Identifier
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Images
=>
Cc0002;cc-rep-0Cc0005;cc-rep-1Cc0010;cc-rep-2
[1]=>[1,0]=>[.,.]=>[1] [2]=>[1,0,1,0]=>[.,[.,.]]=>[2,1] [1,1]=>[1,1,0,0]=>[[.,.],.]=>[1,2] [3]=>[1,0,1,0,1,0]=>[.,[.,[.,.]]]=>[3,2,1] [2,1]=>[1,0,1,1,0,0]=>[.,[[.,.],.]]=>[2,3,1] [1,1,1]=>[1,1,0,1,0,0]=>[[.,[.,.]],.]=>[2,1,3] [4]=>[1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1] [3,1]=>[1,0,1,0,1,1,0,0]=>[.,[.,[[.,.],.]]]=>[3,4,2,1] [2,2]=>[1,1,1,0,0,0]=>[[[.,.],.],.]=>[1,2,3] [2,1,1]=>[1,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],.]]=>[3,2,4,1] [1,1,1,1]=>[1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],.]=>[3,2,1,4] [5]=>[1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1] [4,1]=>[1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1] [3,2]=>[1,0,1,1,1,0,0,0]=>[.,[[[.,.],.],.]]=>[2,3,4,1] [3,1,1]=>[1,0,1,0,1,1,0,1,0,0]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1] [2,2,1]=>[1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],.]=>[1,3,2,4] [2,1,1,1]=>[1,0,1,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1] [1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5] [6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1] [5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1] [4,2]=>[1,0,1,0,1,1,1,0,0,0]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1] [4,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1] [3,3]=>[1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],.]=>[2,1,3,4] [3,2,1]=>[1,0,1,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1] [3,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1] [2,2,2]=>[1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],.]=>[1,2,3,4] [2,2,1,1]=>[1,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5] [2,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1] [1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6] [7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1] [6,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1] [5,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1] [5,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1] [4,3]=>[1,0,1,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1] [4,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1] [4,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1] [3,3,1]=>[1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5] [3,2,2]=>[1,0,1,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1] [3,2,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1] [3,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1] [2,2,2,1]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5] [2,2,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6] [2,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1] [1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7] [8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1] [7,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1] [6,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1] [6,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1] [5,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1] [5,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1] [5,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1] [4,4]=>[1,1,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5] [4,3,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1] [4,2,2]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1] [4,2,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1] [4,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1] [3,3,2]=>[1,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5] [3,3,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6] [3,2,2,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1] [3,2,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1] [3,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1] [2,2,2,2]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5] [2,2,2,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6] [2,2,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7] [2,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1] [1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8] [9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1] [8,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1] [7,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1] [7,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1] [6,3]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1] [6,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1] [6,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1] [5,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1] [5,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1] [5,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1] [5,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1] [5,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1] [4,4,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6] [4,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1] [4,3,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1] [4,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1] [4,2,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1] [4,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1] [3,3,3]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5] [3,3,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6] [3,3,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7] [3,2,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1] [3,2,2,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1] [3,2,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1] [3,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1] [2,2,2,2,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6] [2,2,2,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7] [2,2,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8] [2,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1] [1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9] [10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1] [9,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1] [8,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1] [8,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1] [7,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1] [7,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[6,8,7,9,5,4,3,2,1] [7,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1] [6,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1] [6,3,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1] [6,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1] [6,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[5,8,7,6,9,4,3,2,1] [6,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1] [5,5]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6] [5,4,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1] [5,3,2]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1] [5,3,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[4,3,7,6,5,8,2,1] [5,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1] [5,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[4,8,7,6,5,9,3,2,1] [5,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1] [4,4,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6] [4,4,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7] [4,3,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1] [4,3,2,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1] [4,3,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[3,2,7,6,5,4,8,1] [4,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1] [4,2,2,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1] [4,2,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[3,8,7,6,5,4,9,2,1] [4,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1] [3,3,3,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6] [3,3,2,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6] [3,3,2,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7] [3,3,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8] [3,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1] [3,2,2,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1] [3,2,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[2,8,7,6,5,4,3,9,1] [3,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1] [2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6] [2,2,2,2,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7] [2,2,2,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8] [2,2,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9] [2,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1] [1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10] [10,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1] [9,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1] [9,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[10,9,11,8,7,6,5,4,3,2,1] [7,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1] [7,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1] [6,5]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1] [6,4,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[5,4,3,7,6,8,2,1] [6,3,2]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1] [5,5,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7] [5,4,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1] [5,4,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1] [5,3,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1] [5,3,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1] [5,2,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1] [4,4,3]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6] [4,4,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7] [4,4,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8] [4,3,3,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1] [4,3,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1] [4,3,2,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1] [4,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1] [3,3,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6] [3,3,3,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7] [3,3,2,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7] [3,3,2,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[2,3,1,7,6,5,4,8] [3,3,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9] [3,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1] [3,2,2,2,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1] [2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7] [2,2,2,2,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[2,1,3,7,6,5,4,8] [2,2,2,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,2,8,7,6,5,4,3,9] [2,2,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10] [1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11] [10,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]=>[9,10,11,8,7,6,5,4,3,2,1] [8,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1] [7,5]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1] [6,6]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7] [6,5,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1] [6,4,2]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1] [6,4,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]]=>[5,4,3,8,7,6,9,2,1] [6,3,3]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1] [5,5,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7] [5,5,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8] [5,4,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1] [5,4,2,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[4,5,3,2,7,6,8,1] [5,3,3,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[3,4,5,7,6,8,2,1] [5,3,2,2]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[5,4,6,3,7,8,2,1] [4,4,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6] [4,4,3,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7] [4,4,2,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7] [4,4,2,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[3,4,2,1,7,6,5,8] [4,3,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1] [4,3,3,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1] [4,3,2,2,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1] [4,2,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1] [3,3,3,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6] [3,3,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7] [3,3,3,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8] [3,3,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7] [3,3,2,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8] [3,2,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1] [2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7] [2,2,2,2,2,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8] [9,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]]=>[8,7,6,9,10,5,4,3,2,1] [7,6]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1] [7,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1] [7,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]]=>[7,6,8,9,10,5,4,3,2,1] [6,6,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8] [6,5,2]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[5,6,4,3,2,7,8,1] [6,4,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1] [5,5,3]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7] [5,5,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8] [5,4,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1] [5,4,3,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[3,4,5,2,7,6,8,1] [5,4,2,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1] [5,3,3,2]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[3,5,4,6,7,8,2,1] [4,4,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7] [4,4,3,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7] [4,4,3,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8] [4,4,2,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[4,3,5,2,1,7,6,8] [4,3,3,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1] [4,3,3,2,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1] [4,3,2,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1] [3,3,3,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7] [3,3,3,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7] [3,3,3,2,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8] [3,3,3,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,3,8,7,6,5,4,9] [3,3,2,2,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[4,3,2,5,1,7,6,8] [3,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1] [2,2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8] [8,6]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]=>[7,6,5,4,3,8,9,2,1] [8,3,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1] [7,7]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8] [7,6,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]=>[6,5,4,3,2,8,7,9,1] [6,6,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8] [6,6,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[5,4,3,2,1,8,7,6,9] [6,5,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1] [6,4,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1] [5,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7] [5,5,3,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[3,4,5,2,1,7,6,8] [5,5,2,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8] [5,5,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]],.]=>[4,3,2,1,9,8,7,6,5,10] [5,4,4,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1] [5,4,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[3,5,4,6,2,7,8,1] [5,3,3,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1] [4,4,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7] [4,4,4,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[2,1,3,4,7,6,5,8] [4,4,3,3]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7] [4,4,3,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8] [4,4,2,2,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8] [4,3,3,3,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1] [4,3,3,2,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1] [3,3,3,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7] [3,3,3,3,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8] [3,3,3,2,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8] [3,3,2,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8] [2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8] [8,7]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[7,6,5,4,3,2,8,9,1] [7,7,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[6,5,4,3,2,1,8,7,9] [6,6,3]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8] [6,5,4]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1] [6,3,3,3]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1] [5,5,5]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7] [5,5,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[3,2,4,5,1,7,6,8] [5,5,3,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[3,5,4,6,2,1,7,8] [5,4,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1] [5,4,3,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1] [5,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]]=>[3,5,4,6,2,8,7,9,1] [4,4,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7] [4,4,4,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[2,1,4,3,5,7,6,8] [4,4,3,3,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8] [4,4,3,2,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[2,5,4,3,6,1,7,8] [4,3,3,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1] [3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7] [3,3,3,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8] [3,3,3,3,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,4,8,7,6,5,9] [3,3,3,2,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8] [3,2,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1] [8,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9] [7,7,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9] [7,3,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1] [6,6,4]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8] [6,5,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1] [5,5,5,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8] [5,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[3,2,5,4,6,1,7,8] [5,5,3,3]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8] [5,4,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1] [4,4,4,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7] [4,4,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[2,3,1,4,5,7,6,8] [4,4,4,2,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8] [4,4,3,3,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8] [4,3,3,3,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1] [4,3,3,2,2,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,[.,[.,.]]]],.],.],.]]=>[2,6,5,4,3,7,8,9,1] [3,3,3,3,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8] [3,3,3,3,2,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8] [2,2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9] [9,8]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[8,7,6,5,4,3,2,9,10,1] [8,8,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[7,6,5,4,3,2,1,9,8,10] [7,7,3]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[.,[.,[[[.,.],.],.]]]]],.],.]=>[5,6,7,4,3,2,1,8,9] [6,6,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8] [5,5,5,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[3,2,1,5,4,6,7,8] [5,5,4,3]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8] [5,4,4,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1] [4,4,4,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8] [4,4,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8] [4,4,3,3,3]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[3,2,4,5,6,1,7,8] [3,3,3,3,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[2,1,3,5,4,6,7,8] [3,3,3,2,2,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]=>[1,6,5,4,3,2,7,8,9] [3,2,2,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]=>[7,6,5,4,3,2,8,9,10,1] [6,5,4,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[4,3,6,5,7,2,9,8,10,1] [6,5,4,3,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>[5,4,6,3,8,7,9,2,11,10,12,1] [4,4,4,4,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],[.,.]],.]=>[1,3,2,4,5,6,8,7,9] [5,4,4,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[2,4,3,5,6,7,8,9,1] [4,4,4,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8] [2,2,2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10] [3,3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8] [3,3,3,3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10] [3,3,3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9] [4,3,3,3,3,3]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[4,3,2,5,6,7,8,9,1] [4,4,4,4,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8] [4,4,4,4,4,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9] [5,5,5,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8] [6,6,6,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9] [6,6,6]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8] [7,6,6]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[5,4,3,2,6,7,8,9,1] [6,6,6,6,6]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10] [5,5,5,5,5,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10] [7,7,7,7]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10] [7,7,7]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9] [5,5,5,5,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9] [9,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10] [8,8,8]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10] [4,4,4,4,4,4,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10] [6,5,5,5]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1] [5,4,4,4,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1] [4,4,4,4,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9] [5,5,5,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[2,1,3,4,5,6,8,7,9]
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.