Identifier
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
Images
=>
Cc0002;cc-rep-0Cc0007;cc-rep-1Cc0007;cc-rep-2
[1]=>[[1]]=>[[1]] [2]=>[[1,2]]=>[[1],[2]] [1,1]=>[[1],[2]]=>[[1,2]] [3]=>[[1,2,3]]=>[[1],[2],[3]] [2,1]=>[[1,2],[3]]=>[[1,3],[2]] [1,1,1]=>[[1],[2],[3]]=>[[1,2,3]] [4]=>[[1,2,3,4]]=>[[1],[2],[3],[4]] [3,1]=>[[1,2,3],[4]]=>[[1,4],[2],[3]] [2,2]=>[[1,2],[3,4]]=>[[1,3],[2,4]] [2,1,1]=>[[1,2],[3],[4]]=>[[1,3,4],[2]] [1,1,1,1]=>[[1],[2],[3],[4]]=>[[1,2,3,4]] [5]=>[[1,2,3,4,5]]=>[[1],[2],[3],[4],[5]] [4,1]=>[[1,2,3,4],[5]]=>[[1,5],[2],[3],[4]] [3,2]=>[[1,2,3],[4,5]]=>[[1,4],[2,5],[3]] [3,1,1]=>[[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]] [2,2,1]=>[[1,2],[3,4],[5]]=>[[1,3,5],[2,4]] [2,1,1,1]=>[[1,2],[3],[4],[5]]=>[[1,3,4,5],[2]] [1,1,1,1,1]=>[[1],[2],[3],[4],[5]]=>[[1,2,3,4,5]] [6]=>[[1,2,3,4,5,6]]=>[[1],[2],[3],[4],[5],[6]] [5,1]=>[[1,2,3,4,5],[6]]=>[[1,6],[2],[3],[4],[5]] [4,2]=>[[1,2,3,4],[5,6]]=>[[1,5],[2,6],[3],[4]] [4,1,1]=>[[1,2,3,4],[5],[6]]=>[[1,5,6],[2],[3],[4]] [3,3]=>[[1,2,3],[4,5,6]]=>[[1,4],[2,5],[3,6]] [3,2,1]=>[[1,2,3],[4,5],[6]]=>[[1,4,6],[2,5],[3]] [3,1,1,1]=>[[1,2,3],[4],[5],[6]]=>[[1,4,5,6],[2],[3]] [2,2,2]=>[[1,2],[3,4],[5,6]]=>[[1,3,5],[2,4,6]] [2,2,1,1]=>[[1,2],[3,4],[5],[6]]=>[[1,3,5,6],[2,4]] [2,1,1,1,1]=>[[1,2],[3],[4],[5],[6]]=>[[1,3,4,5,6],[2]] [1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6]]=>[[1,2,3,4,5,6]] [7]=>[[1,2,3,4,5,6,7]]=>[[1],[2],[3],[4],[5],[6],[7]] [6,1]=>[[1,2,3,4,5,6],[7]]=>[[1,7],[2],[3],[4],[5],[6]] [5,2]=>[[1,2,3,4,5],[6,7]]=>[[1,6],[2,7],[3],[4],[5]] [5,1,1]=>[[1,2,3,4,5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]] [4,3]=>[[1,2,3,4],[5,6,7]]=>[[1,5],[2,6],[3,7],[4]] [4,2,1]=>[[1,2,3,4],[5,6],[7]]=>[[1,5,7],[2,6],[3],[4]] [4,1,1,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]] [3,3,1]=>[[1,2,3],[4,5,6],[7]]=>[[1,4,7],[2,5],[3,6]] [3,2,2]=>[[1,2,3],[4,5],[6,7]]=>[[1,4,6],[2,5,7],[3]] [3,2,1,1]=>[[1,2,3],[4,5],[6],[7]]=>[[1,4,6,7],[2,5],[3]] [3,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,4,5,6,7],[2],[3]] [2,2,2,1]=>[[1,2],[3,4],[5,6],[7]]=>[[1,3,5,7],[2,4,6]] [2,2,1,1,1]=>[[1,2],[3,4],[5],[6],[7]]=>[[1,3,5,6,7],[2,4]] [2,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[[1,3,4,5,6,7],[2]] [1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>[[1,2,3,4,5,6,7]] [8]=>[[1,2,3,4,5,6,7,8]]=>[[1],[2],[3],[4],[5],[6],[7],[8]] [7,1]=>[[1,2,3,4,5,6,7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]] [6,2]=>[[1,2,3,4,5,6],[7,8]]=>[[1,7],[2,8],[3],[4],[5],[6]] [6,1,1]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]] [5,3]=>[[1,2,3,4,5],[6,7,8]]=>[[1,6],[2,7],[3,8],[4],[5]] [5,2,1]=>[[1,2,3,4,5],[6,7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]] [5,1,1,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]] [4,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,5],[2,6],[3,7],[4,8]] [4,3,1]=>[[1,2,3,4],[5,6,7],[8]]=>[[1,5,8],[2,6],[3,7],[4]] [4,2,2]=>[[1,2,3,4],[5,6],[7,8]]=>[[1,5,7],[2,6,8],[3],[4]] [4,2,1,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]] [4,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]] [3,3,2]=>[[1,2,3],[4,5,6],[7,8]]=>[[1,4,7],[2,5,8],[3,6]] [3,3,1,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[[1,4,7,8],[2,5],[3,6]] [3,2,2,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[[1,4,6,8],[2,5,7],[3]] [3,2,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[[1,4,6,7,8],[2,5],[3]] [3,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]] [2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[[1,3,5,7],[2,4,6,8]] [2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[[1,3,5,7,8],[2,4,6]] [2,2,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[[1,3,5,6,7,8],[2,4]] [2,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,3,4,5,6,7,8],[2]] [1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[[1,2,3,4,5,6,7,8]] [9]=>[[1,2,3,4,5,6,7,8,9]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]] [8,1]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]] [7,2]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,8],[2,9],[3],[4],[5],[6],[7]] [7,1,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]] [6,3]=>[[1,2,3,4,5,6],[7,8,9]]=>[[1,7],[2,8],[3,9],[4],[5],[6]] [6,2,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[[1,7,9],[2,8],[3],[4],[5],[6]] [6,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,7,8,9],[2],[3],[4],[5],[6]] [5,4]=>[[1,2,3,4,5],[6,7,8,9]]=>[[1,6],[2,7],[3,8],[4,9],[5]] [5,3,1]=>[[1,2,3,4,5],[6,7,8],[9]]=>[[1,6,9],[2,7],[3,8],[4],[5]] [5,2,2]=>[[1,2,3,4,5],[6,7],[8,9]]=>[[1,6,8],[2,7,9],[3],[4],[5]] [5,2,1,1]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[[1,6,8,9],[2,7],[3],[4],[5]] [5,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[1,6,7,8,9],[2],[3],[4],[5]] [4,4,1]=>[[1,2,3,4],[5,6,7,8],[9]]=>[[1,5,9],[2,6],[3,7],[4,8]] [4,3,2]=>[[1,2,3,4],[5,6,7],[8,9]]=>[[1,5,8],[2,6,9],[3,7],[4]] [4,3,1,1]=>[[1,2,3,4],[5,6,7],[8],[9]]=>[[1,5,8,9],[2,6],[3,7],[4]] [4,2,2,1]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[[1,5,7,9],[2,6,8],[3],[4]] [4,2,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[[1,5,7,8,9],[2,6],[3],[4]] [4,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]] [3,3,3]=>[[1,2,3],[4,5,6],[7,8,9]]=>[[1,4,7],[2,5,8],[3,6,9]] [3,3,2,1]=>[[1,2,3],[4,5,6],[7,8],[9]]=>[[1,4,7,9],[2,5,8],[3,6]] [3,3,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9]]=>[[1,4,7,8,9],[2,5],[3,6]] [3,2,2,2]=>[[1,2,3],[4,5],[6,7],[8,9]]=>[[1,4,6,8],[2,5,7,9],[3]] [3,2,2,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9]]=>[[1,4,6,8,9],[2,5,7],[3]] [3,2,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9]]=>[[1,4,6,7,8,9],[2,5],[3]] [3,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]] [2,2,2,2,1]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[[1,3,5,7,9],[2,4,6,8]] [2,2,2,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9]]=>[[1,3,5,7,8,9],[2,4,6]] [2,2,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[[1,3,5,6,7,8,9],[2,4]] [2,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,3,4,5,6,7,8,9],[2]] [1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,2,3,4,5,6,7,8,9]] [10]=>[[1,2,3,4,5,6,7,8,9,10]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] [9,1]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] [8,2]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8]] [8,1,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] [7,3]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[[1,8],[2,9],[3,10],[4],[5],[6],[7]] [7,2,1]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[[1,8,10],[2,9],[3],[4],[5],[6],[7]] [7,1,1,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]] [6,4]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,7],[2,8],[3,9],[4,10],[5],[6]] [6,3,1]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[[1,7,10],[2,8],[3,9],[4],[5],[6]] [6,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[[1,7,9],[2,8,10],[3],[4],[5],[6]] [6,2,1,1]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>[[1,7,9,10],[2,8],[3],[4],[5],[6]] [6,1,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]] [5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[[1,6],[2,7],[3,8],[4,9],[5,10]] [5,4,1]=>[[1,2,3,4,5],[6,7,8,9],[10]]=>[[1,6,10],[2,7],[3,8],[4,9],[5]] [5,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10]]=>[[1,6,9],[2,7,10],[3,8],[4],[5]] [5,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10]]=>[[1,6,9,10],[2,7],[3,8],[4],[5]] [5,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10]]=>[[1,6,8,10],[2,7,9],[3],[4],[5]] [5,2,1,1,1]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[[1,6,8,9,10],[2,7],[3],[4],[5]] [5,1,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[1,6,7,8,9,10],[2],[3],[4],[5]] [4,4,2]=>[[1,2,3,4],[5,6,7,8],[9,10]]=>[[1,5,9],[2,6,10],[3,7],[4,8]] [4,4,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10]]=>[[1,5,9,10],[2,6],[3,7],[4,8]] [4,3,3]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>[[1,5,8],[2,6,9],[3,7,10],[4]] [4,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10]]=>[[1,5,8,10],[2,6,9],[3,7],[4]] [4,3,1,1,1]=>[[1,2,3,4],[5,6,7],[8],[9],[10]]=>[[1,5,8,9,10],[2,6],[3,7],[4]] [4,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[[1,5,7,9],[2,6,8,10],[3],[4]] [4,2,2,1,1]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[[1,5,7,9,10],[2,6,8],[3],[4]] [4,2,1,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[[1,5,7,8,9,10],[2,6],[3],[4]] [4,1,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]] [3,3,3,1]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>[[1,4,7,10],[2,5,8],[3,6,9]] [3,3,2,2]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>[[1,4,7,9],[2,5,8,10],[3,6]] [3,3,2,1,1]=>[[1,2,3],[4,5,6],[7,8],[9],[10]]=>[[1,4,7,9,10],[2,5,8],[3,6]] [3,3,1,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[[1,4,7,8,9,10],[2,5],[3,6]] [3,2,2,2,1]=>[[1,2,3],[4,5],[6,7],[8,9],[10]]=>[[1,4,6,8,10],[2,5,7,9],[3]] [3,2,2,1,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>[[1,4,6,8,9,10],[2,5,7],[3]] [3,2,1,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[[1,4,6,7,8,9,10],[2,5],[3]] [3,1,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]] [2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[[1,3,5,7,9],[2,4,6,8,10]] [2,2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[[1,3,5,7,9,10],[2,4,6,8]] [2,2,2,1,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>[[1,3,5,7,8,9,10],[2,4,6]] [2,2,1,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[[1,3,5,6,7,8,9,10],[2,4]] [2,1,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]] [1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,2,3,4,5,6,7,8,9,10]] [11]=>[[1,2,3,4,5,6,7,8,9,10,11]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]] [10,1]=>[[1,2,3,4,5,6,7,8,9,10],[11]]=>[[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10]] [9,2]=>[[1,2,3,4,5,6,7,8,9],[10,11]]=>[[1,10],[2,11],[3],[4],[5],[6],[7],[8],[9]] [9,1,1]=>[[1,2,3,4,5,6,7,8,9],[10],[11]]=>[[1,10,11],[2],[3],[4],[5],[6],[7],[8],[9]] [8,3]=>[[1,2,3,4,5,6,7,8],[9,10,11]]=>[[1,9],[2,10],[3,11],[4],[5],[6],[7],[8]] [8,2,1]=>[[1,2,3,4,5,6,7,8],[9,10],[11]]=>[[1,9,11],[2,10],[3],[4],[5],[6],[7],[8]] [8,1,1,1]=>[[1,2,3,4,5,6,7,8],[9],[10],[11]]=>[[1,9,10,11],[2],[3],[4],[5],[6],[7],[8]] [7,3,1]=>[[1,2,3,4,5,6,7],[8,9,10],[11]]=>[[1,8,11],[2,9],[3,10],[4],[5],[6],[7]] [7,2,2]=>[[1,2,3,4,5,6,7],[8,9],[10,11]]=>[[1,8,10],[2,9,11],[3],[4],[5],[6],[7]] [7,2,1,1]=>[[1,2,3,4,5,6,7],[8,9],[10],[11]]=>[[1,8,10,11],[2,9],[3],[4],[5],[6],[7]] [6,5]=>[[1,2,3,4,5,6],[7,8,9,10,11]]=>[[1,7],[2,8],[3,9],[4,10],[5,11],[6]] [6,3,2]=>[[1,2,3,4,5,6],[7,8,9],[10,11]]=>[[1,7,10],[2,8,11],[3,9],[4],[5],[6]] [6,3,1,1]=>[[1,2,3,4,5,6],[7,8,9],[10],[11]]=>[[1,7,10,11],[2,8],[3,9],[4],[5],[6]] [6,2,2,1]=>[[1,2,3,4,5,6],[7,8],[9,10],[11]]=>[[1,7,9,11],[2,8,10],[3],[4],[5],[6]] [6,2,1,1,1]=>[[1,2,3,4,5,6],[7,8],[9],[10],[11]]=>[[1,7,9,10,11],[2,8],[3],[4],[5],[6]] [5,5,1]=>[[1,2,3,4,5],[6,7,8,9,10],[11]]=>[[1,6,11],[2,7],[3,8],[4,9],[5,10]] [5,4,2]=>[[1,2,3,4,5],[6,7,8,9],[10,11]]=>[[1,6,10],[2,7,11],[3,8],[4,9],[5]] [5,4,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10],[11]]=>[[1,6,10,11],[2,7],[3,8],[4,9],[5]] [5,3,3]=>[[1,2,3,4,5],[6,7,8],[9,10,11]]=>[[1,6,9],[2,7,10],[3,8,11],[4],[5]] [5,3,2,1]=>[[1,2,3,4,5],[6,7,8],[9,10],[11]]=>[[1,6,9,11],[2,7,10],[3,8],[4],[5]] [5,3,1,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10],[11]]=>[[1,6,9,10,11],[2,7],[3,8],[4],[5]] [5,2,2,2]=>[[1,2,3,4,5],[6,7],[8,9],[10,11]]=>[[1,6,8,10],[2,7,9,11],[3],[4],[5]] [5,2,2,1,1]=>[[1,2,3,4,5],[6,7],[8,9],[10],[11]]=>[[1,6,8,10,11],[2,7,9],[3],[4],[5]] [5,2,1,1,1,1]=>[[1,2,3,4,5],[6,7],[8],[9],[10],[11]]=>[[1,6,8,9,10,11],[2,7],[3],[4],[5]] [4,4,3]=>[[1,2,3,4],[5,6,7,8],[9,10,11]]=>[[1,5,9],[2,6,10],[3,7,11],[4,8]] [4,4,2,1]=>[[1,2,3,4],[5,6,7,8],[9,10],[11]]=>[[1,5,9,11],[2,6,10],[3,7],[4,8]] [4,4,1,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10],[11]]=>[[1,5,9,10,11],[2,6],[3,7],[4,8]] [4,3,3,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11]]=>[[1,5,8,11],[2,6,9],[3,7,10],[4]] [4,3,2,2]=>[[1,2,3,4],[5,6,7],[8,9],[10,11]]=>[[1,5,8,10],[2,6,9,11],[3,7],[4]] [4,3,2,1,1]=>[[1,2,3,4],[5,6,7],[8,9],[10],[11]]=>[[1,5,8,10,11],[2,6,9],[3,7],[4]] [4,2,2,2,1]=>[[1,2,3,4],[5,6],[7,8],[9,10],[11]]=>[[1,5,7,9,11],[2,6,8,10],[3],[4]] [3,3,3,2]=>[[1,2,3],[4,5,6],[7,8,9],[10,11]]=>[[1,4,7,10],[2,5,8,11],[3,6,9]] [3,3,3,1,1]=>[[1,2,3],[4,5,6],[7,8,9],[10],[11]]=>[[1,4,7,10,11],[2,5,8],[3,6,9]] [3,3,2,2,1]=>[[1,2,3],[4,5,6],[7,8],[9,10],[11]]=>[[1,4,7,9,11],[2,5,8,10],[3,6]] [3,3,1,1,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9],[10],[11]]=>[[1,4,7,8,9,10,11],[2,5],[3,6]] [3,2,2,2,2]=>[[1,2,3],[4,5],[6,7],[8,9],[10,11]]=>[[1,4,6,8,10],[2,5,7,9,11],[3]] [2,2,2,2,2,1]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11]]=>[[1,3,5,7,9,11],[2,4,6,8,10]] [2,2,2,1,1,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9],[10],[11]]=>[[1,3,5,7,8,9,10,11],[2,4,6]] [2,1,1,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]=>[[1,3,4,5,6,7,8,9,10,11],[2]] [1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]=>[[1,2,3,4,5,6,7,8,9,10,11]] [12]=>[[1,2,3,4,5,6,7,8,9,10,11,12]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] [11,1]=>[[1,2,3,4,5,6,7,8,9,10,11],[12]]=>[[1,12],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]] [10,2]=>[[1,2,3,4,5,6,7,8,9,10],[11,12]]=>[[1,11],[2,12],[3],[4],[5],[6],[7],[8],[9],[10]] [9,3]=>[[1,2,3,4,5,6,7,8,9],[10,11,12]]=>[[1,10],[2,11],[3,12],[4],[5],[6],[7],[8],[9]] [9,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11],[12]]=>[[1,10,12],[2,11],[3],[4],[5],[6],[7],[8],[9]] [9,1,1,1]=>[[1,2,3,4,5,6,7,8,9],[10],[11],[12]]=>[[1,10,11,12],[2],[3],[4],[5],[6],[7],[8],[9]] [8,3,1]=>[[1,2,3,4,5,6,7,8],[9,10,11],[12]]=>[[1,9,12],[2,10],[3,11],[4],[5],[6],[7],[8]] [8,2,2]=>[[1,2,3,4,5,6,7,8],[9,10],[11,12]]=>[[1,9,11],[2,10,12],[3],[4],[5],[6],[7],[8]] [8,2,1,1]=>[[1,2,3,4,5,6,7,8],[9,10],[11],[12]]=>[[1,9,11,12],[2,10],[3],[4],[5],[6],[7],[8]] [7,3,2]=>[[1,2,3,4,5,6,7],[8,9,10],[11,12]]=>[[1,8,11],[2,9,12],[3,10],[4],[5],[6],[7]] [7,3,1,1]=>[[1,2,3,4,5,6,7],[8,9,10],[11],[12]]=>[[1,8,11,12],[2,9],[3,10],[4],[5],[6],[7]] [7,2,2,1]=>[[1,2,3,4,5,6,7],[8,9],[10,11],[12]]=>[[1,8,10,12],[2,9,11],[3],[4],[5],[6],[7]] [6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] [6,5,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12]]=>[[1,7,12],[2,8],[3,9],[4,10],[5,11],[6]] [6,4,2]=>[[1,2,3,4,5,6],[7,8,9,10],[11,12]]=>[[1,7,11],[2,8,12],[3,9],[4,10],[5],[6]] [6,3,2,1]=>[[1,2,3,4,5,6],[7,8,9],[10,11],[12]]=>[[1,7,10,12],[2,8,11],[3,9],[4],[5],[6]] [6,3,1,1,1]=>[[1,2,3,4,5,6],[7,8,9],[10],[11],[12]]=>[[1,7,10,11,12],[2,8],[3,9],[4],[5],[6]] [6,2,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10],[11,12]]=>[[1,7,9,11],[2,8,10,12],[3],[4],[5],[6]] [6,2,2,1,1]=>[[1,2,3,4,5,6],[7,8],[9,10],[11],[12]]=>[[1,7,9,11,12],[2,8,10],[3],[4],[5],[6]] [5,5,2]=>[[1,2,3,4,5],[6,7,8,9,10],[11,12]]=>[[1,6,11],[2,7,12],[3,8],[4,9],[5,10]] [5,4,3]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12]]=>[[1,6,10],[2,7,11],[3,8,12],[4,9],[5]] [5,4,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12]]=>[[1,6,10,12],[2,7,11],[3,8],[4,9],[5]] [5,4,1,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10],[11],[12]]=>[[1,6,10,11,12],[2,7],[3,8],[4,9],[5]] [5,3,3,1]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12]]=>[[1,6,9,12],[2,7,10],[3,8,11],[4],[5]] [5,3,2,2]=>[[1,2,3,4,5],[6,7,8],[9,10],[11,12]]=>[[1,6,9,11],[2,7,10,12],[3,8],[4],[5]] [5,3,2,1,1]=>[[1,2,3,4,5],[6,7,8],[9,10],[11],[12]]=>[[1,6,9,11,12],[2,7,10],[3,8],[4],[5]] [5,2,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10,11],[12]]=>[[1,6,8,10,12],[2,7,9,11],[3],[4],[5]] [5,2,2,1,1,1]=>[[1,2,3,4,5],[6,7],[8,9],[10],[11],[12]]=>[[1,6,8,10,11,12],[2,7,9],[3],[4],[5]] [4,4,4]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12]]=>[[1,5,9],[2,6,10],[3,7,11],[4,8,12]] [4,4,3,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12]]=>[[1,5,9,12],[2,6,10],[3,7,11],[4,8]] [4,4,2,2]=>[[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>[[1,5,9,11],[2,6,10,12],[3,7],[4,8]] [4,4,2,1,1]=>[[1,2,3,4],[5,6,7,8],[9,10],[11],[12]]=>[[1,5,9,11,12],[2,6,10],[3,7],[4,8]] [4,3,3,2]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12]]=>[[1,5,8,11],[2,6,9,12],[3,7,10],[4]] [4,3,3,1,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11],[12]]=>[[1,5,8,11,12],[2,6,9],[3,7,10],[4]] [4,3,2,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10,11],[12]]=>[[1,5,8,10,12],[2,6,9,11],[3,7],[4]] [4,2,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,5,7,9,11],[2,6,8,10,12],[3],[4]] [3,3,3,3]=>[[1,2,3],[4,5,6],[7,8,9],[10,11,12]]=>[[1,4,7,10],[2,5,8,11],[3,6,9,12]] [3,3,3,2,1]=>[[1,2,3],[4,5,6],[7,8,9],[10,11],[12]]=>[[1,4,7,10,12],[2,5,8,11],[3,6,9]] [3,3,2,2,2]=>[[1,2,3],[4,5,6],[7,8],[9,10],[11,12]]=>[[1,4,7,9,11],[2,5,8,10,12],[3,6]] [3,3,2,2,1,1]=>[[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]]=>[[1,4,7,9,11,12],[2,5,8,10],[3,6]] [3,2,2,2,2,1]=>[[1,2,3],[4,5],[6,7],[8,9],[10,11],[12]]=>[[1,4,6,8,10,12],[2,5,7,9,11],[3]] [2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]] [2,2,2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11],[12]]=>[[1,3,5,7,9,11,12],[2,4,6,8,10]] [2,2,2,2,1,1,1,1]=>[[1,2],[3,4],[5,6],[7,8],[9],[10],[11],[12]]=>[[1,3,5,7,9,10,11,12],[2,4,6,8]] [2,2,2,1,1,1,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9],[10],[11],[12]]=>[[1,3,5,7,8,9,10,11,12],[2,4,6]] [2,2,1,1,1,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[[1,3,5,6,7,8,9,10,11,12],[2,4]] [2,1,1,1,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[[1,3,4,5,6,7,8,9,10,11,12],[2]] [1,1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[[1,2,3,4,5,6,7,8,9,10,11,12]] [13]=>[[1,2,3,4,5,6,7,8,9,10,11,12,13]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13]] [9,3,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12],[13]]=>[[1,10,13],[2,11],[3,12],[4],[5],[6],[7],[8],[9]] [9,2,2]=>[[1,2,3,4,5,6,7,8,9],[10,11],[12,13]]=>[[1,10,12],[2,11,13],[3],[4],[5],[6],[7],[8],[9]] [9,2,1,1]=>[[1,2,3,4,5,6,7,8,9],[10,11],[12],[13]]=>[[1,10,12,13],[2,11],[3],[4],[5],[6],[7],[8],[9]] [8,3,2]=>[[1,2,3,4,5,6,7,8],[9,10,11],[12,13]]=>[[1,9,12],[2,10,13],[3,11],[4],[5],[6],[7],[8]] [8,3,1,1]=>[[1,2,3,4,5,6,7,8],[9,10,11],[12],[13]]=>[[1,9,12,13],[2,10],[3,11],[4],[5],[6],[7],[8]] [8,2,2,1]=>[[1,2,3,4,5,6,7,8],[9,10],[11,12],[13]]=>[[1,9,11,13],[2,10,12],[3],[4],[5],[6],[7],[8]] [7,6]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13]]=>[[1,8],[2,9],[3,10],[4,11],[5,12],[6,13],[7]] [7,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10],[11,12],[13]]=>[[1,8,11,13],[2,9,12],[3,10],[4],[5],[6],[7]] [6,6,1]=>[[1,2,3,4,5,6],[7,8,9,10,11,12],[13]]=>[[1,7,13],[2,8],[3,9],[4,10],[5,11],[6,12]] [6,5,2]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13]]=>[[1,7,12],[2,8,13],[3,9],[4,10],[5,11],[6]] [6,3,2,1,1]=>[[1,2,3,4,5,6],[7,8,9],[10,11],[12],[13]]=>[[1,7,10,12,13],[2,8,11],[3,9],[4],[5],[6]] [6,2,2,2,1]=>[[1,2,3,4,5,6],[7,8],[9,10],[11,12],[13]]=>[[1,7,9,11,13],[2,8,10,12],[3],[4],[5],[6]] [5,5,3]=>[[1,2,3,4,5],[6,7,8,9,10],[11,12,13]]=>[[1,6,11],[2,7,12],[3,8,13],[4,9],[5,10]] [5,4,4]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12,13]]=>[[1,6,10],[2,7,11],[3,8,12],[4,9,13],[5]] [5,4,3,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]]=>[[1,6,10,13],[2,7,11],[3,8,12],[4,9],[5]] [5,4,2,2]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]]=>[[1,6,10,12],[2,7,11,13],[3,8],[4,9],[5]] [5,4,2,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]]=>[[1,6,10,12,13],[2,7,11],[3,8],[4,9],[5]] [5,4,1,1,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10],[11],[12],[13]]=>[[1,6,10,11,12,13],[2,7],[3,8],[4,9],[5]] [5,3,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]]=>[[1,6,9,12],[2,7,10,13],[3,8,11],[4],[5]] [5,3,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]]=>[[1,6,9,12,13],[2,7,10],[3,8,11],[4],[5]] [5,3,2,2,1]=>[[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]]=>[[1,6,9,11,13],[2,7,10,12],[3,8],[4],[5]] [5,3,2,1,1,1]=>[[1,2,3,4,5],[6,7,8],[9,10],[11],[12],[13]]=>[[1,6,9,11,12,13],[2,7,10],[3,8],[4],[5]] [4,4,4,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13]]=>[[1,5,9,13],[2,6,10],[3,7,11],[4,8,12]] [4,4,3,2]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]]=>[[1,5,9,12],[2,6,10,13],[3,7,11],[4,8]] [4,4,3,1,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]]=>[[1,5,9,12,13],[2,6,10],[3,7,11],[4,8]] [4,4,2,2,1]=>[[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]]=>[[1,5,9,11,13],[2,6,10,12],[3,7],[4,8]] [4,3,3,3]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12,13]]=>[[1,5,8,11],[2,6,9,12],[3,7,10,13],[4]] [4,3,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]]=>[[1,5,8,11,13],[2,6,9,12],[3,7,10],[4]] [3,3,3,3,1]=>[[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13]]=>[[1,4,7,10,13],[2,5,8,11],[3,6,9,12]] [3,3,3,2,2]=>[[1,2,3],[4,5,6],[7,8,9],[10,11],[12,13]]=>[[1,4,7,10,12],[2,5,8,11,13],[3,6,9]] [3,3,2,2,2,1]=>[[1,2,3],[4,5,6],[7,8],[9,10],[11,12],[13]]=>[[1,4,7,9,11,13],[2,5,8,10,12],[3,6]] [3,3,2,1,1,1,1,1]=>[[1,2,3],[4,5,6],[7,8],[9],[10],[11],[12],[13]]=>[[1,4,7,9,10,11,12,13],[2,5,8],[3,6]] [3,2,2,2,2,2]=>[[1,2,3],[4,5],[6,7],[8,9],[10,11],[12,13]]=>[[1,4,6,8,10,12],[2,5,7,9,11,13],[3]] [2,2,2,2,2,2,1]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13]]=>[[1,3,5,7,9,11,13],[2,4,6,8,10,12]] [1,1,1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13]]=>[[1,2,3,4,5,6,7,8,9,10,11,12,13]] [14]=>[[1,2,3,4,5,6,7,8,9,10,11,12,13,14]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14]] [9,3,2]=>[[1,2,3,4,5,6,7,8,9],[10,11,12],[13,14]]=>[[1,10,13],[2,11,14],[3,12],[4],[5],[6],[7],[8],[9]] [9,3,1,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12],[13],[14]]=>[[1,10,13,14],[2,11],[3,12],[4],[5],[6],[7],[8],[9]] [9,2,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11],[12,13],[14]]=>[[1,10,12,14],[2,11,13],[3],[4],[5],[6],[7],[8],[9]] [8,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11],[12,13],[14]]=>[[1,9,12,14],[2,10,13],[3,11],[4],[5],[6],[7],[8]] [7,7]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]]=>[[1,8],[2,9],[3,10],[4,11],[5,12],[6,13],[7,14]] [6,6,2]=>[[1,2,3,4,5,6],[7,8,9,10,11,12],[13,14]]=>[[1,7,13],[2,8,14],[3,9],[4,10],[5,11],[6,12]] [6,5,3]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14]]=>[[1,7,12],[2,8,13],[3,9,14],[4,10],[5,11],[6]] [6,5,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13],[14]]=>[[1,7,12,14],[2,8,13],[3,9],[4,10],[5,11],[6]] [6,5,1,1,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12],[13],[14]]=>[[1,7,12,13,14],[2,8],[3,9],[4,10],[5,11],[6]] [6,3,2,2,1]=>[[1,2,3,4,5,6],[7,8,9],[10,11],[12,13],[14]]=>[[1,7,10,12,14],[2,8,11,13],[3,9],[4],[5],[6]] [6,2,2,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10],[11,12],[13,14]]=>[[1,7,9,11,13],[2,8,10,12,14],[3],[4],[5],[6]] [5,5,4]=>[[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14]]=>[[1,6,11],[2,7,12],[3,8,13],[4,9,14],[5,10]] [5,5,1,1,1,1]=>[[1,2,3,4,5],[6,7,8,9,10],[11],[12],[13],[14]]=>[[1,6,11,12,13,14],[2,7],[3,8],[4,9],[5,10]] [5,4,3,2]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]]=>[[1,6,10,13],[2,7,11,14],[3,8,12],[4,9],[5]] [5,4,3,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]]=>[[1,6,10,13,14],[2,7,11],[3,8,12],[4,9],[5]] [5,4,2,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]]=>[[1,6,10,12,14],[2,7,11,13],[3,8],[4,9],[5]] [5,4,2,1,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13],[14]]=>[[1,6,10,12,13,14],[2,7,11],[3,8],[4,9],[5]] [5,3,3,2,1]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]]=>[[1,6,9,12,14],[2,7,10,13],[3,8,11],[4],[5]] [5,2,2,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10,11],[12,13],[14]]=>[[1,6,8,10,12,14],[2,7,9,11,13],[3],[4],[5]] [4,4,4,2]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14]]=>[[1,5,9,13],[2,6,10,14],[3,7,11],[4,8,12]] [4,4,3,3]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12,13,14]]=>[[1,5,9,12],[2,6,10,13],[3,7,11,14],[4,8]] [4,4,3,2,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]]=>[[1,5,9,12,14],[2,6,10,13],[3,7,11],[4,8]] [4,3,2,2,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10,11],[12,13],[14]]=>[[1,5,8,10,12,14],[2,6,9,11,13],[3,7],[4]] [4,2,2,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10],[11,12],[13,14]]=>[[1,5,7,9,11,13],[2,6,8,10,12,14],[3],[4]] [3,3,3,3,2]=>[[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14]]=>[[1,4,7,10,13],[2,5,8,11,14],[3,6,9,12]] [3,3,3,2,2,1]=>[[1,2,3],[4,5,6],[7,8,9],[10,11],[12,13],[14]]=>[[1,4,7,10,12,14],[2,5,8,11,13],[3,6,9]] [3,3,2,2,2,2]=>[[1,2,3],[4,5,6],[7,8],[9,10],[11,12],[13,14]]=>[[1,4,7,9,11,13],[2,5,8,10,12,14],[3,6]] [2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14]]=>[[1,3,5,7,9,11,13],[2,4,6,8,10,12,14]] [1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14]]=>[[1,2,3,4,5,6,7,8,9,10,11,12,13,14]] [15]=>[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15]] [9,3,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12],[13,14],[15]]=>[[1,10,13,15],[2,11,14],[3,12],[4],[5],[6],[7],[8],[9]] [6,6,3]=>[[1,2,3,4,5,6],[7,8,9,10,11,12],[13,14,15]]=>[[1,7,13],[2,8,14],[3,9,15],[4,10],[5,11],[6,12]] [6,5,4]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15]]=>[[1,7,12],[2,8,13],[3,9,14],[4,10,15],[5,11],[6]] [6,5,2,1,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13],[14],[15]]=>[[1,7,12,14,15],[2,8,13],[3,9],[4,10],[5,11],[6]] [6,3,3,3]=>[[1,2,3,4,5,6],[7,8,9],[10,11,12],[13,14,15]]=>[[1,7,10,13],[2,8,11,14],[3,9,12,15],[4],[5],[6]] [6,3,3,2,1]=>[[1,2,3,4,5,6],[7,8,9],[10,11,12],[13,14],[15]]=>[[1,7,10,13,15],[2,8,11,14],[3,9,12],[4],[5],[6]] [5,5,5]=>[[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15]]=>[[1,6,11],[2,7,12],[3,8,13],[4,9,14],[5,10,15]] [5,4,3,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]]=>[[1,6,10,13,15],[2,7,11,14],[3,8,12],[4,9],[5]] [5,4,3,1,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14],[15]]=>[[1,6,10,13,14,15],[2,7,11],[3,8,12],[4,9],[5]] [5,3,2,2,2,1]=>[[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13,14],[15]]=>[[1,6,9,11,13,15],[2,7,10,12,14],[3,8],[4],[5]] [4,4,4,3]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15]]=>[[1,5,9,13],[2,6,10,14],[3,7,11,15],[4,8,12]] [4,4,4,1,1,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13],[14],[15]]=>[[1,5,9,13,14,15],[2,6,10],[3,7,11],[4,8,12]] [3,3,3,3,3]=>[[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15]]=>[[1,4,7,10,13],[2,5,8,11,14],[3,6,9,12,15]] [3,3,3,3,2,1]=>[[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14],[15]]=>[[1,4,7,10,13,15],[2,5,8,11,14],[3,6,9,12]] [3,3,3,2,2,2]=>[[1,2,3],[4,5,6],[7,8,9],[10,11],[12,13],[14,15]]=>[[1,4,7,10,12,14],[2,5,8,11,13,15],[3,6,9]] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15]]=>[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]] [12,4]=>[[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16]]=>[[1,13],[2,14],[3,15],[4,16],[5],[6],[7],[8],[9],[10],[11],[12]] [10,6]=>[[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16]]=>[[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7],[8],[9],[10]] [8,8]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16]]=>[[1,9],[2,10],[3,11],[4,12],[5,13],[6,14],[7,15],[8,16]] [7,5,3,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12],[13,14,15],[16]]=>[[1,8,13,16],[2,9,14],[3,10,15],[4,11],[5,12],[6],[7]] [6,6,4]=>[[1,2,3,4,5,6],[7,8,9,10,11,12],[13,14,15,16]]=>[[1,7,13],[2,8,14],[3,9,15],[4,10,16],[5,11],[6,12]] [6,5,4,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16]]=>[[1,7,12,16],[2,8,13],[3,9,14],[4,10,15],[5,11],[6]] [6,5,2,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13],[14,15],[16]]=>[[1,7,12,14,16],[2,8,13,15],[3,9],[4,10],[5,11],[6]] [6,4,3,2,1]=>[[1,2,3,4,5,6],[7,8,9,10],[11,12,13],[14,15],[16]]=>[[1,7,11,14,16],[2,8,12,15],[3,9,13],[4,10],[5],[6]] [5,4,3,2,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15],[16]]=>[[1,6,10,13,15,16],[2,7,11,14],[3,8,12],[4,9],[5]] [5,4,2,2,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14,15],[16]]=>[[1,6,10,12,14,16],[2,7,11,13,15],[3,8],[4,9],[5]] [4,4,4,4]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]]=>[[1,5,9,13],[2,6,10,14],[3,7,11,15],[4,8,12,16]] [4,3,3,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12,13],[14,15],[16]]=>[[1,5,8,11,14,16],[2,6,9,12,15],[3,7,10,13],[4]] [4,3,3,2,2,1,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13,14],[15],[16]]=>[[1,5,8,11,13,15,16],[2,6,9,12,14],[3,7,10],[4]] [4,2,2,2,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16]]=>[[1,5,7,9,11,13,15],[2,6,8,10,12,14,16],[3],[4]] [3,3,3,3,2,2]=>[[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14],[15,16]]=>[[1,4,7,10,13,15],[2,5,8,11,14,16],[3,6,9,12]] [2,2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16]]=>[[1,3,5,7,9,11,13,15],[2,4,6,8,10,12,14,16]] [2,2,2,2,2,2,1,1,1,1]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13],[14],[15],[16]]=>[[1,3,5,7,9,11,13,14,15,16],[2,4,6,8,10,12]] [2,2,2,2,1,1,1,1,1,1,1,1]=>[[1,2],[3,4],[5,6],[7,8],[9],[10],[11],[12],[13],[14],[15],[16]]=>[[1,3,5,7,9,10,11,12,13,14,15,16],[2,4,6,8]] [8,8,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16],[17]]=>[[1,9,17],[2,10],[3,11],[4,12],[5,13],[6,14],[7,15],[8,16]] [6,5,4,1,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16],[17]]=>[[1,7,12,16,17],[2,8,13],[3,9,14],[4,10,15],[5,11],[6]] [6,5,3,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14],[15,16],[17]]=>[[1,7,12,15,17],[2,8,13,16],[3,9,14],[4,10],[5,11],[6]] [5,4,3,2,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15,16],[17]]=>[[1,6,10,13,15,17],[2,7,11,14,16],[3,8,12],[4,9],[5]] [5,3,3,3,2,1]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12,13,14],[15,16],[17]]=>[[1,6,9,12,15,17],[2,7,10,13,16],[3,8,11,14],[4],[5]] [3,2,2,2,2,2,2,2]=>[[1,2,3],[4,5],[6,7],[8,9],[10,11],[12,13],[14,15],[16,17]]=>[[1,4,6,8,10,12,14,16],[2,5,7,9,11,13,15,17],[3]] []=>[]=>[] [6,5,4,3,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17,18],[19,20],[21]]=>[[1,7,12,16,19,21],[2,8,13,17,20],[3,9,14,18],[4,10,15],[5,11],[6]] [5,5,4,3,2,1]=>[[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14],[15,16,17],[18,19],[20]]=>[[1,6,11,15,18,20],[2,7,12,16,19],[3,8,13,17],[4,9,14],[5,10]] [5,4,4,3,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12,13],[14,15,16],[17,18],[19]]=>[[1,6,10,14,17,19],[2,7,11,15,18],[3,8,12,16],[4,9,13],[5]] [4,4,4,3,2,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15],[16,17],[18]]=>[[1,5,9,13,16,18],[2,6,10,14,17],[3,7,11,15],[4,8,12]] [5,4,3,3,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14,15],[16,17],[18]]=>[[1,6,10,13,16,18],[2,7,11,14,17],[3,8,12,15],[4,9],[5]] [6,5,4,3,2]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17,18],[19,20]]=>[[1,7,12,16,19],[2,8,13,17,20],[3,9,14,18],[4,10,15],[5,11],[6]] [6,5,4,3,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17,18],[19]]=>[[1,7,12,16,19],[2,8,13,17],[3,9,14,18],[4,10,15],[5,11],[6]] [6,5,4,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17],[18]]=>[[1,7,12,16,18],[2,8,13,17],[3,9,14],[4,10,15],[5,11],[6]] [6,5,4,3]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17,18]]=>[[1,7,12,16],[2,8,13,17],[3,9,14,18],[4,10,15],[5,11],[6]] [7,6,5,4,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24,25],[26,27],[28]]=>[[1,8,14,19,23,26,28],[2,9,15,20,24,27],[3,10,16,21,25],[4,11,17,22],[5,12,18],[6,13],[7]] [6,6,5,4,3,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11,12],[13,14,15,16,17],[18,19,20,21],[22,23,24],[25,26],[27]]=>[[1,7,13,18,22,25,27],[2,8,14,19,23,26],[3,9,15,20,24],[4,10,16,21],[5,11,17],[6,12]] [6,5,5,4,3,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15,16],[17,18,19,20],[21,22,23],[24,25],[26]]=>[[1,7,12,17,21,24,26],[2,8,13,18,22,25],[3,9,14,19,23],[4,10,15,20],[5,11,16],[6]] [5,5,5,4,3,2,1]=>[[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19],[20,21,22],[23,24],[25]]=>[[1,6,11,16,20,23,25],[2,7,12,17,21,24],[3,8,13,18,22],[4,9,14,19],[5,10,15]] [6,5,4,4,3,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17,18,19],[20,21,22],[23,24],[25]]=>[[1,7,12,16,20,23,25],[2,8,13,17,21,24],[3,9,14,18,22],[4,10,15,19],[5,11],[6]] [6,4,4,4,3,2,1]=>[[1,2,3,4,5,6],[7,8,9,10],[11,12,13,14],[15,16,17,18],[19,20,21],[22,23],[24]]=>[[1,7,11,15,19,22,24],[2,8,12,16,20,23],[3,9,13,17,21],[4,10,14,18],[5],[6]] [5,4,4,4,3,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12,13],[14,15,16,17],[18,19,20],[21,22],[23]]=>[[1,6,10,14,18,21,23],[2,7,11,15,19,22],[3,8,12,16,20],[4,9,13,17],[5]] [4,4,4,4,3,2,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16],[17,18,19],[20,21],[22]]=>[[1,5,9,13,17,20,22],[2,6,10,14,18,21],[3,7,11,15,19],[4,8,12,16]] [6,5,4,3,3,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17,18],[19,20,21],[22,23],[24]]=>[[1,7,12,16,19,22,24],[2,8,13,17,20,23],[3,9,14,18,21],[4,10,15],[5,11],[6]] [6,5,3,3,3,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14],[15,16,17],[18,19,20],[21,22],[23]]=>[[1,7,12,15,18,21,23],[2,8,13,16,19,22],[3,9,14,17,20],[4,10],[5,11],[6]] [6,4,3,3,3,2,1]=>[[1,2,3,4,5,6],[7,8,9,10],[11,12,13],[14,15,16],[17,18,19],[20,21],[22]]=>[[1,7,11,14,17,20,22],[2,8,12,15,18,21],[3,9,13,16,19],[4,10],[5],[6]] [6,3,3,3,3,2,1]=>[[1,2,3,4,5,6],[7,8,9],[10,11,12],[13,14,15],[16,17,18],[19,20],[21]]=>[[1,7,10,13,16,19,21],[2,8,11,14,17,20],[3,9,12,15,18],[4],[5],[6]] [6,5,4,3,2,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17,18],[19,20],[21,22],[23]]=>[[1,7,12,16,19,21,23],[2,8,13,17,20,22],[3,9,14,18],[4,10,15],[5,11],[6]] [6,5,4,2,2,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17],[18,19],[20,21],[22]]=>[[1,7,12,16,18,20,22],[2,8,13,17,19,21],[3,9,14],[4,10,15],[5,11],[6]] [6,5,3,2,2,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14],[15,16],[17,18],[19,20],[21]]=>[[1,7,12,15,17,19,21],[2,8,13,16,18,20],[3,9,14],[4,10],[5,11],[6]] [6,5,2,2,2,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13],[14,15],[16,17],[18,19],[20]]=>[[1,7,12,14,16,18,20],[2,8,13,15,17,19],[3,9],[4,10],[5,11],[6]] [6,5,4,3,2,1,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17,18],[19,20],[21],[22]]=>[[1,7,12,16,19,21,22],[2,8,13,17,20],[3,9,14,18],[4,10,15],[5,11],[6]] [5,4,4,3,2,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12,13],[14,15,16],[17,18],[19],[20]]=>[[1,6,10,14,17,19,20],[2,7,11,15,18],[3,8,12,16],[4,9,13],[5]] [6,5,4,3,1,1,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17,18],[19],[20],[21]]=>[[1,7,12,16,19,20,21],[2,8,13,17],[3,9,14,18],[4,10,15],[5,11],[6]] [6,5,4,2,1,1,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17],[18],[19],[20]]=>[[1,7,12,16,18,19,20],[2,8,13,17],[3,9,14],[4,10,15],[5,11],[6]] [6,5,4,1,1,1,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16],[17],[18],[19]]=>[[1,7,12,16,17,18,19],[2,8,13],[3,9,14],[4,10,15],[5,11],[6]] [7,6,5,4,3,2]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24,25],[26,27]]=>[[1,8,14,19,23,26],[2,9,15,20,24,27],[3,10,16,21,25],[4,11,17,22],[5,12,18],[6,13],[7]] [6,6,2,2,2,2]=>[[1,2,3,4,5,6],[7,8,9,10,11,12],[13,14],[15,16],[17,18],[19,20]]=>[[1,7,13,15,17,19],[2,8,14,16,18,20],[3,9],[4,10],[5,11],[6,12]] [7,6,5,4,3,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24,25],[26]]=>[[1,8,14,19,23,26],[2,9,15,20,24],[3,10,16,21,25],[4,11,17,22],[5,12,18],[6,13],[7]] [7,6,5,4,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24],[25]]=>[[1,8,14,19,23,25],[2,9,15,20,24],[3,10,16,21],[4,11,17,22],[5,12,18],[6,13],[7]] [7,6,5,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21],[22,23],[24]]=>[[1,8,14,19,22,24],[2,9,15,20,23],[3,10,16,21],[4,11,17],[5,12,18],[6,13],[7]] [7,6,4,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17],[18,19,20],[21,22],[23]]=>[[1,8,14,18,21,23],[2,9,15,19,22],[3,10,16,20],[4,11,17],[5,12],[6,13],[7]] [7,5,4,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12],[13,14,15,16],[17,18,19],[20,21],[22]]=>[[1,8,13,17,20,22],[2,9,14,18,21],[3,10,15,19],[4,11,16],[5,12],[6],[7]] [7,4,4,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11],[12,13,14,15],[16,17,18],[19,20],[21]]=>[[1,8,12,16,19,21],[2,9,13,17,20],[3,10,14,18],[4,11,15],[5],[6],[7]] [7,6,3,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16],[17,18,19],[20,21],[22]]=>[[1,8,14,17,20,22],[2,9,15,18,21],[3,10,16,19],[4,11],[5,12],[6,13],[7]] [7,4,3,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11],[12,13,14],[15,16,17],[18,19],[20]]=>[[1,8,12,15,18,20],[2,9,13,16,19],[3,10,14,17],[4,11],[5],[6],[7]] [7,3,3,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10],[11,12,13],[14,15,16],[17,18],[19]]=>[[1,8,11,14,17,19],[2,9,12,15,18],[3,10,13,16],[4],[5],[6],[7]] [7,6,5,2,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20],[21,22],[23]]=>[[1,8,14,19,21,23],[2,9,15,20,22],[3,10,16],[4,11,17],[5,12,18],[6,13],[7]] [7,6,3,2,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16],[17,18],[19,20],[21]]=>[[1,8,14,17,19,21],[2,9,15,18,20],[3,10,16],[4,11],[5,12],[6,13],[7]] [7,6,2,2,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15],[16,17],[18,19],[20]]=>[[1,8,14,16,18,20],[2,9,15,17,19],[3,10],[4,11],[5,12],[6,13],[7]] [7,6,5,4,1,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23],[24]]=>[[1,8,14,19,23,24],[2,9,15,20],[3,10,16,21],[4,11,17,22],[5,12,18],[6,13],[7]] [7,6,5,2,1,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20],[21],[22]]=>[[1,8,14,19,21,22],[2,9,15,20],[3,10,16],[4,11,17],[5,12,18],[6,13],[7]] [7,6,5,1,1,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19],[20],[21]]=>[[1,8,14,19,20,21],[2,9,15],[3,10,16],[4,11,17],[5,12,18],[6,13],[7]] [7,6,5,4,3]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24,25]]=>[[1,8,14,19,23],[2,9,15,20,24],[3,10,16,21,25],[4,11,17,22],[5,12,18],[6,13],[7]] [7,6,5,4,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23]]=>[[1,8,14,19,23],[2,9,15,20],[3,10,16,21],[4,11,17,22],[5,12,18],[6,13],[7]] [7,5,4,3,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12],[13,14,15,16],[17,18,19],[20]]=>[[1,8,13,17,20],[2,9,14,18],[3,10,15,19],[4,11,16],[5,12],[6],[7]] [7,6,5,4]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22]]=>[[1,8,14,19],[2,9,15,20],[3,10,16,21],[4,11,17,22],[5,12,18],[6,13],[7]] [2,2,2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18]]=>[[1,3,5,7,9,11,13,15,17],[2,4,6,8,10,12,14,16,18]] [3,3,3,3,3,3]=>[[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15],[16,17,18]]=>[[1,4,7,10,13,16],[2,5,8,11,14,17],[3,6,9,12,15,18]] [3,3,3,3,3,3,3,3]=>[[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15],[16,17,18],[19,20,21],[22,23,24]]=>[[1,4,7,10,13,16,19,22],[2,5,8,11,14,17,20,23],[3,6,9,12,15,18,21,24]] [2,2,2,2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18],[19,20]]=>[[1,3,5,7,9,11,13,15,17,19],[2,4,6,8,10,12,14,16,18,20]] [3,3,3,3,3,3,3]=>[[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15],[16,17,18],[19,20,21]]=>[[1,4,7,10,13,16,19],[2,5,8,11,14,17,20],[3,6,9,12,15,18,21]] [4,4,4,4,4]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16],[17,18,19,20]]=>[[1,5,9,13,17],[2,6,10,14,18],[3,7,11,15,19],[4,8,12,16,20]] [4,4,4,4,4,4]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16],[17,18,19,20],[21,22,23,24]]=>[[1,5,9,13,17,21],[2,6,10,14,18,22],[3,7,11,15,19,23],[4,8,12,16,20,24]] [5,5,5,5]=>[[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20]]=>[[1,6,11,16],[2,7,12,17],[3,8,13,18],[4,9,14,19],[5,10,15,20]] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18],[19,20],[21,22],[23,24],[25,26],[27,28],[29,30],[31,32]]=>[[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31],[2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32]] [6,6,6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12],[13,14,15,16,17,18],[19,20,21,22,23,24]]=>[[1,7,13,19],[2,8,14,20],[3,9,15,21],[4,10,16,22],[5,11,17,23],[6,12,18,24]] [6,2,2,2,2,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18]]=>[[1,7,9,11,13,15,17],[2,8,10,12,14,16,18],[3],[4],[5],[6]] [6,6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12],[13,14,15,16,17,18]]=>[[1,7,13],[2,8,14],[3,9,15],[4,10,16],[5,11,17],[6,12,18]] [10,4,4]=>[[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]=>[[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]] [10,10]=>[[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]=>[[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]] [6,6,6,6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12],[13,14,15,16,17,18],[19,20,21,22,23,24],[25,26,27,28,29,30]]=>[[1,7,13,19,25],[2,8,14,20,26],[3,9,15,21,27],[4,10,16,22,28],[5,11,17,23,29],[6,12,18,24,30]] [10,10,10,10]=>[[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20],[21,22,23,24,25,26,27,28,29,30],[31,32,33,34,35,36,37,38,39,40]]=>[[1,11,21,31],[2,12,22,32],[3,13,23,33],[4,14,24,34],[5,15,25,35],[6,16,26,36],[7,17,27,37],[8,18,28,38],[9,19,29,39],[10,20,30,40]] [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]=>[[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20],[21,22,23,24,25],[26,27,28,29,30],[31,32,33,34,35],[36,37,38,39,40],[41,42,43,44,45],[46,47,48,49,50],[51,52,53,54,55],[56,57,58,59,60],[61,62,63,64,65],[66,67,68,69,70],[71,72,73,74,75],[76,77,78,79,80],[81,82,83,84,85],[86,87,88,89,90],[91,92,93,94,95],[96,97,98,99,100],[101,102,103,104,105],[106,107,108,109,110],[111,112,113,114,115],[116,117,118,119,120]]=>[[1,6,11,16,21,26,31,36,41,46,51,56,61,66,71,76,81,86,91,96,101,106,111,116],[2,7,12,17,22,27,32,37,42,47,52,57,62,67,72,77,82,87,92,97,102,107,112,117],[3,8,13,18,23,28,33,38,43,48,53,58,63,68,73,78,83,88,93,98,103,108,113,118],[4,9,14,19,24,29,34,39,44,49,54,59,64,69,74,79,84,89,94,99,104,109,114,119],[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120]] [5,5,5,5,5,5,5,5,5,5,5,5]=>[[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20],[21,22,23,24,25],[26,27,28,29,30],[31,32,33,34,35],[36,37,38,39,40],[41,42,43,44,45],[46,47,48,49,50],[51,52,53,54,55],[56,57,58,59,60]]=>[[1,6,11,16,21,26,31,36,41,46,51,56],[2,7,12,17,22,27,32,37,42,47,52,57],[3,8,13,18,23,28,33,38,43,48,53,58],[4,9,14,19,24,29,34,39,44,49,54,59],[5,10,15,20,25,30,35,40,45,50,55,60]] [15,15]=>[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]=>[[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]] [5,5,5,5,5,5]=>[[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20],[21,22,23,24,25],[26,27,28,29,30]]=>[[1,6,11,16,21,26],[2,7,12,17,22,27],[3,8,13,18,23,28],[4,9,14,19,24,29],[5,10,15,20,25,30]] [15,5,5]=>[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20],[21,22,23,24,25]]=>[[1,16,21],[2,17,22],[3,18,23],[4,19,24],[5,20,25],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15]] [7,7,7,7]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13,14],[15,16,17,18,19,20,21],[22,23,24,25,26,27,28]]=>[[1,8,15,22],[2,9,16,23],[3,10,17,24],[4,11,18,25],[5,12,19,26],[6,13,20,27],[7,14,21,28]] [7,7,7]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13,14],[15,16,17,18,19,20,21]]=>[[1,8,15],[2,9,16],[3,10,17],[4,11,18],[5,12,19],[6,13,20],[7,14,21]] [11,7,5,1]=>[[1,2,3,4,5,6,7,8,9,10,11],[12,13,14,15,16,17,18],[19,20,21,22,23],[24]]=>[[1,12,19,24],[2,13,20],[3,14,21],[4,15,22],[5,16,23],[6,17],[7,18],[8],[9],[10],[11]] [9,7,5,3,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16],[17,18,19,20,21],[22,23,24],[25]]=>[[1,10,17,22,25],[2,11,18,23],[3,12,19,24],[4,13,20],[5,14,21],[6,15],[7,16],[8],[9]] [11,9,7,5,3,1]=>[[1,2,3,4,5,6,7,8,9,10,11],[12,13,14,15,16,17,18,19,20],[21,22,23,24,25,26,27],[28,29,30,31,32],[33,34,35],[36]]=>[[1,12,21,28,33,36],[2,13,22,29,34],[3,14,23,30,35],[4,15,24,31],[5,16,25,32],[6,17,26],[7,18,27],[8,19],[9,20],[10],[11]] [9,7,5,5,3,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16],[17,18,19,20,21],[22,23,24,25,26],[27,28,29],[30]]=>[[1,10,17,22,27,30],[2,11,18,23,28],[3,12,19,24,29],[4,13,20,25],[5,14,21,26],[6,15],[7,16],[8],[9]] [11,8,7,5,4,1]=>[[1,2,3,4,5,6,7,8,9,10,11],[12,13,14,15,16,17,18,19],[20,21,22,23,24,25,26],[27,28,29,30,31],[32,33,34,35],[36]]=>[[1,12,20,27,32,36],[2,13,21,28,33],[3,14,22,29,34],[4,15,23,30,35],[5,16,24,31],[6,17,25],[7,18,26],[8,19],[9],[10],[11]] [8,7,6,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29,30],[31,32,33],[34,35],[36]]=>[[1,9,16,22,27,31,34,36],[2,10,17,23,28,32,35],[3,11,18,24,29,33],[4,12,19,25,30],[5,13,20,26],[6,14,21],[7,15],[8]] [7,7,6,5,4,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13,14],[15,16,17,18,19,20],[21,22,23,24,25],[26,27,28,29],[30,31,32],[33,34],[35]]=>[[1,8,15,21,26,30,33,35],[2,9,16,22,27,31,34],[3,10,17,23,28,32],[4,11,18,24,29],[5,12,19,25],[6,13,20],[7,14]] [7,6,6,5,4,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18,19],[20,21,22,23,24],[25,26,27,28],[29,30,31],[32,33],[34]]=>[[1,8,14,20,25,29,32,34],[2,9,15,21,26,30,33],[3,10,16,22,27,31],[4,11,17,23,28],[5,12,18,24],[6,13,19],[7]] [7,6,5,5,4,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22,23],[24,25,26,27],[28,29,30],[31,32],[33]]=>[[1,8,14,19,24,28,31,33],[2,9,15,20,25,29,32],[3,10,16,21,26,30],[4,11,17,22,27],[5,12,18,23],[6,13],[7]] [7,6,5,4,4,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24,25,26],[27,28,29],[30,31],[32]]=>[[1,8,14,19,23,27,30,32],[2,9,15,20,24,28,31],[3,10,16,21,25,29],[4,11,17,22,26],[5,12,18],[6,13],[7]] [7,6,5,4,3,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24,25],[26,27,28],[29,30],[31]]=>[[1,8,14,19,23,26,29,31],[2,9,15,20,24,27,30],[3,10,16,21,25,28],[4,11,17,22],[5,12,18],[6,13],[7]] [7,6,5,4,3,2,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24,25],[26,27],[28,29],[30]]=>[[1,8,14,19,23,26,28,30],[2,9,15,20,24,27,29],[3,10,16,21,25],[4,11,17,22],[5,12,18],[6,13],[7]] [7,6,5,4,3,2,1,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24,25],[26,27],[28],[29]]=>[[1,8,14,19,23,26,28,29],[2,9,15,20,24,27],[3,10,16,21,25],[4,11,17,22],[5,12,18],[6,13],[7]] [9,8,7,6,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17],[18,19,20,21,22,23,24],[25,26,27,28,29,30],[31,32,33,34,35],[36,37,38,39],[40,41,42],[43,44],[45]]=>[[1,10,18,25,31,36,40,43,45],[2,11,19,26,32,37,41,44],[3,12,20,27,33,38,42],[4,13,21,28,34,39],[5,14,22,29,35],[6,15,23,30],[7,16,24],[8,17],[9]] [8,8,7,6,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16],[17,18,19,20,21,22,23],[24,25,26,27,28,29],[30,31,32,33,34],[35,36,37,38],[39,40,41],[42,43],[44]]=>[[1,9,17,24,30,35,39,42,44],[2,10,18,25,31,36,40,43],[3,11,19,26,32,37,41],[4,12,20,27,33,38],[5,13,21,28,34],[6,14,22,29],[7,15,23],[8,16]] [6,6,6,5,4,3,2,1]=>[[1,2,3,4,5,6],[7,8,9,10,11,12],[13,14,15,16,17,18],[19,20,21,22,23],[24,25,26,27],[28,29,30],[31,32],[33]]=>[[1,7,13,19,24,28,31,33],[2,8,14,20,25,29,32],[3,9,15,21,26,30],[4,10,16,22,27],[5,11,17,23],[6,12,18]] [8,7,7,6,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21,22],[23,24,25,26,27,28],[29,30,31,32,33],[34,35,36,37],[38,39,40],[41,42],[43]]=>[[1,9,16,23,29,34,38,41,43],[2,10,17,24,30,35,39,42],[3,11,18,25,31,36,40],[4,12,19,26,32,37],[5,13,20,27,33],[6,14,21,28],[7,15,22],[8]] [7,5,5,5,4,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12],[13,14,15,16,17],[18,19,20,21,22],[23,24,25,26],[27,28,29],[30,31],[32]]=>[[1,8,13,18,23,27,30,32],[2,9,14,19,24,28,31],[3,10,15,20,25,29],[4,11,16,21,26],[5,12,17,22],[6],[7]] [8,7,6,6,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26,27],[28,29,30,31,32],[33,34,35,36],[37,38,39],[40,41],[42]]=>[[1,9,16,22,28,33,37,40,42],[2,10,17,23,29,34,38,41],[3,11,18,24,30,35,39],[4,12,19,25,31,36],[5,13,20,26,32],[6,14,21,27],[7,15],[8]] [7,6,4,4,4,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17],[18,19,20,21],[22,23,24,25],[26,27,28],[29,30],[31]]=>[[1,8,14,18,22,26,29,31],[2,9,15,19,23,27,30],[3,10,16,20,24,28],[4,11,17,21,25],[5,12],[6,13],[7]] [8,7,6,5,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29,30,31],[32,33,34,35],[36,37,38],[39,40],[41]]=>[[1,9,16,22,27,32,36,39,41],[2,10,17,23,28,33,37,40],[3,11,18,24,29,34,38],[4,12,19,25,30,35],[5,13,20,26,31],[6,14,21],[7,15],[8]] [7,6,5,3,3,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21],[22,23,24],[25,26,27],[28,29],[30]]=>[[1,8,14,19,22,25,28,30],[2,9,15,20,23,26,29],[3,10,16,21,24,27],[4,11,17],[5,12,18],[6,13],[7]] [8,7,6,5,4,4,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29,30],[31,32,33,34],[35,36,37],[38,39],[40]]=>[[1,9,16,22,27,31,35,38,40],[2,10,17,23,28,32,36,39],[3,11,18,24,29,33,37],[4,12,19,25,30,34],[5,13,20,26],[6,14,21],[7,15],[8]] [7,6,5,4,2,2,2,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24],[25,26],[27,28],[29]]=>[[1,8,14,19,23,25,27,29],[2,9,15,20,24,26,28],[3,10,16,21],[4,11,17,22],[5,12,18],[6,13],[7]] [8,7,6,5,4,3,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29,30],[31,32,33],[34,35,36],[37,38],[39]]=>[[1,9,16,22,27,31,34,37,39],[2,10,17,23,28,32,35,38],[3,11,18,24,29,33,36],[4,12,19,25,30],[5,13,20,26],[6,14,21],[7,15],[8]] [7,6,5,4,3,1,1,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24,25],[26],[27],[28]]=>[[1,8,14,19,23,26,27,28],[2,9,15,20,24],[3,10,16,21,25],[4,11,17,22],[5,12,18],[6,13],[7]] [8,7,6,5,4,3,2,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29,30],[31,32,33],[34,35],[36,37],[38]]=>[[1,9,16,22,27,31,34,36,38],[2,10,17,23,28,32,35,37],[3,11,18,24,29,33],[4,12,19,25,30],[5,13,20,26],[6,14,21],[7,15],[8]] [8,7,6,5,4,3,2,1,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29,30],[31,32,33],[34,35],[36],[37]]=>[[1,9,16,22,27,31,34,36,37],[2,10,17,23,28,32,35],[3,11,18,24,29,33],[4,12,19,25,30],[5,13,20,26],[6,14,21],[7,15],[8]] [8,7,6,5,4,3,2]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29,30],[31,32,33],[34,35]]=>[[1,9,16,22,27,31,34],[2,10,17,23,28,32,35],[3,11,18,24,29,33],[4,12,19,25,30],[5,13,20,26],[6,14,21],[7,15],[8]] [8,7,6,5,4,3,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29,30],[31,32,33],[34]]=>[[1,9,16,22,27,31,34],[2,10,17,23,28,32],[3,11,18,24,29,33],[4,12,19,25,30],[5,13,20,26],[6,14,21],[7,15],[8]] [8,7,6,5,4,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29,30],[31,32],[33]]=>[[1,9,16,22,27,31,33],[2,10,17,23,28,32],[3,11,18,24,29],[4,12,19,25,30],[5,13,20,26],[6,14,21],[7,15],[8]] [8,7,6,5,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29],[30,31],[32]]=>[[1,9,16,22,27,30,32],[2,10,17,23,28,31],[3,11,18,24,29],[4,12,19,25],[5,13,20,26],[6,14,21],[7,15],[8]] [8,7,6,4,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25],[26,27,28],[29,30],[31]]=>[[1,9,16,22,26,29,31],[2,10,17,23,27,30],[3,11,18,24,28],[4,12,19,25],[5,13,20],[6,14,21],[7,15],[8]] [8,7,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20],[21,22,23,24],[25,26,27],[28,29],[30]]=>[[1,9,16,21,25,28,30],[2,10,17,22,26,29],[3,11,18,23,27],[4,12,19,24],[5,13,20],[6,14],[7,15],[8]] [8,6,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14],[15,16,17,18,19],[20,21,22,23],[24,25,26],[27,28],[29]]=>[[1,9,15,20,24,27,29],[2,10,16,21,25,28],[3,11,17,22,26],[4,12,18,23],[5,13,19],[6,14],[7],[8]] [9,8,7,6,5,4,3,2]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17],[18,19,20,21,22,23,24],[25,26,27,28,29,30],[31,32,33,34,35],[36,37,38,39],[40,41,42],[43,44]]=>[[1,10,18,25,31,36,40,43],[2,11,19,26,32,37,41,44],[3,12,20,27,33,38,42],[4,13,21,28,34,39],[5,14,22,29,35],[6,15,23,30],[7,16,24],[8,17],[9]] [8,7,6,5,4,3]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29,30],[31,32,33]]=>[[1,9,16,22,27,31],[2,10,17,23,28,32],[3,11,18,24,29,33],[4,12,19,25,30],[5,13,20,26],[6,14,21],[7,15],[8]] [9,8,7,6,5,4,3,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17],[18,19,20,21,22,23,24],[25,26,27,28,29,30],[31,32,33,34,35],[36,37,38,39],[40,41,42],[43]]=>[[1,10,18,25,31,36,40,43],[2,11,19,26,32,37,41],[3,12,20,27,33,38,42],[4,13,21,28,34,39],[5,14,22,29,35],[6,15,23,30],[7,16,24],[8,17],[9]] [8,7,6,5,4,1,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28,29,30],[31],[32]]=>[[1,9,16,22,27,31,32],[2,10,17,23,28],[3,11,18,24,29],[4,12,19,25,30],[5,13,20,26],[6,14,21],[7,15],[8]] [9,8,7,6,5,4,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17],[18,19,20,21,22,23,24],[25,26,27,28,29,30],[31,32,33,34,35],[36,37,38,39],[40,41],[42]]=>[[1,10,18,25,31,36,40,42],[2,11,19,26,32,37,41],[3,12,20,27,33,38],[4,13,21,28,34,39],[5,14,22,29,35],[6,15,23,30],[7,16,24],[8,17],[9]] [8,7,6,5,2,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24,25,26],[27,28],[29,30],[31]]=>[[1,9,16,22,27,29,31],[2,10,17,23,28,30],[3,11,18,24],[4,12,19,25],[5,13,20,26],[6,14,21],[7,15],[8]] [9,8,7,6,5,3,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17],[18,19,20,21,22,23,24],[25,26,27,28,29,30],[31,32,33,34,35],[36,37,38],[39,40],[41]]=>[[1,10,18,25,31,36,39,41],[2,11,19,26,32,37,40],[3,12,20,27,33,38],[4,13,21,28,34],[5,14,22,29,35],[6,15,23,30],[7,16,24],[8,17],[9]] [8,7,6,3,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19,20,21],[22,23,24],[25,26,27],[28,29],[30]]=>[[1,9,16,22,25,28,30],[2,10,17,23,26,29],[3,11,18,24,27],[4,12,19],[5,13,20],[6,14,21],[7,15],[8]] [9,8,7,6,4,3,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17],[18,19,20,21,22,23,24],[25,26,27,28,29,30],[31,32,33,34],[35,36,37],[38,39],[40]]=>[[1,10,18,25,31,35,38,40],[2,11,19,26,32,36,39],[3,12,20,27,33,37],[4,13,21,28,34],[5,14,22,29],[6,15,23,30],[7,16,24],[8,17],[9]] [8,7,4,4,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15],[16,17,18,19],[20,21,22,23],[24,25,26],[27,28],[29]]=>[[1,9,16,20,24,27,29],[2,10,17,21,25,28],[3,11,18,22,26],[4,12,19,23],[5,13],[6,14],[7,15],[8]] [9,8,7,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17],[18,19,20,21,22,23,24],[25,26,27,28,29],[30,31,32,33],[34,35,36],[37,38],[39]]=>[[1,10,18,25,30,34,37,39],[2,11,19,26,31,35,38],[3,12,20,27,32,36],[4,13,21,28,33],[5,14,22,29],[6,15,23],[7,16,24],[8,17],[9]] [8,5,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13],[14,15,16,17,18],[19,20,21,22],[23,24,25],[26,27],[28]]=>[[1,9,14,19,23,26,28],[2,10,15,20,24,27],[3,11,16,21,25],[4,12,17,22],[5,13,18],[6],[7],[8]] [9,8,6,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17],[18,19,20,21,22,23],[24,25,26,27,28],[29,30,31,32],[33,34,35],[36,37],[38]]=>[[1,10,18,24,29,33,36,38],[2,11,19,25,30,34,37],[3,12,20,26,31,35],[4,13,21,27,32],[5,14,22,28],[6,15,23],[7,16],[8,17],[9]] [9,7,6,5,4,3,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16],[17,18,19,20,21,22],[23,24,25,26,27],[28,29,30,31],[32,33,34],[35,36],[37]]=>[[1,10,17,23,28,32,35,37],[2,11,18,24,29,33,36],[3,12,19,25,30,34],[4,13,20,26,31],[5,14,21,27],[6,15,22],[7,16],[8],[9]] [24,24,24,24,24]=>[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],[25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72],[73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96],[97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120]]=>[[1,25,49,73,97],[2,26,50,74,98],[3,27,51,75,99],[4,28,52,76,100],[5,29,53,77,101],[6,30,54,78,102],[7,31,55,79,103],[8,32,56,80,104],[9,33,57,81,105],[10,34,58,82,106],[11,35,59,83,107],[12,36,60,84,108],[13,37,61,85,109],[14,38,62,86,110],[15,39,63,87,111],[16,40,64,88,112],[17,41,65,89,113],[18,42,66,90,114],[19,43,67,91,115],[20,44,68,92,116],[21,45,69,93,117],[22,46,70,94,118],[23,47,71,95,119],[24,48,72,96,120]] [12,12,12,12,12]=>[[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16,17,18,19,20,21,22,23,24],[25,26,27,28,29,30,31,32,33,34,35,36],[37,38,39,40,41,42,43,44,45,46,47,48],[49,50,51,52,53,54,55,56,57,58,59,60]]=>[[1,13,25,37,49],[2,14,26,38,50],[3,15,27,39,51],[4,16,28,40,52],[5,17,29,41,53],[6,18,30,42,54],[7,19,31,43,55],[8,20,32,44,56],[9,21,33,45,57],[10,22,34,46,58],[11,23,35,47,59],[12,24,36,48,60]] [4,4,4,4,4,4,4,4,4,4]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16],[17,18,19,20],[21,22,23,24],[25,26,27,28],[29,30,31,32],[33,34,35,36],[37,38,39,40]]=>[[1,5,9,13,17,21,25,29,33,37],[2,6,10,14,18,22,26,30,34,38],[3,7,11,15,19,23,27,31,35,39],[4,8,12,16,20,24,28,32,36,40]] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18],[19,20],[21,22],[23,24],[25,26],[27,28],[29,30]]=>[[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29],[2,4,6,8,10,12,14,16,18,20,22,24,26,28,30]] [3,3,3,3,1,1,1,1,1,1]=>[[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13],[14],[15],[16],[17],[18]]=>[[1,4,7,10,13,14,15,16,17,18],[2,5,8,11],[3,6,9,12]] [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1]=>[[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15],[16],[17],[18],[19],[20],[21],[22],[23],[24],[25]]=>[[1,4,7,10,13,16,17,18,19,20,21,22,23,24,25],[2,5,8,11,14],[3,6,9,12,15]] [4,3,3,3,3,2,2,1,1,1,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12,13],[14,15,16],[17,18],[19,20],[21],[22],[23],[24]]=>[[1,5,8,11,14,17,19,21,22,23,24],[2,6,9,12,15,18,20],[3,7,10,13,16],[4]] [5,4,4,3,3,2,2,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12,13],[14,15,16],[17,18,19],[20,21],[22,23],[24],[25]]=>[[1,6,10,14,17,20,22,24,25],[2,7,11,15,18,21,23],[3,8,12,16,19],[4,9,13],[5]] [6,5,5,4,4,3,3,2,2,1,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15,16],[17,18,19,20],[21,22,23,24],[25,26,27],[28,29,30],[31,32],[33,34],[35],[36]]=>[[1,7,12,17,21,25,28,31,33,35,36],[2,8,13,18,22,26,29,32,34],[3,9,14,19,23,27,30],[4,10,15,20,24],[5,11,16],[6]] [6,5,5,4,4,2,2,1,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15,16],[17,18,19,20],[21,22,23,24],[25,26],[27,28],[29],[30]]=>[[1,7,12,17,21,25,27,29,30],[2,8,13,18,22,26,28],[3,9,14,19,23],[4,10,15,20,24],[5,11,16],[6]] [6,5,5,5,4,3,3,2,1,1,1]=>[[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15,16],[17,18,19,20,21],[22,23,24,25],[26,27,28],[29,30,31],[32,33],[34],[35],[36]]=>[[1,7,12,17,22,26,29,32,34,35,36],[2,8,13,18,23,27,30,33],[3,9,14,19,24,28,31],[4,10,15,20,25],[5,11,16,21],[6]] [5,5,5,5,5]=>[[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20],[21,22,23,24,25]]=>[[1,6,11,16,21],[2,7,12,17,22],[3,8,13,18,23],[4,9,14,19,24],[5,10,15,20,25]] [9,9]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17,18]]=>[[1,10],[2,11],[3,12],[4,13],[5,14],[6,15],[7,16],[8,17],[9,18]] [8,8,8]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16],[17,18,19,20,21,22,23,24]]=>[[1,9,17],[2,10,18],[3,11,19],[4,12,20],[5,13,21],[6,14,22],[7,15,23],[8,16,24]] [4,4,4,4,4,4,4]=>[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16],[17,18,19,20],[21,22,23,24],[25,26,27,28]]=>[[1,5,9,13,17,21,25],[2,6,10,14,18,22,26],[3,7,11,15,19,23,27],[4,8,12,16,20,24,28]] [16,16]=>[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]]=>[[1,17],[2,18],[3,19],[4,20],[5,21],[6,22],[7,23],[8,24],[9,25],[10,26],[11,27],[12,28],[13,29],[14,30],[15,31],[16,32]] [7,7,1,1,1,1]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13,14],[15],[16],[17],[18]]=>[[1,8,15,16,17,18],[2,9],[3,10],[4,11],[5,12],[6,13],[7,14]]
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
Map
conjugate
Description
Sends a standard tableau to its conjugate tableau.