Identifier
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ 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
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.