Identifier
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-2
[1,0]=>[1]=>[.,.] [1,0,1,0]=>[2,1]=>[[.,.],.] [1,1,0,0]=>[1,2]=>[.,[.,.]] [1,0,1,0,1,0]=>[3,2,1]=>[[[.,.],.],.] [1,0,1,1,0,0]=>[2,3,1]=>[[.,.],[.,.]] [1,1,0,0,1,0]=>[3,1,2]=>[[.,[.,.]],.] [1,1,0,1,0,0]=>[2,1,3]=>[[.,.],[.,.]] [1,1,1,0,0,0]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[[[[.,.],.],.],.] [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[[[.,.],.],[.,.]] [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[[[.,.],.],[.,.]] [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[[.,.],[.,[.,.]]] [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[[[.,[.,.]],.],.] [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[[.,[.,.]],[.,.]] [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[[[.,.],[.,.]],.] [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[[.,.],[.,[.,.]]] [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[[.,[.,[.,.]]],.] [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[[.,[.,.]],[.,.]] [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]] [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.] [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[[[[.,.],.],.],[.,.]] [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.] [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]] [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.] [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[[[[.,.],.],.],[.,.]] [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.] [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[[[.,.],[.,.]],[.,.]] [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.] [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]] [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[[[.,[.,.]],[.,.]],.] [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[[[.,[.,.]],.],[.,.]] [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[[[[.,.],[.,.]],.],.] [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[[[.,.],[.,.]],[.,.]] [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.] [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[[[.,.],.],[.,[.,.]]] [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[[[.,.],[.,[.,.]]],.] [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]] [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]] [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.] [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[[[.,[.,.]],[.,.]],.] [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[[[.,[.,.]],.],[.,.]] [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.] [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]] [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.] [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]] [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.] [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[[[[[.,.],.],.],.],[.,.]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],.] [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[[[[[.,.],.],.],.],[.,.]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[[[[.,.],.],[.,.]],[.,.]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.] [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[[[.,.],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],.] [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,.]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.] [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],.],[.,.]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[[[[.,.],.],[.,.]],[.,.]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[[[[.,.],[.,.]],.],[.,.]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[[[.,.],[.,.]],[.,[.,.]]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,.]],[.,.]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[[[.,.],[.,.]],[.,[.,.]]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.] [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],.] [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],.] [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],.] [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[[[[.,[.,.]],.],.],[.,.]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],.] [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],.] [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],.] [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.] [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],.] [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.] [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],.] [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],.] [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],.] [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[.,.]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],.] [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],.] [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.] [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],.] [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[.,.]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],.] [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],.] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],.] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],.] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.] [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.] [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.] [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.] [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]] [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.