] [[1,3,4,5,6,11],[2,7,8,9,10,12]]=>[2,5,5] [[1,3,4,5,6,10],[2,7,8,9,11,12]]=>[2,5,4,1] [[1,3,4,5,6,9],[2,7,8,10,11,12]]=>[2,5,3,2] [[1,3,4,5,6,8],[2,7,9,10,11,12]]=>[2,5,2,3] [[1,3,4,5,6,7],[2,8,9,10,11,12]]=>[2,6,4] [[1,2,5,7,9,11],[3,4,6,8,10,12]]=>[3,3,2,2,2] [[1,2,5,7,9,10],[3,4,6,8,11,12]]=>[3,3,2,3,1] [[1,2,5,7,8,11],[3,4,6,9,10,12]]=>[3,3,3,3] [[1,2,5,7,8,10],[3,4,6,9,11,12]]=>[3,3,3,2,1] [[1,2,5,7,8,9],[3,4,6,10,11,12]]=>[3,3,4,2] [[1,2,5,6,9,11],[3,4,7,8,10,12]]=>[3,4,3,2] [[1,2,5,6,9,10],[3,4,7,8,11,12]]=>[3,4,4,1] [[1,2,5,6,8,11],[3,4,7,9,10,12]]=>[3,4,2,3] [[1,2,5,6,8,10],[3,4,7,9,11,12]]=>[3,4,2,2,1] [[1,2,5,6,8,9],[3,4,7,10,11,12]]=>[3,4,3,2] [[1,2,5,6,7,11],[3,4,8,9,10,12]]=>[3,5,4] [[1,2,5,6,7,10],[3,4,8,9,11,12]]=>[3,5,3,1] [[1,2,5,6,7,9],[3,4,8,10,11,12]]=>[3,5,2,2] [[1,2,5,6,7,8],[3,4,9,10,11,12]]=>[3,6,3] [[1,2,4,7,9,11],[3,5,6,8,10,12]]=>[3,2,3,2,2] [[1,2,4,7,9,10],[3,5,6,8,11,12]]=>[3,2,3,3,1] [[1,2,4,7,8,11],[3,5,6,9,10,12]]=>[3,2,4,3] [[1,2,4,7,8,10],[3,5,6,9,11,12]]=>[3,2,4,2,1] [[1,2,4,7,8,9],[3,5,6,10,11,12]]=>[3,2,5,2] [[1,2,4,6,9,11],[3,5,7,8,10,12]]=>[3,2,2,3,2] [[1,2,4,6,9,10],[3,5,7,8,11,12]]=>[3,2,2,4,1] [[1,2,4,6,8,11],[3,5,7,9,10,12]]=>[3,2,2,2,3] [[1,2,4,6,8,10],[3,5,7,9,11,12]]=>[3,2,2,2,2,1] [[1,2,4,6,8,9],[3,5,7,10,11,12]]=>[3,2,2,3,2] [[1,2,4,6,7,11],[3,5,8,9,10,12]]=>[3,2,3,4] [[1,2,4,6,7,10],[3,5,8,9,11,12]]=>[3,2,3,3,1] [[1,2,4,6,7,9],[3,5,8,10,11,12]]=>[3,2,3,2,2] [[1,2,4,6,7,8],[3,5,9,10,11,12]]=>[3,2,4,3] [[1,2,4,5,9,11],[3,6,7,8,10,12]]=>[3,3,4,2] [[1,2,4,5,9,10],[3,6,7,8,11,12]]=>[3,3,5,1] [[1,2,4,5,8,11],[3,6,7,9,10,12]]=>[3,3,3,3] [[1,2,4,5,8,10],[3,6,7,9,11,12]]=>[3,3,3,2,1] [[1,2,4,5,8,9],[3,6,7,10,11,12]]=>[3,3,4,2] [[1,2,4,5,7,11],[3,6,8,9,10,12]]=>[3,3,2,4] [[1,2,4,5,7,10],[3,6,8,9,11,12]]=>[3,3,2,3,1] [[1,2,4,5,7,9],[3,6,8,10,11,12]]=>[3,3,2,2,2] [[1,2,4,5,7,8],[3,6,9,10,11,12]]=>[3,3,3,3] [[1,2,4,5,6,11],[3,7,8,9,10,12]]=>[3,4,5] [[1,2,4,5,6,10],[3,7,8,9,11,12]]=>[3,4,4,1] [[1,2,4,5,6,9],[3,7,8,10,11,12]]=>[3,4,3,2] [[1,2,4,5,6,8],[3,7,9,10,11,12]]=>[3,4,2,3] [[1,2,4,5,6,7],[3,8,9,10,11,12]]=>[3,5,4] [[1,2,3,7,9,11],[4,5,6,8,10,12]]=>[4,4,2,2] [[1,2,3,7,9,10],[4,5,6,8,11,12]]=>[4,4,3,1] [[1,2,3,7,8,11],[4,5,6,9,10,12]]=>[4,5,3] [[1,2,3,7,8,10],[4,5,6,9,11,12]]=>[4,5,2,1] [[1,2,3,7,8,9],[4,5,6,10,11,12]]=>[4,6,2] [[1,2,3,6,9,11],[4,5,7,8,10,12]]=>[4,3,3,2] [[1,2,3,6,9,10],[4,5,7,8,11,12]]=>[4,3,4,1] [[1,2,3,6,8,11],[4,5,7,9,10,12]]=>[4,3,2,3] [[1,2,3,6,8,10],[4,5,7,9,11,12]]=>[4,3,2,2,1] [[1,2,3,6,8,9],[4,5,7,10,11,12]]=>[4,3,3,2] [[1,2,3,6,7,11],[4,5,8,9,10,12]]=>[4,4,4] [[1,2,3,6,7,10],[4,5,8,9,11,12]]=>[4,4,3,1] [[1,2,3,6,7,9],[4,5,8,10,11,12]]=>[4,4,2,2] [[1,2,3,6,7,8],[4,5,9,10,11,12]]=>[4,5,3] [[1,2,3,5,9,11],[4,6,7,8,10,12]]=>[4,2,4,2] [[1,2,3,5,9,10],[4,6,7,8,11,12]]=>[4,2,5,1] [[1,2,3,5,8,11],[4,6,7,9,10,12]]=>[4,2,3,3] [[1,2,3,5,8,10],[4,6,7,9,11,12]]=>[4,2,3,2,1] [[1,2,3,5,8,9],[4,6,7,10,11,12]]=>[4,2,4,2] [[1,2,3,5,7,11],[4,6,8,9,10,12]]=>[4,2,2,4] [[1,2,3,5,7,10],[4,6,8,9,11,12]]=>[4,2,2,3,1] [[1,2,3,5,7,9],[4,6,8,10,11,12]]=>[4,2,2,2,2] [[1,2,3,5,7,8],[4,6,9,10,11,12]]=>[4,2,3,3] [[1,2,3,5,6,11],[4,7,8,9,10,12]]=>[4,3,5] [[1,2,3,5,6,10],[4,7,8,9,11,12]]=>[4,3,4,1] [[1,2,3,5,6,9],[4,7,8,10,11,12]]=>[4,3,3,2] [[1,2,3,5,6,8],[4,7,9,10,11,12]]=>[4,3,2,3] [[1,2,3,5,6,7],[4,8,9,10,11,12]]=>[4,4,4] [[1,2,3,4,9,11],[5,6,7,8,10,12]]=>[5,5,2] [[1,2,3,4,9,10],[5,6,7,8,11,12]]=>[5,6,1] [[1,2,3,4,8,11],[5,6,7,9,10,12]]=>[5,4,3] [[1,2,3,4,8,10],[5,6,7,9,11,12]]=>[5,4,2,1] [[1,2,3,4,8,9],[5,6,7,10,11,12]]=>[5,5,2] [[1,2,3,4,7,11],[5,6,8,9,10,12]]=>[5,3,4] [[1,2,3,4,7,10],[5,6,8,9,11,12]]=>[5,3,3,1] [[1,2,3,4,7,9],[5,6,8,10,11,12]]=>[5,3,2,2] [[1,2,3,4,7,8],[5,6,9,10,11,12]]=>[5,4,3] [[1,2,3,4,6,11],[5,7,8,9,10,12]]=>[5,2,5] [[1,2,3,4,6,10],[5,7,8,9,11,12]]=>[5,2,4,1] [[1,2,3,4,6,9],[5,7,8,10,11,12]]=>[5,2,3,2] [[1,2,3,4,6,8],[5,7,9,10,11,12]]=>[5,2,2,3] [[1,2,3,4,6,7],[5,8,9,10,11,12]]=>[5,3,4] [[1,2,3,4,5,11],[6,7,8,9,10,12]]=>[6,6] [[1,2,3,4,5,10],[6,7,8,9,11,12]]=>[6,5,1] [[1,2,3,4,5,9],[6,7,8,10,11,12]]=>[6,4,2] [[1,2,3,4,5,8],[6,7,9,10,11,12]]=>[6,3,3] [[1,2,3,4,5,7],[6,8,9,10,11,12]]=>[6,2,4] [[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[7,5] [[1,2,3,4,5,6,7,8,9,10,11,12]]=>[12] [[1,2,3,4,5,6],[7,8,9,10],[11,12]]=>[7,4,1] [[1,2,3,4,5],[6,7,8,9],[10,11,12]]=>[6,4,2] [[1,2,3,4,5],[6,7,8,9],[10,11],[12]]=>[6,4,2] [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]]=>[6,6] [[1,2,3,4,5],[6,7,8],[9,10,11],[12]]=>[6,3,3] [[1,2,3,4,5],[6,7,8],[9,10],[11,12]]=>[6,3,2,1] [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]]=>[6,3,3] [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]]=>[6,2,2,2] [[1,2,3,4],[5,6,7,8],[9,10,11],[12]]=>[5,4,3] [[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>[5,4,2,1] [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]]=>[5,4,3] [[1,2,3,4],[5,6,7],[8,9,10],[11,12]]=>[5,3,3,1] [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]]=>[5,3,4] [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]]=>[5,3,2,2] [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]]=>[4,3,3,2] [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]]=>[4,3,2,3] [[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>[3,4,5] [[1,2,3,7,12],[4,5,6,11],[8,9,10]]=>[4,4,4] [[1,3,6,7,12],[2,5,10,11],[4,9],[8]]=>[2,2,4,4] [[1,5,6,7,12],[2,9,10,11],[3],[4],[8]]=>[4,4,4] [[1,3,4,11,12],[2,6,7],[5,9,10],[8]]=>[2,3,3,4] [[1,2,7,11,12],[3,4,10],[5,6],[8,9]]=>[3,2,3,4] [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]]=>[3,2,3,4] [[1,3,10,11,12],[2,5],[4,7],[6,9],[8]]=>[2,2,2,2,4] [[1,3,4,8],[2,6,7,12],[5,10,11],[9]]=>[2,3,4,3] [[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>[3,2,4,3] [[1,4,7,8],[2,6,11,12],[3,10],[5],[9]]=>[3,2,4,3] [[1,2,5,12],[3,4,8],[6,7,11],[9,10]]=>[3,3,3,3] [[1,4,5,12],[2,7,8],[3,10,11],[6],[9]]=>[3,3,3,3] [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]]=>[2,2,2,3,3] [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]]=>[2,2,3,3,2] [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[3,2,2,3,2] [[1,2,4,6,8,10,12],[3,5,7,9,11]]=>[3,2,2,2,2,1] [[1,2,4,6,8,10,11,12],[3,5,7,9]]=>[3,2,2,2,3] [[1,2,4,6,8,9,10,12],[3,5,7,11]]=>[3,2,2,4,1] [[1,2,4,6,8,9,11,12],[3,5,7,10]]=>[3,2,2,3,2] [[1,2,4,6,8,9,10,11,12],[3,5,7]]=>[3,2,2,5] [[1,2,4,6,7,8,10,12],[3,5,9,11]]=>[3,2,4,2,1] [[1,2,4,6,7,8,11,12],[3,5,9,10]]=>[3,2,4,3] [[1,2,4,6,7,9,10,12],[3,5,8,11]]=>[3,2,3,3,1] [[1,2,4,6,7,9,11,12],[3,5,8,10]]=>[3,2,3,2,2] [[1,2,4,6,7,9,10,11,12],[3,5,8]]=>[3,2,3,4] [[1,2,4,6,7,8,9,10,12],[3,5,11]]=>[3,2,6,1] [[1,2,4,6,7,8,9,11,12],[3,5,10]]=>[3,2,5,2] [[1,2,4,6,7,8,10,11,12],[3,5,9]]=>[3,2,4,3] [[1,2,4,6,7,8,9,10,11,12],[3,5]]=>[3,2,7] [[1,2,4,5,6,8,10,12],[3,7,9,11]]=>[3,4,2,2,1] [[1,2,4,5,6,8,11,12],[3,7,9,10]]=>[3,4,2,3] [[1,2,4,5,6,9,10,12],[3,7,8,11]]=>[3,4,4,1] [[1,2,4,5,6,9,11,12],[3,7,8,10]]=>[3,4,3,2] [[1,2,4,5,6,9,10,11,12],[3,7,8]]=>[3,4,5] [[1,2,4,5,7,8,10,12],[3,6,9,11]]=>[3,3,3,2,1] [[1,2,4,5,7,8,11,12],[3,6,9,10]]=>[3,3,3,3] [[1,2,4,5,7,9,10,12],[3,6,8,11]]=>[3,3,2,3,1] [[1,2,4,5,7,9,11,12],[3,6,8,10]]=>[3,3,2,2,2] [[1,2,4,5,7,9,10,11,12],[3,6,8]]=>[3,3,2,4] [[1,2,4,5,7,8,9,10,12],[3,6,11]]=>[3,3,5,1] [[1,2,4,5,7,8,9,11,12],[3,6,10]]=>[3,3,4,2] [[1,2,4,5,7,8,10,11,12],[3,6,9]]=>[3,3,3,3] [[1,2,4,5,7,8,9,10,11,12],[3,6]]=>[3,3,6] [[1,2,4,5,6,7,8,10,12],[3,9,11]]=>[3,6,2,1] [[1,2,4,5,6,7,8,11,12],[3,9,10]]=>[3,6,3] [[1,2,4,5,6,7,9,10,12],[3,8,11]]=>[3,5,3,1] [[1,2,4,5,6,7,9,11,12],[3,8,10]]=>[3,5,2,2] [[1,2,4,5,6,7,10,11,12],[3,8,9]]=>[3,5,4] [[1,2,4,5,6,8,9,10,12],[3,7,11]]=>[3,4,4,1] [[1,2,4,5,6,8,9,11,12],[3,7,10]]=>[3,4,3,2] [[1,2,4,5,6,8,10,11,12],[3,7,9]]=>[3,4,2,3] [[1,2,4,5,6,8,9,10,11,12],[3,7]]=>[3,4,5] [[1,2,4,5,6,7,8,9,10,12],[3,11]]=>[3,8,1] [[1,2,4,5,6,7,8,9,11,12],[3,10]]=>[3,7,2] [[1,2,4,5,6,7,8,10,11,12],[3,9]]=>[3,6,3] [[1,2,4,5,6,7,9,10,11,12],[3,8]]=>[3,5,4] [[1,2,4,5,6,7,8,9,10,11,12],[3]]=>[3,9] [[1,2,3,4,6,8,10,12],[5,7,9,11]]=>[5,2,2,2,1] [[1,2,3,4,6,8,11,12],[5,7,9,10]]=>[5,2,2,3] [[1,2,3,4,6,9,10,12],[5,7,8,11]]=>[5,2,4,1] [[1,2,3,4,6,9,11,12],[5,7,8,10]]=>[5,2,3,2] [[1,2,3,4,6,9,10,11,12],[5,7,8]]=>[5,2,5] [[1,2,3,4,7,8,10,12],[5,6,9,11]]=>[5,4,2,1] [[1,2,3,4,7,8,11,12],[5,6,9,10]]=>[5,4,3] [[1,2,3,4,7,9,10,12],[5,6,8,11]]=>[5,3,3,1] [[1,2,3,4,7,9,11,12],[5,6,8,10]]=>[5,3,2,2] [[1,2,3,4,7,9,10,11,12],[5,6,8]]=>[5,3,4] [[1,2,3,4,7,8,9,10,12],[5,6,11]]=>[5,6,1] [[1,2,3,4,7,8,9,11,12],[5,6,10]]=>[5,5,2] [[1,2,3,4,7,8,10,11,12],[5,6,9]]=>[5,4,3] [[1,2,3,4,7,8,9,10,11,12],[5,6]]=>[5,7] [[1,2,3,5,6,8,10,12],[4,7,9,11]]=>[4,3,2,2,1] [[1,2,3,5,6,8,11,12],[4,7,9,10]]=>[4,3,2,3] [[1,2,3,5,6,9,10,12],[4,7,8,11]]=>[4,3,4,1] [[1,2,3,5,6,9,11,12],[4,7,8,10]]=>[4,3,3,2] [[1,2,3,5,6,9,10,11,12],[4,7,8]]=>[4,3,5] [[1,2,3,5,7,8,10,12],[4,6,9,11]]=>[4,2,3,2,1] [[1,2,3,5,7,8,11,12],[4,6,9,10]]=>[4,2,3,3] [[1,2,3,5,7,9,10,12],[4,6,8,11]]=>[4,2,2,3,1] [[1,2,3,5,7,9,11,12],[4,6,8,10]]=>[4,2,2,2,2] [[1,2,3,5,7,9,10,11,12],[4,6,8]]=>[4,2,2,4] [[1,2,3,5,7,8,9,10,12],[4,6,11]]=>[4,2,5,1] [[1,2,3,5,7,8,9,11,12],[4,6,10]]=>[4,2,4,2] [[1,2,3,5,7,8,10,11,12],[4,6,9]]=>[4,2,3,3] [[1,2,3,5,7,8,9,10,11,12],[4,6]]=>[4,2,6] [[1,2,3,5,6,7,8,10,12],[4,9,11]]=>[4,5,2,1] [[1,2,3,5,6,7,8,11,12],[4,9,10]]=>[4,5,3] [[1,2,3,5,6,7,9,10,12],[4,8,11]]=>[4,4,3,1] [[1,2,3,5,6,7,9,11,12],[4,8,10]]=>[4,4,2,2] [[1,2,3,5,6,7,10,11,12],[4,8,9]]=>[4,4,4] [[1,2,3,5,6,8,9,10,12],[4,7,11]]=>[4,3,4,1] [[1,2,3,5,6,8,9,11,12],[4,7,10]]=>[4,3,3,2] [[1,2,3,5,6,8,10,11,12],[4,7,9]]=>[4,3,2,3] [[1,2,3,5,6,8,9,10,11,12],[4,7]]=>[4,3,5] [[1,2,3,5,6,7,8,9,10,12],[4,11]]=>[4,7,1] [[1,2,3,5,6,7,8,9,11,12],[4,10]]=>[4,6,2] [[1,2,3,5,6,7,8,10,11,12],[4,9]]=>[4,5,3] [[1,2,3,5,6,7,9,10,11,12],[4,8]]=>[4,4,4] [[1,2,3,5,6,7,8,9,10,11,12],[4]]=>[4,8] [[1,2,3,4,5,6,8,10,12],[7,9,11]]=>[7,2,2,1] [[1,2,3,4,5,6,8,11,12],[7,9,10]]=>[7,2,3] [[1,2,3,4,5,6,9,10,12],[7,8,11]]=>[7,4,1] [[1,2,3,4,5,6,9,11,12],[7,8,10]]=>[7,3,2] [[1,2,3,4,5,6,10,11,12],[7,8,9]]=>[7,5] [[1,2,3,4,5,7,8,10,12],[6,9,11]]=>[6,3,2,1] [[1,2,3,4,5,7,8,11,12],[6,9,10]]=>[6,3,3] [[1,2,3,4,5,7,9,10,12],[6,8,11]]=>[6,2,3,1] [[1,2,3,4,5,7,9,11,12],[6,8,10]]=>[6,2,2,2] [[1,2,3,4,5,7,10,11,12],[6,8,9]]=>[6,2,4] [[1,2,3,4,5,8,9,10,12],[6,7,11]]=>[6,5,1] [[1,2,3,4,5,8,9,11,12],[6,7,10]]=>[6,4,2] [[1,2,3,4,5,8,10,11,12],[6,7,9]]=>[6,3,3] [[1,2,3,4,5,8,9,10,11,12],[6,7]]=>[6,6] [[1,2,3,4,6,7,8,10,12],[5,9,11]]=>[5,4,2,1] [[1,2,3,4,6,7,8,11,12],[5,9,10]]=>[5,4,3] [[1,2,3,4,6,7,9,10,12],[5,8,11]]=>[5,3,3,1] [[1,2,3,4,6,7,9,11,12],[5,8,10]]=>[5,3,2,2] [[1,2,3,4,6,7,10,11,12],[5,8,9]]=>[5,3,4] [[1,2,3,4,6,8,9,10,12],[5,7,11]]=>[5,2,4,1] [[1,2,3,4,6,8,9,11,12],[5,7,10]]=>[5,2,3,2] [[1,2,3,4,6,8,10,11,12],[5,7,9]]=>[5,2,2,3] [[1,2,3,4,6,8,9,10,11,12],[5,7]]=>[5,2,5] [[1,2,3,4,6,7,8,9,10,12],[5,11]]=>[5,6,1] [[1,2,3,4,6,7,8,9,11,12],[5,10]]=>[5,5,2] [[1,2,3,4,6,7,8,10,11,12],[5,9]]=>[5,4,3] [[1,2,3,4,6,7,9,10,11,12],[5,8]]=>[5,3,4] [[1,2,3,4,6,7,8,9,10,11,12],[5]]=>[5,7] [[1,2,3,4,5,6,7,8,10,12],[9,11]]=>[9,2,1] [[1,2,3,4,5,6,7,8,11,12],[9,10]]=>[9,3] [[1,2,3,4,5,6,7,9,10,12],[8,11]]=>[8,3,1] [[1,2,3,4,5,6,7,9,11,12],[8,10]]=>[8,2,2] [[1,2,3,4,5,6,7,10,11,12],[8,9]]=>[8,4] [[1,2,3,4,5,6,8,9,10,12],[7,11]]=>[7,4,1] [[1,2,3,4,5,6,8,9,11,12],[7,10]]=>[7,3,2] [[1,2,3,4,5,6,8,10,11,12],[7,9]]=>[7,2,3] [[1,2,3,4,5,6,9,10,11,12],[7,8]]=>[7,5] [[1,2,3,4,5,7,8,9,10,12],[6,11]]=>[6,5,1] [[1,2,3,4,5,7,8,9,11,12],[6,10]]=>[6,4,2] [[1,2,3,4,5,7,8,10,11,12],[6,9]]=>[6,3,3] [[1,2,3,4,5,7,9,10,11,12],[6,8]]=>[6,2,4] [[1,2,3,4,5,7,8,9,10,11,12],[6]]=>[6,6] [[1,2,3,4,5,6,7,8,9,10,12],[11]]=>[11,1] [[1,2,3,4,5,6,7,8,9,11,12],[10]]=>[10,2] [[1,2,3,4,5,6,7,8,10,11,12],[9]]=>[9,3] [[1,2,3,4,5,6,7,9,10,11,12],[8]]=>[8,4] [[1,2,3,4,5,6,8,9,10,11,12],[7]]=>[7,5] [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]]=>[6,4,3] [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]]=>[6,4,2,1] [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]]=>[6,4,3] [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]]=>[6,3,3,1] [[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]]=>[6,3,4] [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]]=>[6,3,2,2] [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]]=>[5,4,3,1] [[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]]=>[5,4,4] [[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]]=>[5,4,2,2] [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]]=>[5,3,3,2] [[1,3,4,8,13],[2,6,7,12],[5,10,11],[9]]=>[2,3,4,4] [[1,2,7,8,13],[3,4,11,12],[5,6],[9,10]]=>[3,2,4,4] [[1,4,7,8,13],[2,6,11,12],[3,10],[5],[9]]=>[3,2,4,4] [[1,2,5,12,13],[3,4,8],[6,7,11],[9,10]]=>[3,3,3,4] [[1,4,5,12,13],[2,7,8],[3,10,11],[6],[9]]=>[3,3,3,4] [[1,3,8,12,13],[2,5,11],[4,7],[6,10],[9]]=>[2,2,2,3,4] [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]]=>[3,3,4,3] [[1,4,5,9],[2,7,8,13],[3,11,12],[6],[10]]=>[3,3,4,3] [[1,3,8,9],[2,5,12,13],[4,7],[6,11],[10]]=>[2,2,2,4,3] [[1,3,6,13],[2,5,9],[4,8,12],[7,11],[10]]=>[2,2,3,3,3] [[1,3,5,7,9,11,13],[2,4,6,8,10,12,14]]=>[2,2,2,2,2,2,2] [[1,3,5,7,9,11,12],[2,4,6,8,10,13,14]]=>[2,2,2,2,2,3,1] [[1,3,5,7,9,10,12],[2,4,6,8,11,13,14]]=>[2,2,2,2,3,2,1] [[1,3,5,7,9,10,11],[2,4,6,8,12,13,14]]=>[2,2,2,2,4,2] [[1,3,5,7,8,10,12],[2,4,6,9,11,13,14]]=>[2,2,2,3,2,2,1] [[1,3,5,7,8,9,12],[2,4,6,10,11,13,14]]=>[2,2,2,4,3,1] [[1,3,5,7,8,9,11],[2,4,6,10,12,13,14]]=>[2,2,2,4,2,2] [[1,3,5,7,8,9,10],[2,4,6,11,12,13,14]]=>[2,2,2,5,3] [[1,3,5,6,8,10,12],[2,4,7,9,11,13,14]]=>[2,2,3,2,2,2,1] [[1,3,5,6,7,10,12],[2,4,8,9,11,13,14]]=>[2,2,4,3,2,1] [[1,3,5,6,7,9,12],[2,4,8,10,11,13,14]]=>[2,2,4,2,3,1] [[1,3,5,6,7,9,11],[2,4,8,10,12,13,14]]=>[2,2,4,2,2,2] [[1,3,5,6,7,9,10],[2,4,8,11,12,13,14]]=>[2,2,4,3,3] [[1,3,5,6,7,8,12],[2,4,9,10,11,13,14]]=>[2,2,5,4,1] [[1,3,5,6,7,8,10],[2,4,9,11,12,13,14]]=>[2,2,5,2,3] [[1,3,4,6,8,10,12],[2,5,7,9,11,13,14]]=>[2,3,2,2,2,2,1] [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]]=>[2,3,5,4] [[1,3,4,5,8,10,12],[2,6,7,9,11,13,14]]=>[2,4,3,2,2,1] [[1,3,4,5,7,10,12],[2,6,8,9,11,13,14]]=>[2,4,2,3,2,1] [[1,3,4,5,7,9,12],[2,6,8,10,11,13,14]]=>[2,4,2,2,3,1] [[1,3,4,5,7,8,12],[2,6,9,10,11,13,14]]=>[2,4,3,4,1] [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]]=>[2,4,3,2,3] [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]]=>[2,4,4,4] [[1,3,4,5,6,10,12],[2,7,8,9,11,13,14]]=>[2,5,4,2,1] [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]]=>[2,5,4,3] [[1,3,4,5,6,8,12],[2,7,9,10,11,13,14]]=>[2,5,2,4,1] [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]]=>[2,5,2,3,2] [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]]=>[2,5,2,2,3] [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]]=>[2,5,3,4] [[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]]=>[2,6,5,1] [[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]]=>[2,6,4,2] [[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]]=>[2,6,3,3] [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]]=>[2,6,2,4] [[1,3,4,5,6,7,8],[2,9,10,11,12,13,14]]=>[2,7,5] [[1,2,5,6,7,8,9],[3,4,10,11,12,13,14]]=>[3,7,4] [[1,2,4,6,8,10,12],[3,5,7,9,11,13,14]]=>[3,2,2,2,2,2,1] [[1,2,4,6,8,10,11],[3,5,7,9,12,13,14]]=>[3,2,2,2,3,2] [[1,2,4,6,8,9,12],[3,5,7,10,11,13,14]]=>[3,2,2,3,3,1] [[1,2,4,6,8,9,11],[3,5,7,10,12,13,14]]=>[3,2,2,3,2,2] [[1,2,4,6,8,9,10],[3,5,7,11,12,13,14]]=>[3,2,2,4,3] [[1,2,4,6,7,10,12],[3,5,8,9,11,13,14]]=>[3,2,3,3,2,1] [[1,2,4,6,7,10,11],[3,5,8,9,12,13,14]]=>[3,2,3,4,2] [[1,2,4,6,7,9,12],[3,5,8,10,11,13,14]]=>[3,2,3,2,3,1] [[1,2,4,6,7,9,11],[3,5,8,10,12,13,14]]=>[3,2,3,2,2,2] [[1,2,4,6,7,9,10],[3,5,8,11,12,13,14]]=>[3,2,3,3,3] [[1,2,4,6,7,8,12],[3,5,9,10,11,13,14]]=>[3,2,4,4,1] [[1,2,4,6,7,8,11],[3,5,9,10,12,13,14]]=>[3,2,4,3,2] [[1,2,4,6,7,8,10],[3,5,9,11,12,13,14]]=>[3,2,4,2,3] [[1,2,4,6,7,8,9],[3,5,10,11,12,13,14]]=>[3,2,5,4] [[1,2,4,5,8,10,12],[3,6,7,9,11,13,14]]=>[3,3,3,2,2,1] [[1,2,4,5,8,10,11],[3,6,7,9,12,13,14]]=>[3,3,3,3,2] [[1,2,4,5,8,9,12],[3,6,7,10,11,13,14]]=>[3,3,4,3,1] [[1,2,4,5,8,9,11],[3,6,7,10,12,13,14]]=>[3,3,4,2,2] [[1,2,4,5,8,9,10],[3,6,7,11,12,13,14]]=>[3,3,5,3] [[1,2,4,5,7,10,12],[3,6,8,9,11,13,14]]=>[3,3,2,3,2,1] [[1,2,4,5,7,10,11],[3,6,8,9,12,13,14]]=>[3,3,2,4,2] [[1,2,4,5,7,9,12],[3,6,8,10,11,13,14]]=>[3,3,2,2,3,1] [[1,2,4,5,7,9,11],[3,6,8,10,12,13,14]]=>[3,3,2,2,2,2] [[1,2,4,5,7,9,10],[3,6,8,11,12,13,14]]=>[3,3,2,3,3] [[1,2,4,5,7,8,12],[3,6,9,10,11,13,14]]=>[3,3,3,4,1] [[1,2,4,5,7,8,11],[3,6,9,10,12,13,14]]=>[3,3,3,3,2] [[1,2,4,5,7,8,10],[3,6,9,11,12,13,14]]=>[3,3,3,2,3] [[1,2,4,5,7,8,9],[3,6,10,11,12,13,14]]=>[3,3,4,4] [[1,2,4,5,6,10,12],[3,7,8,9,11,13,14]]=>[3,4,4,2,1] [[1,2,4,5,6,10,11],[3,7,8,9,12,13,14]]=>[3,4,5,2] [[1,2,4,5,6,9,12],[3,7,8,10,11,13,14]]=>[3,4,3,3,1] [[1,2,4,5,6,9,11],[3,7,8,10,12,13,14]]=>[3,4,3,2,2] [[1,2,4,5,6,9,10],[3,7,8,11,12,13,14]]=>[3,4,4,3] [[1,2,4,5,6,8,12],[3,7,9,10,11,13,14]]=>[3,4,2,4,1] [[1,2,4,5,6,8,11],[3,7,9,10,12,13,14]]=>[3,4,2,3,2] [[1,2,4,5,6,8,10],[3,7,9,11,12,13,14]]=>[3,4,2,2,3] [[1,2,4,5,6,8,9],[3,7,10,11,12,13,14]]=>[3,4,3,4] [[1,2,4,5,6,7,13],[3,8,9,10,11,12,14]]=>[3,5,6] [[1,2,4,5,6,7,12],[3,8,9,10,11,13,14]]=>[3,5,5,1] [[1,2,4,5,6,7,11],[3,8,9,10,12,13,14]]=>[3,5,4,2] [[1,2,4,5,6,7,10],[3,8,9,11,12,13,14]]=>[3,5,3,3] [[1,2,4,5,6,7,9],[3,8,10,11,12,13,14]]=>[3,5,2,4] [[1,2,4,5,6,7,8],[3,9,10,11,12,13,14]]=>[3,6,5] [[1,2,3,6,8,10,12],[4,5,7,9,11,13,14]]=>[4,3,2,2,2,1] [[1,2,3,6,8,10,11],[4,5,7,9,12,13,14]]=>[4,3,2,3,2] [[1,2,3,6,8,9,12],[4,5,7,10,11,13,14]]=>[4,3,3,3,1] [[1,2,3,6,8,9,11],[4,5,7,10,12,13,14]]=>[4,3,3,2,2] [[1,2,3,6,8,9,10],[4,5,7,11,12,13,14]]=>[4,3,4,3] [[1,2,3,6,7,10,12],[4,5,8,9,11,13,14]]=>[4,4,3,2,1] [[1,2,3,6,7,10,11],[4,5,8,9,12,13,14]]=>[4,4,4,2] [[1,2,3,6,7,9,12],[4,5,8,10,11,13,14]]=>[4,4,2,3,1] [[1,2,3,6,7,9,11],[4,5,8,10,12,13,14]]=>[4,4,2,2,2] [[1,2,3,6,7,9,10],[4,5,8,11,12,13,14]]=>[4,4,3,3] [[1,2,3,6,7,8,12],[4,5,9,10,11,13,14]]=>[4,5,4,1] [[1,2,3,6,7,8,11],[4,5,9,10,12,13,14]]=>[4,5,3,2] [[1,2,3,6,7,8,10],[4,5,9,11,12,13,14]]=>[4,5,2,3] [[1,2,3,6,7,8,9],[4,5,10,11,12,13,14]]=>[4,6,4] [[1,2,3,5,8,10,12],[4,6,7,9,11,13,14]]=>[4,2,3,2,2,1] [[1,2,3,5,8,10,11],[4,6,7,9,12,13,14]]=>[4,2,3,3,2] [[1,2,3,5,8,9,12],[4,6,7,10,11,13,14]]=>[4,2,4,3,1] [[1,2,3,5,8,9,11],[4,6,7,10,12,13,14]]=>[4,2,4,2,2] [[1,2,3,5,8,9,10],[4,6,7,11,12,13,14]]=>[4,2,5,3] [[1,2,3,5,7,10,12],[4,6,8,9,11,13,14]]=>[4,2,2,3,2,1] [[1,2,3,5,7,10,11],[4,6,8,9,12,13,14]]=>[4,2,2,4,2] [[1,2,3,5,7,9,12],[4,6,8,10,11,13,14]]=>[4,2,2,2,3,1] [[1,2,3,5,7,9,11],[4,6,8,10,12,13,14]]=>[4,2,2,2,2,2] [[1,2,3,5,7,9,10],[4,6,8,11,12,13,14]]=>[4,2,2,3,3] [[1,2,3,5,7,8,12],[4,6,9,10,11,13,14]]=>[4,2,3,4,1] [[1,2,3,5,7,8,11],[4,6,9,10,12,13,14]]=>[4,2,3,3,2] [[1,2,3,5,7,8,10],[4,6,9,11,12,13,14]]=>[4,2,3,2,3] [[1,2,3,5,7,8,9],[4,6,10,11,12,13,14]]=>[4,2,4,4] [[1,2,3,5,6,10,12],[4,7,8,9,11,13,14]]=>[4,3,4,2,1] [[1,2,3,5,6,10,11],[4,7,8,9,12,13,14]]=>[4,3,5,2] [[1,2,3,5,6,9,12],[4,7,8,10,11,13,14]]=>[4,3,3,3,1] [[1,2,3,5,6,9,11],[4,7,8,10,12,13,14]]=>[4,3,3,2,2] [[1,2,3,5,6,9,10],[4,7,8,11,12,13,14]]=>[4,3,4,3] [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]]=>[4,3,2,5] [[1,2,3,5,6,8,12],[4,7,9,10,11,13,14]]=>[4,3,2,4,1] [[1,2,3,5,6,8,11],[4,7,9,10,12,13,14]]=>[4,3,2,3,2] [[1,2,3,5,6,8,10],[4,7,9,11,12,13,14]]=>[4,3,2,2,3] [[1,2,3,5,6,8,9],[4,7,10,11,12,13,14]]=>[4,3,3,4] [[1,2,3,5,6,7,13],[4,8,9,10,11,12,14]]=>[4,4,6] [[1,2,3,5,6,7,12],[4,8,9,10,11,13,14]]=>[4,4,5,1] [[1,2,3,5,6,7,11],[4,8,9,10,12,13,14]]=>[4,4,4,2] [[1,2,3,5,6,7,10],[4,8,9,11,12,13,14]]=>[4,4,3,3] [[1,2,3,5,6,7,9],[4,8,10,11,12,13,14]]=>[4,4,2,4] [[1,2,3,5,6,7,8],[4,9,10,11,12,13,14]]=>[4,5,5] [[1,2,3,4,8,10,12],[5,6,7,9,11,13,14]]=>[5,4,2,2,1] [[1,2,3,4,8,10,11],[5,6,7,9,12,13,14]]=>[5,4,3,2] [[1,2,3,4,8,9,12],[5,6,7,10,11,13,14]]=>[5,5,3,1] [[1,2,3,4,8,9,11],[5,6,7,10,12,13,14]]=>[5,5,2,2] [[1,2,3,4,8,9,10],[5,6,7,11,12,13,14]]=>[5,6,3] [[1,2,3,4,7,10,12],[5,6,8,9,11,13,14]]=>[5,3,3,2,1] [[1,2,3,4,7,10,11],[5,6,8,9,12,13,14]]=>[5,3,4,2] [[1,2,3,4,7,9,12],[5,6,8,10,11,13,14]]=>[5,3,2,3,1] [[1,2,3,4,7,9,11],[5,6,8,10,12,13,14]]=>[5,3,2,2,2] [[1,2,3,4,7,9,10],[5,6,8,11,12,13,14]]=>[5,3,3,3] [[1,2,3,4,7,8,13],[5,6,9,10,11,12,14]]=>[5,4,5] [[1,2,3,4,7,8,12],[5,6,9,10,11,13,14]]=>[5,4,4,1] [[1,2,3,4,7,8,11],[5,6,9,10,12,13,14]]=>[5,4,3,2] [[1,2,3,4,7,8,10],[5,6,9,11,12,13,14]]=>[5,4,2,3] [[1,2,3,4,7,8,9],[5,6,10,11,12,13,14]]=>[5,5,4] [[1,2,3,4,6,10,12],[5,7,8,9,11,13,14]]=>[5,2,4,2,1] [[1,2,3,4,6,10,11],[5,7,8,9,12,13,14]]=>[5,2,5,2] [[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]]=>[5,2,3,4] [[1,2,3,4,6,9,12],[5,7,8,10,11,13,14]]=>[5,2,3,3,1] [[1,2,3,4,6,9,11],[5,7,8,10,12,13,14]]=>[5,2,3,2,2] [[1,2,3,4,6,9,10],[5,7,8,11,12,13,14]]=>[5,2,4,3] [[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]]=>[5,2,2,5] [[1,2,3,4,6,8,12],[5,7,9,10,11,13,14]]=>[5,2,2,4,1] [[1,2,3,4,6,8,11],[5,7,9,10,12,13,14]]=>[5,2,2,3,2] [[1,2,3,4,6,8,10],[5,7,9,11,12,13,14]]=>[5,2,2,2,3] [[1,2,3,4,6,8,9],[5,7,10,11,12,13,14]]=>[5,2,3,4] [[1,2,3,4,6,7,13],[5,8,9,10,11,12,14]]=>[5,3,6] [[1,2,3,4,6,7,12],[5,8,9,10,11,13,14]]=>[5,3,5,1] [[1,2,3,4,6,7,11],[5,8,9,10,12,13,14]]=>[5,3,4,2] [[1,2,3,4,6,7,10],[5,8,9,11,12,13,14]]=>[5,3,3,3] [[1,2,3,4,6,7,9],[5,8,10,11,12,13,14]]=>[5,3,2,4] [[1,2,3,4,6,7,8],[5,9,10,11,12,13,14]]=>[5,4,5] [[1,2,3,4,5,11,12],[6,7,8,9,10,13,14]]=>[6,7,1] [[1,2,3,4,5,10,13],[6,7,8,9,11,12,14]]=>[6,5,3] [[1,2,3,4,5,10,12],[6,7,8,9,11,13,14]]=>[6,5,2,1] [[1,2,3,4,5,10,11],[6,7,8,9,12,13,14]]=>[6,6,2] [[1,2,3,4,5,9,13],[6,7,8,10,11,12,14]]=>[6,4,4] [[1,2,3,4,5,9,12],[6,7,8,10,11,13,14]]=>[6,4,3,1] [[1,2,3,4,5,9,11],[6,7,8,10,12,13,14]]=>[6,4,2,2] [[1,2,3,4,5,9,10],[6,7,8,11,12,13,14]]=>[6,5,3] [[1,2,3,4,5,8,13],[6,7,9,10,11,12,14]]=>[6,3,5] [[1,2,3,4,5,8,12],[6,7,9,10,11,13,14]]=>[6,3,4,1] [[1,2,3,4,5,8,11],[6,7,9,10,12,13,14]]=>[6,3,3,2] [[1,2,3,4,5,8,10],[6,7,9,11,12,13,14]]=>[6,3,2,3] [[1,2,3,4,5,8,9],[6,7,10,11,12,13,14]]=>[6,4,4] [[1,2,3,4,5,7,13],[6,8,9,10,11,12,14]]=>[6,2,6] [[1,2,3,4,5,7,12],[6,8,9,10,11,13,14]]=>[6,2,5,1] [[1,2,3,4,5,7,11],[6,8,9,10,12,13,14]]=>[6,2,4,2] [[1,2,3,4,5,7,10],[6,8,9,11,12,13,14]]=>[6,2,3,3] [[1,2,3,4,5,7,9],[6,8,10,11,12,13,14]]=>[6,2,2,4] [[1,2,3,4,5,7,8],[6,9,10,11,12,13,14]]=>[6,3,5] [[1,2,3,4,5,6,13],[7,8,9,10,11,12,14]]=>[7,7] [[1,2,3,4,5,6,12],[7,8,9,10,11,13,14]]=>[7,6,1] [[1,2,3,4,5,6,11],[7,8,9,10,12,13,14]]=>[7,5,2] [[1,2,3,4,5,6,10],[7,8,9,11,12,13,14]]=>[7,4,3] [[1,2,3,4,5,6,9],[7,8,10,11,12,13,14]]=>[7,3,4] [[1,2,3,4,5,6,8],[7,9,10,11,12,13,14]]=>[7,2,5] [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]]=>[8,6] [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]]=>[6,4,3,1] [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]]=>[6,4,4] [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]]=>[6,4,2,2] [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]]=>[6,3,3,2] [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]]=>[5,4,3,2] [[1,2,5,9,14],[3,4,8,13],[6,7,12],[10,11]]=>[3,3,4,4] [[1,4,5,9,14],[2,7,8,13],[3,11,12],[6],[10]]=>[3,3,4,4] [[1,3,8,9,14],[2,5,12,13],[4,7],[6,11],[10]]=>[2,2,2,4,4] [[1,3,6,13,14],[2,5,9],[4,8,12],[7,11],[10]]=>[2,2,3,3,4] [[1,3,6,10],[2,5,9,14],[4,8,13],[7,12],[11]]=>[2,2,3,4,3] [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]]=>[6,4,3,2] [[1,3,6,10,15],[2,5,9,14],[4,8,13],[7,12],[11]]=>[2,2,3,4,4] [[1,3,5,7,9,11,13,15],[2,4,6,8,10,12,14,16]]=>[2,2,2,2,2,2,2,2] [[1,3,5,7,9,11,13,14],[2,4,6,8,10,12,15,16]]=>[2,2,2,2,2,2,3,1] [[1,3,5,7,9,11,12,14],[2,4,6,8,10,13,15,16]]=>[2,2,2,2,2,3,2,1] [[1,3,5,7,9,11,12,13],[2,4,6,8,10,14,15,16]]=>[2,2,2,2,2,4,2] [[1,3,5,7,9,10,12,14],[2,4,6,8,11,13,15,16]]=>[2,2,2,2,3,2,2,1] [[1,3,5,7,9,10,11,14],[2,4,6,8,12,13,15,16]]=>[2,2,2,2,4,3,1] [[1,3,5,7,9,10,11,13],[2,4,6,8,12,14,15,16]]=>[2,2,2,2,4,2,2] [[1,3,5,7,9,10,11,12],[2,4,6,8,13,14,15,16]]=>[2,2,2,2,5,3] [[1,3,5,7,8,10,12,14],[2,4,6,9,11,13,15,16]]=>[2,2,2,3,2,2,2,1] [[1,3,5,7,8,9,12,14],[2,4,6,10,11,13,15,16]]=>[2,2,2,4,3,2,1] [[1,3,5,7,8,9,11,14],[2,4,6,10,12,13,15,16]]=>[2,2,2,4,2,3,1] [[1,3,5,7,8,9,10,14],[2,4,6,11,12,13,15,16]]=>[2,2,2,5,4,1] [[1,3,5,6,8,10,12,14],[2,4,7,9,11,13,15,16]]=>[2,2,3,2,2,2,2,1] [[1,3,5,6,7,10,12,14],[2,4,8,9,11,13,15,16]]=>[2,2,4,3,2,2,1] [[1,3,5,6,7,9,12,14],[2,4,8,10,11,13,15,16]]=>[2,2,4,2,3,2,1] [[1,3,5,6,7,8,12,14],[2,4,9,10,11,13,15,16]]=>[2,2,5,4,2,1] [[1,3,4,6,8,10,12,14],[2,5,7,9,11,13,15,16]]=>[2,3,2,2,2,2,2,1] [[1,3,4,5,8,10,12,14],[2,6,7,9,11,13,15,16]]=>[2,4,3,2,2,2,1] [[1,3,4,5,7,10,12,14],[2,6,8,9,11,13,15,16]]=>[2,4,2,3,2,2,1] [[1,3,4,5,6,10,12,14],[2,7,8,9,11,13,15,16]]=>[2,5,4,2,2,1] [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]]=>[2,5,4,5] [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]]=>[2,6,2,2,4] [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]]=>[2,6,3,5] [[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]]=>[2,7,4,3] [[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]]=>[2,7,3,4] [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]]=>[2,7,2,5] [[1,3,4,5,6,7,8,9],[2,10,11,12,13,14,15,16]]=>[2,8,6] [[1,2,4,6,8,10,12,14],[3,5,7,9,11,13,15,16]]=>[3,2,2,2,2,2,2,1] [[1,2,3,6,8,10,12,14],[4,5,7,9,11,13,15,16]]=>[4,3,2,2,2,2,1] [[1,2,3,5,8,10,12,14],[4,6,7,9,11,13,15,16]]=>[4,2,3,2,2,2,1] [[1,2,3,4,8,10,12,14],[5,6,7,9,11,13,15,16]]=>[5,4,2,2,2,1] [[1,2,3,4,6,7,8,15],[5,9,10,11,12,13,14,16]]=>[5,4,7] [[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]]=>[6,2,2,6] [[1,2,3,4,5,7,8,15],[6,9,10,11,12,13,14,16]]=>[6,3,7] [[1,2,3,4,5,6,10,15],[7,8,9,11,12,13,14,16]]=>[7,4,5] [[1,2,3,4,5,6,9,15],[7,8,10,11,12,13,14,16]]=>[7,3,6] [[1,2,3,4,5,6,8,15],[7,9,10,11,12,13,14,16]]=>[7,2,7] [[1,2,3,4,5,6,7,15],[8,9,10,11,12,13,14,16]]=>[8,8] [[1,3,5,7,9,11,13,15,17],[2,4,6,8,10,12,14,16,18]]=>[2,2,2,2,2,2,2,2,2] [[1,3,5,7,9,11,13,15,16],[2,4,6,8,10,12,14,17,18]]=>[2,2,2,2,2,2,2,3,1] [[1,3,5,7,9,11,13,14,16],[2,4,6,8,10,12,15,17,18]]=>[2,2,2,2,2,2,3,2,1] [[1,3,5,7,9,11,12,14,16],[2,4,6,8,10,13,15,17,18]]=>[2,2,2,2,2,3,2,2,1] [[1,3,5,7,9,10,12,14,16],[2,4,6,8,11,13,15,17,18]]=>[2,2,2,2,3,2,2,2,1] [[1,3,5,7,8,10,12,14,16],[2,4,6,9,11,13,15,17,18]]=>[2,2,2,3,2,2,2,2,1] [[1,3,5,6,8,10,12,14,16],[2,4,7,9,11,13,15,17,18]]=>[2,2,3,2,2,2,2,2,1] [[1,3,4,6,8,10,12,14,16],[2,5,7,9,11,13,15,17,18]]=>[2,3,2,2,2,2,2,2,1] [[1,2,4,6,8,10,12,14,16],[3,5,7,9,11,13,15,17,18]]=>[3,2,2,2,2,2,2,2,1] [[1,3,5,7,9,11,13,14,15],[2,4,6,8,10,12,16,17,18]]=>[2,2,2,2,2,2,4,2] [[1,3,5,7,9,11,12,13,16],[2,4,6,8,10,14,15,17,18]]=>[2,2,2,2,2,4,3,1] [[1,3,5,7,9,10,11,14,16],[2,4,6,8,12,13,15,17,18]]=>[2,2,2,2,4,3,2,1] [[1,3,5,7,8,9,12,14,16],[2,4,6,10,11,13,15,17,18]]=>[2,2,2,4,3,2,2,1] [[1,3,5,6,7,10,12,14,16],[2,4,8,9,11,13,15,17,18]]=>[2,2,4,3,2,2,2,1] [[1,3,4,5,8,10,12,14,16],[2,6,7,9,11,13,15,17,18]]=>[2,4,3,2,2,2,2,1] [[1,2,3,6,8,10,12,14,16],[4,5,7,9,11,13,15,17,18]]=>[4,3,2,2,2,2,2,1] [[1,2,3,4,5,6,7,8,17],[9,10,11,12,13,14,15,16,18]]=>[9,9] [[1,3,4,5,6,7,8,9,10],[2,11,12,13,14,15,16,17,18]]=>[2,9,7] [[1,2,3,4,5,6,7,9,17],[8,10,11,12,13,14,15,16,18]]=>[8,2,8] [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]]=>[2,8,2,6] [[1,2,3,4,5,6,7,10,17],[8,9,11,12,13,14,15,16,18]]=>[8,3,7] [[1,2,3,4,5,6,8,9,17],[7,10,11,12,13,14,15,16,18]]=>[7,3,8] [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]]=>[2,8,3,5] [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]]=>[2,7,3,6] [[1,3,5,7,9,11,13,15,17,19],[2,4,6,8,10,12,14,16,18,20]]=>[2,2,2,2,2,2,2,2,2,2] [[1,3,5,7,9,11,13,15,17,18],[2,4,6,8,10,12,14,16,19,20]]=>[2,2,2,2,2,2,2,2,3,1] [[1,3,5,7,9,11,13,15,16,18],[2,4,6,8,10,12,14,17,19,20]]=>[2,2,2,2,2,2,2,3,2,1] [[1,3,5,7,9,11,13,14,16,18],[2,4,6,8,10,12,15,17,19,20]]=>[2,2,2,2,2,2,3,2,2,1] [[1,3,5,7,9,11,12,14,16,18],[2,4,6,8,10,13,15,17,19,20]]=>[2,2,2,2,2,3,2,2,2,1] [[1,3,5,7,9,10,12,14,16,18],[2,4,6,8,11,13,15,17,19,20]]=>[2,2,2,2,3,2,2,2,2,1] [[1,3,5,7,8,10,12,14,16,18],[2,4,6,9,11,13,15,17,19,20]]=>[2,2,2,3,2,2,2,2,2,1] [[1,3,5,6,8,10,12,14,16,18],[2,4,7,9,11,13,15,17,19,20]]=>[2,2,3,2,2,2,2,2,2,1] [[1,3,4,6,8,10,12,14,16,18],[2,5,7,9,11,13,15,17,19,20]]=>[2,3,2,2,2,2,2,2,2,1] [[1,2,4,6,8,10,12,14,16,18],[3,5,7,9,11,13,15,17,19,20]]=>[3,2,2,2,2,2,2,2,2,1] [[1,2,3,4,5,6,7,8,9,19],[10,11,12,13,14,15,16,17,18,20]]=>[10,10] [[1,3,4,5,6,7,8,9,10,11],[2,12,13,14,15,16,17,18,19,20]]=>[2,10,8] [[1,2,3,4,5,6,7,8,10,19],[9,11,12,13,14,15,16,17,18,20]]=>[9,2,9] [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]]=>[2,9,2,7] [[1,2,3,4,5,6,7,8,9,10,21],[11,12,13,14,15,16,17,18,19,20,22]]=>[11,11] [[1,3,4,5,6,7,8,9,10,11,12],[2,13,14,15,16,17,18,19,20,21,22]]=>[2,11,9]
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Description
The composition corresponding to the valley set of a standard tableau.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a valley if $i-1$ is a descent and $i$ is an ascent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the valley set of $T$.
References
[1] Zhou, R. D. P., Yan, S. H. F. Equidistribution of set-valued statistics on standard Young tableaux and transversals arXiv:2306.04382
Properties
graded
Sage code
def mapping(T):
    d = T.standard_descents()
    c = [i for i in range(2, T.size()) if i-1 in d and i not in d]
    return Composition(from_subset=(c, T.size()))

Weight
40
Created
Jun 12, 2023 at 07:47 by Martin Rubey
Updated
Jun 12, 2023 at 07:47 by Martin Rubey