Identifier
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.] [1,0,1,0]=>[2,1]=>[1,2]=>[.,[.,.]] [1,1,0,0]=>[1,2]=>[2,1]=>[[.,.],.] [1,0,1,0,1,0]=>[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,1,0,0]=>[2,3,1]=>[1,3,2]=>[.,[[.,.],.]] [1,1,0,0,1,0]=>[3,1,2]=>[2,1,3]=>[[.,.],[.,.]] [1,1,0,1,0,0]=>[2,1,3]=>[3,1,2]=>[[.,[.,.]],.] [1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]=>[[[.,.],.],.] [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]] [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[1,4,2,3]=>[.,[[.,[.,.]],.]] [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[1,4,3,2]=>[.,[[[.,.],.],.]] [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,1,4,3]=>[[.,.],[[.,.],.]] [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[3,1,2,4]=>[[.,[.,.]],[.,.]] [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[4,1,2,3]=>[[.,[.,[.,.]]],.] [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[4,1,3,2]=>[[.,[[.,.],.]],.] [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[4,2,1,3]=>[[[.,.],[.,.]],.] [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[4,3,1,2]=>[[[.,[.,.]],.],.] [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[4,3,2,1]=>[[[[.,.],.],.],.] [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]] [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]] [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]] [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]] [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]] [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]] [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]] [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[1,5,3,2,4]=>[.,[[[.,.],[.,.]],.]] [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[.,[[[.,[.,.]],.],.]] [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]] [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]] [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]] [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[2,1,5,3,4]=>[[.,.],[[.,[.,.]],.]] [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]] [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[3,1,2,5,4]=>[[.,[.,.]],[[.,.],.]] [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]] [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.] [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[4,1,3,2,5]=>[[.,[[.,.],.]],[.,.]] [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[5,1,3,2,4]=>[[.,[[.,.],[.,.]]],.] [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[5,1,4,2,3]=>[[.,[[.,[.,.]],.]],.] [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[[.,[[[.,.],.],.]],.] [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]] [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]] [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.] [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[5,2,1,4,3]=>[[[.,.],[[.,.],.]],.] [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[4,3,1,2,5]=>[[[.,[.,.]],.],[.,.]] [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[5,3,1,2,4]=>[[[.,[.,.]],[.,.]],.] [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.] [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[[[.,[[.,.],.]],.],.] [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.] [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[5,4,2,1,3]=>[[[[.,.],[.,.]],.],.] [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.] [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[.,[.,[[.,[[.,.],.]],.]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>[.,[.,[[[.,.],[.,.]],.]]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[.,[.,[[[.,[.,.]],.],.]]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>[.,[[.,.],[[.,[.,.]],.]]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>[.,[[.,[.,.]],[[.,.],.]]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],.]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>[.,[[.,[[.,.],.]],[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>[.,[[.,[[.,.],[.,.]]],.]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],.]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],.]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>[.,[[[.,.],[.,.]],[.,.]]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>[.,[[[.,.],[.,[.,.]]],.]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>[.,[[[.,.],[[.,.],.]],.]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>[.,[[[.,[.,.]],.],[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>[.,[[[.,[.,.]],[.,.]],.]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],.]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],.]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[.,[[[[.,.],.],[.,.]],.]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>[.,[[[[.,.],[.,.]],.],.]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],.]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>[[.,.],[.,[[.,[.,.]],.]]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>[[.,.],[[.,[.,.]],[.,.]]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>[[.,.],[[.,[[.,.],.]],.]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>[[.,.],[[[.,.],[.,.]],.]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>[[.,.],[[[.,[.,.]],.],.]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.] [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>[[.,[.,[[.,.],.]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],.] [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],.] [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],.] [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>[[.,[[.,.],.]],[.,[.,.]]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>[[.,[[.,.],.]],[[.,.],.]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>[[.,[[.,.],[[.,.],.]]],.] [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>[[.,[[.,[.,.]],.]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>[[.,[[.,[.,.]],[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],.] [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],.] [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[[.,[[[.,.],.],.]],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>[[.,[[[.,.],.],[.,.]]],.] [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>[[.,[[[.,.],[.,.]],.]],.] [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],.] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],.] [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>[[[.,.],.],[[.,[.,.]],.]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>[[[.,.],[.,[[.,.],.]]],.] [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>[[[.,.],[[.,.],.]],[.,.]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],.] [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>[[[.,.],[[.,[.,.]],.]],.] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>[[[.,.],[[[.,.],.],.]],.] [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>[[[.,[.,.]],.],[[.,.],.]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],.] [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>[[[.,[.,.]],[[.,.],.]],.] [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],.] [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>[[[.,[[.,.],.]],.],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>[[[.,[[.,.],.]],[.,.]],.] [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>[[[.,[[.,.],[.,.]]],.],.] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],.] [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],.] [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>[[[[.,.],.],[[.,.],.]],.] [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],.] [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],.] [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],.] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],.] [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.] [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],.] [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.] [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],.] [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],.] [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,[[.,.],.]],.]]]] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>[.,[.,[.,[[[.,.],[.,.]],.]]]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],.]]]] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>[.,[.,[[.,.],[[.,[.,.]],.]]]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,[.,[[.,.],.]]],.]]] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>[.,[.,[[.,[[.,.],[.,.]]],.]]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>[.,[.,[[.,[[.,[.,.]],.]],.]]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>[.,[.,[[.,[[[.,.],.],.]],.]]] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>[.,[.,[[[.,.],[[.,.],.]],.]]] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>[.,[.,[[[.,[.,.]],.],[.,.]]]] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>[.,[.,[[[.,[.,.]],[.,.]],.]]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>[.,[.,[[[.,[.,[.,.]]],.],.]]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>[.,[.,[[[.,[[.,.],.]],.],.]]] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>[.,[.,[[[[.,.],.],[.,.]],.]]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>[.,[.,[[[[.,.],[.,.]],.],.]]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>[.,[.,[[[[.,[.,.]],.],.],.]]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],.]]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>[.,[[.,.],[[.,[[.,.],.]],.]]] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>[.,[[.,.],[[[.,.],[.,.]],.]]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>[.,[[.,.],[[[.,[.,.]],.],.]]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>[.,[[.,[.,[.,[[.,.],.]]]],.]] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>[.,[[.,[.,[[.,.],[.,.]]]],.]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>[.,[[.,[.,[[.,[.,.]],.]]],.]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>[.,[[.,[.,[[[.,.],.],.]]],.]] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>[.,[[.,[[.,.],[[.,.],.]]],.]] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>[.,[[.,[[.,[.,.]],[.,.]]],.]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>[.,[[.,[[.,[.,[.,.]]],.]],.]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>[.,[[.,[[.,[[.,.],.]],.]],.]] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>[.,[[.,[[[.,.],.],.]],[.,.]]] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>[.,[[.,[[[.,.],.],[.,.]]],.]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>[.,[[.,[[[.,.],[.,.]],.]],.]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>[.,[[.,[[[.,[.,.]],.],.]],.]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>[.,[[.,[[[[.,.],.],.],.]],.]] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>[.,[[[.,.],.],[[.,[.,.]],.]]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>[.,[[[.,.],[.,[[.,.],.]]],.]] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>[.,[[[.,.],[[.,.],[.,.]]],.]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>[.,[[[.,.],[[.,[.,.]],.]],.]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>[.,[[[.,.],[[[.,.],.],.]],.]] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>[.,[[[.,[.,.]],.],[[.,.],.]]] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>[.,[[[.,[.,.]],[.,.]],[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>[.,[[[.,[.,.]],[.,[.,.]]],.]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>[.,[[[.,[.,.]],[[.,.],.]],.]] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>[.,[[[.,[.,[.,.]]],.],[.,.]]] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>[.,[[[.,[.,[.,.]]],[.,.]],.]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>[.,[[[.,[.,[.,[.,.]]]],.],.]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>[.,[[[.,[.,[[.,.],.]]],.],.]] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>[.,[[[.,[[.,.],.]],.],[.,.]]] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>[.,[[[.,[[.,.],.]],[.,.]],.]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>[.,[[[.,[[.,.],[.,.]]],.],.]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>[.,[[[.,[[.,[.,.]],.]],.],.]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>[.,[[[.,[[[.,.],.],.]],.],.]] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>[.,[[[[.,.],.],.],[[.,.],.]]] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>[.,[[[[.,.],.],[.,[.,.]]],.]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>[.,[[[[.,.],.],[[.,.],.]],.]] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>[.,[[[[.,.],[.,.]],.],[.,.]]] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>[.,[[[[.,.],[.,.]],[.,.]],.]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>[.,[[[[.,.],[.,[.,.]]],.],.]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>[.,[[[[.,.],[[.,.],.]],.],.]] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>[.,[[[[.,[.,.]],.],.],[.,.]]] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>[.,[[[[.,[.,.]],.],[.,.]],.]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>[.,[[[[.,[.,.]],[.,.]],.],.]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>[.,[[[[.,[.,[.,.]]],.],.],.]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>[.,[[[[.,[[.,.],.]],.],.],.]] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>[.,[[[[[.,.],.],.],[.,.]],.]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>[.,[[[[[.,.],.],[.,.]],.],.]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>[.,[[[[[.,.],[.,.]],.],.],.]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>[.,[[[[[.,[.,.]],.],.],.],.]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>[[.,.],[.,[[.,[[.,.],.]],.]]] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],.]]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],.]] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],.]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>[[.,.],[[.,[[.,[.,.]],.]],.]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>[[.,.],[[.,[[[.,.],.],.]],.]] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>[[.,.],[[[.,.],[[.,.],.]],.]] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>[[.,.],[[[.,[.,.]],[.,.]],.]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>[[.,.],[[[.,[.,[.,.]]],.],.]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>[[.,.],[[[.,[[.,.],.]],.],.]] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>[[.,.],[[[[.,.],.],[.,.]],.]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>[[.,.],[[[[.,.],[.,.]],.],.]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>[[.,.],[[[[.,[.,.]],.],.],.]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],.] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>[[.,[.,[.,[[.,.],[.,.]]]]],.] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>[[.,[.,[.,[[.,[.,.]],.]]]],.] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>[[.,[.,[.,[[[.,.],.],.]]]],.] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>[[.,[.,[[.,.],[[.,.],.]]]],.] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>[[.,[.,[[.,[.,.]],.]]],[.,.]] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>[[.,[.,[[.,[.,.]],[.,.]]]],.] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>[[.,[.,[[.,[.,[.,.]]],.]]],.] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>[[.,[.,[[.,[[.,.],.]],.]]],.] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>[[.,[.,[[[.,.],.],[.,.]]]],.] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>[[.,[.,[[[.,.],[.,.]],.]]],.] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>[[.,[.,[[[.,[.,.]],.],.]]],.] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>[[.,[.,[[[[.,.],.],.],.]]],.] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>[[.,[[.,.],[.,[[.,.],.]]]],.] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],.] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>[[.,[[.,.],[[.,[.,.]],.]]],.] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>[[.,[[.,.],[[[.,.],.],.]]],.] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>[[.,[[.,[.,.]],[.,[.,.]]]],.] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>[[.,[[.,[.,.]],[[.,.],.]]],.] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>[[.,[[.,[.,[.,.]]],.]],[.,.]] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>[[.,[[.,[.,[.,.]]],[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],.]],.] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>[[.,[[.,[.,[[.,.],.]]],.]],.] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>[[.,[[.,[[.,.],.]],.]],[.,.]] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>[[.,[[.,[[.,.],.]],[.,.]]],.] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>[[.,[[.,[[.,.],[.,.]]],.]],.] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>[[.,[[.,[[.,[.,.]],.]],.]],.] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>[[.,[[.,[[[.,.],.],.]],.]],.] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>[[.,[[[.,.],.],.]],[[.,.],.]] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>[[.,[[[.,.],.],[.,[.,.]]]],.] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>[[.,[[[.,.],.],[[.,.],.]]],.] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>[[.,[[[.,.],[.,.]],[.,.]]],.] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>[[.,[[[.,.],[.,[.,.]]],.]],.] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>[[.,[[[.,.],[[.,.],.]],.]],.] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>[[.,[[[.,[.,.]],.],.]],[.,.]] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>[[.,[[[.,[.,.]],.],[.,.]]],.] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>[[.,[[[.,[.,.]],[.,.]],.]],.] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>[[.,[[[.,[.,[.,.]]],.],.]],.] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>[[.,[[[.,[[.,.],.]],.],.]],.] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>[[.,[[[[.,.],.],.],.]],[.,.]] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>[[.,[[[[.,.],.],.],[.,.]]],.] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>[[.,[[[[.,.],.],[.,.]],.]],.] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>[[.,[[[[.,.],[.,.]],.],.]],.] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>[[.,[[[[.,[.,.]],.],.],.]],.] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],.] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>[[[.,.],.],[[.,[[.,.],.]],.]] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>[[[.,.],[.,[[.,[.,.]],.]]],.] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>[[[.,.],[.,[[[.,.],.],.]]],.] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],.] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>[[[.,.],[[.,[.,.]],[.,.]]],.] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>[[[.,.],[[.,[.,[.,.]]],.]],.] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>[[[.,.],[[.,[[.,.],.]],.]],.] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>[[[.,.],[[[.,.],.],.]],[.,.]] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>[[[.,.],[[[.,.],.],[.,.]]],.] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>[[[.,.],[[[.,.],[.,.]],.]],.] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>[[[.,.],[[[.,[.,.]],.],.]],.] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>[[[.,.],[[[[.,.],.],.],.]],.] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>[[[.,[.,.]],.],[[[.,.],.],.]] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>[[[.,[.,.]],[.,[[.,.],.]]],.] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>[[[.,[.,.]],[[.,.],[.,.]]],.] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>[[[.,[.,.]],[[.,[.,.]],.]],.] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>[[[.,[.,.]],[[[.,.],.],.]],.] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>[[[.,[.,[.,.]]],.],[[.,.],.]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>[[[.,[.,[.,.]]],[[.,.],.]],.] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>[[[.,[.,[.,[[.,.],.]]]],.],.] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>[[[.,[.,[[.,.],.]]],[.,.]],.] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>[[[.,[.,[[.,.],[.,.]]]],.],.] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>[[[.,[.,[[.,[.,.]],.]]],.],.] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>[[[.,[.,[[[.,.],.],.]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>[[[.,[[.,.],.]],.],[[.,.],.]] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>[[[.,[[.,.],.]],[[.,.],.]],.] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>[[[.,[[.,.],[.,.]]],.],[.,.]] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>[[[.,[[.,.],[.,.]]],[.,.]],.] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>[[[.,[[.,.],[.,[.,.]]]],.],.] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>[[[.,[[.,.],[[.,.],.]]],.],.] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>[[[.,[[.,[.,.]],.]],.],[.,.]] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>[[[.,[[.,[.,.]],.]],[.,.]],.] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>[[[.,[[.,[.,.]],[.,.]]],.],.] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>[[[.,[[.,[.,[.,.]]],.]],.],.] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>[[[.,[[.,[[.,.],.]],.]],.],.] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>[[[.,[[[.,.],.],.]],.],[.,.]] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>[[[.,[[[.,.],.],.]],[.,.]],.] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>[[[.,[[[.,.],.],[.,.]]],.],.] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>[[[.,[[[.,.],[.,.]],.]],.],.] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>[[[.,[[[.,[.,.]],.],.]],.],.] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[[[.,[[[[.,.],.],.],.]],.],.] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>[[[[.,.],.],[.,[[.,.],.]]],.] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>[[[[.,.],.],[[.,.],[.,.]]],.] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>[[[[.,.],.],[[.,[.,.]],.]],.] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>[[[[.,.],.],[[[.,.],.],.]],.] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>[[[[.,.],[.,.]],.],[[.,.],.]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>[[[[.,.],[.,.]],[[.,.],.]],.] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>[[[[.,.],[.,[[.,.],.]]],.],.] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>[[[[.,.],[[.,.],.]],.],[.,.]] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>[[[[.,.],[[.,.],.]],[.,.]],.] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>[[[[.,.],[[.,.],[.,.]]],.],.] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>[[[[.,.],[[.,[.,.]],.]],.],.] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>[[[[.,.],[[[.,.],.],.]],.],.] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>[[[[.,[.,.]],.],.],[[.,.],.]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>[[[[.,[.,.]],.],[[.,.],.]],.] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>[[[[.,[.,.]],[[.,.],.]],.],.] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>[[[[.,[.,[[.,.],.]]],.],.],.] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>[[[[.,[[.,.],.]],.],.],[.,.]] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>[[[[.,[[.,.],.]],.],[.,.]],.] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>[[[[.,[[.,.],.]],[.,.]],.],.] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>[[[[.,[[.,.],[.,.]]],.],.],.] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>[[[[.,[[.,[.,.]],.]],.],.],.] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],.] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>[[[[[.,.],.],.],[[.,.],.]],.] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>[[[[[.,.],.],[[.,.],.]],.],.] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>[[[[[.,.],[[.,.],.]],.],.],.] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],.] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],.] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],.] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]] [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]] [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]] [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]] [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]] [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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.