Identifier
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Images
=>
Cc0005;cc-rep-2Cc0010;cc-rep-3
[1]=>[1]=>[1,0]=>[.,.] [1,1]=>[2]=>[1,1,0,0]=>[.,[.,.]] [2]=>[1,1]=>[1,0,1,0]=>[[.,.],.] [1,1,1]=>[3]=>[1,1,1,0,0,0]=>[.,[.,[.,.]]] [1,2]=>[2,1]=>[1,1,0,0,1,0]=>[[.,[.,.]],.] [2,1]=>[1,2]=>[1,0,1,1,0,0]=>[[.,.],[.,.]] [3]=>[1,1,1]=>[1,0,1,0,1,0]=>[[[.,.],.],.] [1,1,1,1]=>[4]=>[1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,.]]]] [1,1,2]=>[3,1]=>[1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],.] [1,2,1]=>[2,2]=>[1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,.]] [1,3]=>[2,1,1]=>[1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],.] [2,1,1]=>[1,3]=>[1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,.]]] [2,2]=>[1,2,1]=>[1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],.] [3,1]=>[1,1,2]=>[1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,.]] [4]=>[1,1,1,1]=>[1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],.] [1,1,1,1,1]=>[5]=>[1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,.]]]]] [1,1,1,2]=>[4,1]=>[1,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[.,.]]]],.] [1,1,2,1]=>[3,2]=>[1,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,.]] [1,1,3]=>[3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],.] [1,2,1,1]=>[2,3]=>[1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,.]]] [1,2,2]=>[2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],.] [1,3,1]=>[2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,.]] [1,4]=>[2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],.] [2,1,1,1]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[.,.]]]] [2,1,2]=>[1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],.] [2,2,1]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[.,.]] [2,3]=>[1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],.] [3,1,1]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,.]]] [3,2]=>[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,.]],.] [4,1]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,.]] [5]=>[1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],.] [1,1,1,1,1,1]=>[6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,2]=>[5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,1,1,2,1]=>[4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,3]=>[4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],.] [1,1,2,1,1]=>[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,2,2]=>[3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],.] [1,1,3,1]=>[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[.,.]] [1,1,4]=>[3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,.]]],.],.],.] [1,2,1,1,1]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,2,1,2]=>[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],.] [1,2,2,1]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[.,.]] [1,2,3]=>[2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,.]],.],.] [1,3,1,1]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[.,.]]] [1,3,2]=>[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],.] [1,4,1]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[.,.]] [1,5]=>[2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],.],.],.],.] [2,1,1,1,1]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,.]]]]] [2,1,1,2]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],.] [2,1,2,1]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,.]] [2,1,3]=>[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,.]]],.],.] [2,2,1,1]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[.,.]]] [2,2,2]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],.] [2,3,1]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[.,.]] [2,4]=>[1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,.]],.],.],.] [3,1,1,1]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[.,[.,.]]]] [3,1,2]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],.] [3,2,1]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[.,.]] [3,3]=>[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],.],.] [4,1,1]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[.,[.,.]]] [4,2]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],.] [5,1]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,.]] [6]=>[1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],.] [1,1,1,1,1,1,1]=>[7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [1,1,1,1,1,2]=>[6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [1,1,1,1,2,1]=>[5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,1,1,3]=>[5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.] [1,1,1,2,1,1]=>[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,2,2]=>[4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [1,1,1,3,1]=>[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,1,1,4]=>[4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.] [1,1,2,1,1,1]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,2,1,2]=>[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,1,2,2,1]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,1,2,3]=>[3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [1,1,3,1,1]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,3,2]=>[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,1,4,1]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,1,5]=>[3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],.],.] [1,2,1,1,1,1]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,2,1,1,2]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,2,1,2,1]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,2,1,3]=>[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,2,2,1,1]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,2,2,2]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,2,3,1]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,2,4]=>[2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],.],.] [1,3,1,1,1]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,3,1,2]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,3,2,1]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,3,3]=>[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,4,1,1]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,4,2]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,5,1]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,6]=>[2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],.] [2,1,1,1,1,1]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [2,1,1,1,2]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [2,1,1,2,1]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [2,1,1,3]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [2,1,2,1,1]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [2,1,2,2]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [2,1,3,1]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [2,1,4]=>[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],.] [2,2,1,1,1]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [2,2,1,2]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [2,2,2,1]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [2,2,3]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],.],.] [2,3,1,1]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [2,3,2]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,.]],.] [2,4,1]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],.],[.,.]] [2,5]=>[1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],.] [3,1,1,1,1]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [3,1,1,2]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [3,1,2,1]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [3,1,3]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],.] [3,2,1,1]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [3,2,2]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],.] [3,3,1]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],.],[.,.]] [3,4]=>[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],.],.],.] [4,1,1,1]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [4,1,2]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],.] [4,2,1]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[.,.]] [4,3]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],.] [5,1,1]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,.]]] [5,2]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],.] [6,1]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[.,.]] [7]=>[1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],.] [1,1,1,1,1,1,1,1]=>[8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,1,2]=>[7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] [1,1,1,1,1,2,1]=>[6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] [1,1,1,1,1,3]=>[6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] [1,1,1,1,2,1,1]=>[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] [1,1,1,1,2,2]=>[5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] [1,1,1,1,3,1]=>[5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] [1,1,1,1,4]=>[5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] [1,1,1,2,1,1,1]=>[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [1,1,1,2,1,2]=>[4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] [1,1,1,2,2,1]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] [1,1,1,2,3]=>[4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] [1,1,1,3,1,1]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] [1,1,1,3,2]=>[4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] [1,1,1,4,1]=>[4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] [1,1,1,5]=>[4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.] [1,1,2,1,1,1,1]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] [1,1,2,1,1,2]=>[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] [1,1,2,1,2,1]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] [1,1,2,1,3]=>[3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] [1,1,2,2,1,1]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] [1,1,2,2,2]=>[3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] [1,1,2,3,1]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]] [1,1,2,4]=>[3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.] [1,1,3,1,1,1]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] [1,1,3,1,2]=>[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] [1,1,3,2,1]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] [1,1,3,3]=>[3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.] [1,1,4,1,1]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] [1,1,4,2]=>[3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.] [1,1,5,1]=>[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]] [1,1,6]=>[3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.] [1,2,1,1,1,1,1]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [1,2,1,1,1,2]=>[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] [1,2,1,1,2,1]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] [1,2,1,1,3]=>[2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] [1,2,1,2,1,1]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] [1,2,1,2,2]=>[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] [1,2,1,3,1]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] [1,2,1,4]=>[2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.] [1,2,2,1,1,1]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] [1,2,2,1,2]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] [1,2,2,2,1]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] [1,2,2,3]=>[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.] [1,2,3,1,1]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] [1,2,3,2]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.] [1,2,4,1]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]] [1,2,5]=>[2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.] [1,3,1,1,1,1]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] [1,3,1,1,2]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.] [1,3,1,2,1]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] [1,3,1,3]=>[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.] [1,3,2,1,1]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] [1,3,2,2]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.] [1,3,3,1]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]] [1,3,4]=>[2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.] [1,4,1,1,1]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] [1,4,1,2]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.] [1,4,2,1]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]] [1,4,3]=>[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.] [1,5,1,1]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]] [1,5,2]=>[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.] [1,6,1]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]] [1,7]=>[2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],.] [2,1,1,1,1,1,1]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] [2,1,1,1,1,2]=>[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] [2,1,1,1,2,1]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] [2,1,1,1,3]=>[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] [2,1,1,2,1,1]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] [2,1,1,2,2]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] [2,1,1,3,1]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]] [2,1,1,4]=>[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.] [2,1,2,1,1,1]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] [2,1,2,1,2]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] [2,1,2,2,1]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] [2,1,2,3]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.] [2,1,3,1,1]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] [2,1,3,2]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.] [2,1,4,1]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]] [2,1,5]=>[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.] [2,2,1,1,1,1]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] [2,2,1,1,2]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] [2,2,1,2,1]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] [2,2,1,3]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.] [2,2,2,1,1]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] [2,2,2,2]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.] [2,2,3,1]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]] [2,2,4]=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.] [2,3,1,1,1]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] [2,3,1,2]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.] [2,3,2,1]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]] [2,3,3]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.] [2,4,1,1]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]] [2,4,2]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.] [2,5,1]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]] [2,6]=>[1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],.] [3,1,1,1,1,1]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [3,1,1,1,2]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] [3,1,1,2,1]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] [3,1,1,3]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.] [3,1,2,1,1]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] [3,1,2,2]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.] [3,1,3,1]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]] [3,1,4]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.] [3,2,1,1,1]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] [3,2,1,2]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.] [3,2,2,1]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]] [3,2,3]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.] [3,3,1,1]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]] [3,3,2]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.] [3,4,1]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]] [3,5]=>[1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[.,.]],.],.],.],.] [4,1,1,1,1]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] [4,1,1,2]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.] [4,1,2,1]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]] [4,1,3]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.] [4,2,1,1]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]] [4,2,2]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.] [4,3,1]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]] [4,4]=>[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],[.,.]],.],.],.] [5,1,1,1]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]] [5,1,2]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.] [5,2,1]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]] [5,3]=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],.] [6,1,1]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]] [6,2]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],.] [7,1]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]] [8]=>[1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.] [1,1,1,1,1,1,1,1,1]=>[9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [1,1,1,1,1,1,1,2]=>[8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] [1,1,1,1,1,1,2,1]=>[7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] [1,1,1,1,1,1,3]=>[7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] [1,1,1,1,1,2,1,1]=>[6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] [1,1,1,1,1,2,2]=>[6,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] [1,1,1,1,1,3,1]=>[6,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]] [1,1,1,1,1,4]=>[6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] [1,1,1,1,2,1,1,1]=>[5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] [1,1,1,1,2,1,2]=>[5,3,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] [1,1,1,1,2,3]=>[5,2,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.] [1,1,1,1,3,1,1]=>[5,1,3]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]] [1,1,1,1,3,2]=>[5,1,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]],.] [1,1,1,1,4,1]=>[5,1,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]] [1,1,1,1,5]=>[5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] [1,1,1,2,1,1,1,1]=>[4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] [1,1,1,2,1,1,2]=>[4,4,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.] [1,1,1,2,1,2,1]=>[4,3,2]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,.]] [1,1,1,2,1,3]=>[4,3,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.],.] [1,1,1,2,2,1,1]=>[4,2,3]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,.]]] [1,1,1,2,2,2]=>[4,2,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],.] [1,1,1,2,4]=>[4,2,1,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.] [1,1,1,3,1,1,1]=>[4,1,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]] [1,1,1,3,1,2]=>[4,1,3,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]],.] [1,1,1,4,1,1]=>[4,1,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,[.,.]]] [1,1,1,5,1]=>[4,1,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]] [1,1,1,6]=>[4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] [1,1,2,1,1,1,1,1]=>[3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] [1,1,2,1,1,1,2]=>[3,5,1]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.] [1,1,2,1,1,2,1]=>[3,4,2]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],[.,.]] [1,1,2,1,2,1,1]=>[3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]] [1,1,2,1,4]=>[3,3,1,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],[.,[.,.]]],.],.],.] [1,1,2,2,2,1]=>[3,2,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]] [1,1,2,5]=>[3,2,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] [1,1,3,1,1,1,1]=>[3,1,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]] [1,1,3,1,1,2]=>[3,1,4,1]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]],.] [1,1,3,2,2]=>[3,1,2,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],[.,.]],.] [1,1,3,3,1]=>[3,1,2,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],[.,.]] [1,1,5,1,1]=>[3,1,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,[.,.]]] [1,1,5,2]=>[3,1,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[.,[.,.]]],.],.],.],[.,.]],.] [1,1,6,1]=>[3,1,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]] [1,1,7]=>[3,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] [1,2,1,1,1,1,1,1]=>[2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] [1,2,1,1,1,1,2]=>[2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] [1,2,1,1,1,2,1]=>[2,5,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]] [1,2,1,1,1,3]=>[2,5,1,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.],.] [1,2,1,1,2,1,1]=>[2,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]] [1,2,1,1,4]=>[2,4,1,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,[.,.]]]],.],.],.] [1,2,1,2,1,1,1]=>[2,3,4]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]] [1,2,1,2,1,2]=>[2,3,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]],.] [1,2,1,5]=>[2,3,1,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,[.,.]]],.],.],.],.] [1,2,2,1,1,1,1]=>[2,2,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]] [1,2,2,1,2,1]=>[2,2,3,2]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,.]] [1,2,2,1,3]=>[2,2,3,1,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,[.,.]]],.],.] [1,2,2,2,1,1]=>[2,2,2,3]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]] [1,2,2,2,2]=>[2,2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.] [1,2,2,3,1]=>[2,2,2,1,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]] [1,2,2,4]=>[2,2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.] [1,2,3,1,1,1]=>[2,2,1,4]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,[.,.]]]] [1,2,5,1]=>[2,2,1,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],[.,.]] [1,2,6]=>[2,2,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] [1,3,1,1,1,1,1]=>[2,1,6]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]] [1,3,1,1,1,2]=>[2,1,5,1]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]],.] [1,3,1,2,1,1]=>[2,1,3,3]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,[.,.]]] [1,3,2,2,1]=>[2,1,2,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],[.,.]] [1,3,5]=>[2,1,2,1,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.] [1,4,1,1,1,1]=>[2,1,1,5]=>[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]] [1,4,1,1,2]=>[2,1,1,4,1]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[.,[.,.]]]],.] [1,4,2,1,1]=>[2,1,1,2,3]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],[.,[.,.]]] [1,4,4]=>[2,1,1,2,1,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],.],[.,.]],.],.],.] [1,5,1,1,1]=>[2,1,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]] [1,5,1,2]=>[2,1,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],[.,[.,.]]],.] [1,5,2,1]=>[2,1,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],[.,.]] [1,5,3]=>[2,1,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],[.,.]],.],.] [1,6,1,1]=>[2,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]] [1,6,2]=>[2,1,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] [1,7,1]=>[2,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] [1,8]=>[2,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] [2,1,1,1,1,1,1,1]=>[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [2,1,1,1,1,1,2]=>[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] [2,1,1,1,1,2,1]=>[1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] [2,1,1,1,1,3]=>[1,6,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.] [2,1,1,1,2,1,1]=>[1,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]] [2,1,1,1,4]=>[1,5,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] [2,1,1,2,1,1,1]=>[1,4,4]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]] [2,1,1,2,3]=>[1,4,2,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],.] [2,1,1,3,1,1]=>[1,4,1,3]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,[.,.]]] [2,1,1,5]=>[1,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] [2,1,2,1,1,1,1]=>[1,3,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]] [2,1,2,1,2,1]=>[1,3,3,2]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],[.,.]] [2,1,2,1,3]=>[1,3,3,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,[.,.]]],.],.] [2,1,2,2,2]=>[1,3,2,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],.] [2,1,6]=>[1,3,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] [2,2,1,1,1,1,1]=>[1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] [2,2,1,1,1,2]=>[1,2,5,1]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]],.] [2,2,1,2,1,1]=>[1,2,3,3]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,[.,.]]] [2,2,1,4]=>[1,2,3,1,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],[.,[.,.]]],.],.],.] [2,2,2,1,1,1]=>[1,2,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,[.,.]]]] [2,2,2,1,2]=>[1,2,2,3,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],[.,[.,.]]],.] [2,2,2,2,1]=>[1,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]] [2,2,2,3]=>[1,2,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],.],.] [2,2,4,1]=>[1,2,2,1,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],[.,.]] [2,2,5]=>[1,2,2,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] [2,3,1,1,1,1]=>[1,2,1,5]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,[.,.]]]]] [2,3,4]=>[1,2,1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],.],[.,.]],.],.],.] [2,5,1,1]=>[1,2,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,[.,.]]] [2,5,2]=>[1,2,1,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],[.,.]],.],.],.],[.,.]],.] [2,6,1]=>[1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] [2,7]=>[1,2,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] [3,1,1,1,1,1,1]=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] [3,1,1,1,1,2]=>[1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] [3,1,1,1,2,1]=>[1,1,5,2]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]] [3,1,1,1,3]=>[1,1,5,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.] [3,1,1,2,1,1]=>[1,1,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,[.,.]]] [3,1,1,4]=>[1,1,4,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,[.,[.,.]]]],.],.],.] [3,1,2,2,1]=>[1,1,3,2,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],[.,.]] [3,1,5]=>[1,1,3,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.] [3,2,1,1,1,1]=>[1,1,2,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] [3,2,1,2,1]=>[1,1,2,3,2]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],[.,.]] [3,2,2,1,1]=>[1,1,2,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,[.,.]]] [3,2,2,2]=>[1,1,2,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[.,.]],[.,.]],[.,.]],.] [3,2,4]=>[1,1,2,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[.,.]],[.,.]],.],.],.] [3,3,2,1]=>[1,1,2,1,2,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],[.,.]] [3,4,1,1]=>[1,1,2,1,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,[.,.]]] [3,4,2]=>[1,1,2,1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],[.,.]],.],.],[.,.]],.] [3,5,1]=>[1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],[.,.]],.],.],.],[.,.]] [3,6]=>[1,1,2,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] [4,1,1,1,1,1]=>[1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] [4,1,1,1,2]=>[1,1,1,5,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.] [4,1,2,1,1]=>[1,1,1,3,3]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]] [4,1,2,2]=>[1,1,1,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[.,[.,.]]],[.,.]],.] [4,1,4]=>[1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.] [4,2,1,1,1]=>[1,1,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] [4,2,2,1]=>[1,1,1,2,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]] [4,2,3]=>[1,1,1,2,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],[.,.]],[.,.]],.],.] [4,3,2]=>[1,1,1,2,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],[.,.]],.],[.,.]],.] [4,5]=>[1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] [5,1,1,1,1]=>[1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] [5,1,1,2]=>[1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.] [5,1,2,1]=>[1,1,1,1,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],[.,.]] [5,1,3]=>[1,1,1,1,3,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.] [5,2,1,1]=>[1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] [5,2,2]=>[1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],.] [5,3,1]=>[1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]] [5,4]=>[1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] [6,1,1,1]=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] [6,1,2]=>[1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] [6,2,1]=>[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] [6,3]=>[1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] [7,1,1]=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] [7,2]=>[1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] [8,1]=>[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] [9]=>[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]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.] [1,1,1,1,1,1,1,1,1,1]=>[10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] [1,1,1,1,1,1,1,1,2]=>[9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] [1,1,1,1,1,1,1,2,1]=>[8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] [1,1,1,1,1,1,1,3]=>[8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] [1,1,1,1,1,1,2,1,1]=>[7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] [1,1,1,1,1,1,2,2]=>[7,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] [1,1,1,1,1,1,3,1]=>[7,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]] [1,1,1,1,1,1,4]=>[7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] [1,1,1,1,1,2,1,1,1]=>[6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] [1,1,1,1,1,2,1,2]=>[6,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]],.] [1,1,1,1,1,3,1,1]=>[6,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,[.,.]]] [1,1,1,1,1,3,2]=>[6,1,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]],.] [1,1,1,1,1,4,1]=>[6,1,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],[.,.]] [1,1,1,1,1,5]=>[6,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] [1,1,1,1,2,1,1,1,1]=>[5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] [1,1,1,1,2,1,1,2]=>[5,4,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]],.] [1,1,1,1,2,2,2]=>[5,2,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]],.] [1,1,1,1,3,1,1,1]=>[5,1,4]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,[.,.]]]] [1,1,1,1,3,1,2]=>[5,1,3,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]],.] [1,1,1,1,5,1]=>[5,1,1,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],[.,.]] [1,1,1,1,6]=>[5,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] [1,1,1,2,1,1,1,1,1]=>[4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,2,1,1,1,2]=>[4,5,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]],.] [1,1,1,2,1,1,2,1]=>[4,4,2]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]] [1,1,1,2,1,1,3]=>[4,4,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.],.] [1,1,1,2,1,2,1,1]=>[4,3,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,[.,.]]] [1,1,1,2,2,1,1,1]=>[4,2,4]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]] [1,1,1,2,2,2,1]=>[4,2,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]] [1,1,1,3,1,1,2]=>[4,1,4,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]],.] [1,1,1,4,1,1,1]=>[4,1,1,4]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,[.,[.,.]]]] [1,1,1,6,1]=>[4,1,1,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],[.,.]] [1,1,1,7]=>[4,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] [1,1,2,1,1,1,1,1,1]=>[3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] [1,1,2,1,1,1,1,2]=>[3,6,1]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]],.] [1,1,2,1,1,2,1,1]=>[3,4,3]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],[.,[.,.]]] [1,1,2,1,2,1,1,1]=>[3,3,4]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]] [1,1,2,1,2,2,1]=>[3,3,2,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]],[.,.]] [1,1,2,2,2,1,1]=>[3,2,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,[.,.]]] [1,1,2,2,2,2]=>[3,2,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]],.] [1,1,2,6]=>[3,2,1,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.],.] [1,1,3,1,1,1,2]=>[3,1,5,1]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]],.] [1,1,6,2]=>[3,1,1,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]],.] [1,1,7,1]=>[3,1,1,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]] [1,1,8]=>[3,1,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] [1,2,1,1,1,1,1,1,1]=>[2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,2,1,1,1,1,1,2]=>[2,7,1]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.] [1,2,1,1,1,1,2,1]=>[2,6,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]] [1,2,1,1,1,1,3]=>[2,6,1,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.],.] [1,2,1,1,2,1,1,1]=>[2,4,4]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]] [1,2,1,1,2,1,2]=>[2,4,3,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]],.] [1,2,1,2,1,2,1]=>[2,3,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]],[.,.]] [1,2,1,6]=>[2,3,1,1,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],[.,[.,.]]],.],.],.],.],.] [1,2,2,1,2,1,1]=>[2,2,3,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]] [1,2,2,1,4]=>[2,2,3,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],[.,[.,.]]],.],.],.] [1,2,2,2,1,1,1]=>[2,2,2,4]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]] [1,2,2,2,1,2]=>[2,2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.] [1,2,2,2,2,1]=>[2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] [1,2,2,2,3]=>[2,2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],.] [1,2,2,3,2]=>[2,2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]],.] [1,2,2,5]=>[2,2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.],.] [1,2,4,2,1]=>[2,2,1,1,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],[.,.]],[.,.]] [1,2,7]=>[2,2,1,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.] [1,3,1,1,1,1,1,1]=>[2,1,7]=>[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]] [1,3,1,1,1,1,2]=>[2,1,6,1]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]],.] [1,3,1,1,3,1]=>[2,1,4,1,2]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],[.,[.,[.,.]]]],.],[.,.]] [1,3,6]=>[2,1,2,1,1,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.],.] [1,5,1,1,1,1]=>[2,1,1,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]] [1,6,1,1,1]=>[2,1,1,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]] [1,6,1,2]=>[2,1,1,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]],.] [1,6,3]=>[2,1,1,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.],.] [1,7,1,1]=>[2,1,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,[.,.]]] [1,7,2]=>[2,1,1,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.] [1,8,1]=>[2,1,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] [1,9]=>[2,1,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] [2,1,1,1,1,1,1,1,1]=>[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [2,1,1,1,1,1,1,2]=>[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] [2,1,1,1,1,1,2,1]=>[1,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] [2,1,1,1,1,1,3]=>[1,7,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] [2,1,1,1,1,4]=>[1,6,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.] [2,1,1,1,2,1,1,1]=>[1,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] [2,1,1,1,5]=>[1,5,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.],.] [2,1,1,2,1,1,1,1]=>[1,4,5]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] [2,1,1,6]=>[1,4,1,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.],.] [2,1,2,1,1,1,1,1]=>[1,3,6]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] [2,1,2,1,2,1,1]=>[1,3,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],[.,[.,.]]] [2,1,2,2,2,1]=>[1,3,2,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]] [2,1,7]=>[1,3,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.],.] [2,2,1,1,1,1,1,1]=>[1,2,7]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] [2,2,1,1,4]=>[1,2,4,1,1,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],[.,[.,[.,.]]]],.],.],.] [2,2,1,2,1,1,1]=>[1,2,3,4]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,[.,[.,.]]]] [2,2,1,2,2,1]=>[1,2,3,2,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],[.,.]],[.,.]] [2,2,2,2,1,1]=>[1,2,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]] [2,2,2,2,2]=>[1,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.] [2,2,2,4]=>[1,2,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],.],.],.] [2,2,6]=>[1,2,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.],.] [2,3,1,3,1]=>[1,2,1,3,1,2]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],.],[.,[.,.]]],.],[.,.]] [2,6,2]=>[1,2,1,1,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]],.] [2,7,1]=>[1,2,1,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] [2,8]=>[1,2,1,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] [3,1,1,1,1,1,1,1]=>[1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [3,1,1,1,1,1,2]=>[1,1,7,1]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] [3,1,1,1,1,2,1]=>[1,1,6,2]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] [3,1,1,1,4]=>[1,1,5,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.],.] [3,1,1,2,1,1,1]=>[1,1,4,4]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]] [3,1,1,5]=>[1,1,4,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[.,[.,[.,.]]]],.],.],.],.] [3,1,6]=>[1,1,3,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.],.] [3,2,2,2,1]=>[1,1,2,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]] [3,2,5]=>[1,1,2,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],[.,.]],[.,.]],.],.],.],.] [3,7]=>[1,1,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] [4,1,1,1,1,1,1]=>[1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] [4,1,1,1,1,2]=>[1,1,1,6,1]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]],.] [4,1,1,2,2]=>[1,1,1,4,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[.,[.,[.,.]]]],[.,.]],.] [4,1,5]=>[1,1,1,3,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.],.] [4,2,2,2]=>[1,1,1,2,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]],.] [4,2,4]=>[1,1,1,2,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],[.,.]],[.,.]],.],.],.] [4,5,1]=>[1,1,1,2,1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]] [4,6]=>[1,1,1,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] [5,1,1,1,1,1]=>[1,1,1,1,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] [5,1,1,1,2]=>[1,1,1,1,5,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]],.] [5,1,4]=>[1,1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.],.] [5,2,2,1]=>[1,1,1,1,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]] [5,5]=>[1,1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] [6,1,1,1,1]=>[1,1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] [6,1,1,2]=>[1,1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]],.] [6,2,2]=>[1,1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]],.] [6,4]=>[1,1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] [7,1,1,1]=>[1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] [7,1,2]=>[1,1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.] [7,2,1]=>[1,1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] [7,3]=>[1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] [8,1,1]=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] [8,2]=>[1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] [9,1]=>[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] [10]=>[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]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] [10,1]=>[1,1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] [2,2,2,2,2,2]=>[1,2,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.] [1,2,2,2,2,2,1]=>[2,2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] [1,1,1,1,1,1,1,1,1,2]=>[10,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] [2,1,1,1,1,1,1,1,1,1]=>[1,10]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] [2,1,1,1,1,1,1,2,1]=>[1,8,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
Map
complement
Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ 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.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.