Identifier
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-4
[1,0]=>[1]=>[1]=>[1]=>[.,.] [1,0,1,0]=>[2,1]=>[2,1]=>[1,2]=>[.,[.,.]] [1,1,0,0]=>[1,2]=>[1,2]=>[2,1]=>[[.,.],.] [1,0,1,0,1,0]=>[3,2,1]=>[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,1,0,0]=>[2,3,1]=>[1,3,2]=>[2,3,1]=>[[.,.],[.,.]] [1,1,0,0,1,0]=>[3,1,2]=>[2,3,1]=>[1,3,2]=>[.,[[.,.],.]] [1,1,0,1,0,0]=>[2,1,3]=>[2,1,3]=>[3,1,2]=>[[.,[.,.]],.] [1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[3,2,1]=>[[[.,.],.],.] [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[1,4,3,2]=>[2,3,4,1]=>[[.,.],[.,[.,.]]] [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[2,4,3,1]=>[1,3,4,2]=>[.,[[.,.],[.,.]]] [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[2,1,4,3]=>[3,4,1,2]=>[[.,[.,.]],[.,.]] [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[1,2,4,3]=>[3,4,2,1]=>[[[.,.],.],[.,.]] [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[3,4,2,1]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[3,1,4,2]=>[2,4,1,3]=>[[.,.],[[.,.],.]] [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[3,2,4,1]=>[1,4,2,3]=>[.,[[.,[.,.]],.]] [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[3,2,1,4]=>[4,1,2,3]=>[[.,[.,[.,.]]],.] [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[1,3,2,4]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[2,3,4,1]=>[1,4,3,2]=>[.,[[[.,.],.],.]] [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[2,3,1,4]=>[4,1,3,2]=>[[.,[[.,.],.]],.] [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[4,3,1,2]=>[[[.,[.,.]],.],.] [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[4,3,2,1]=>[[[[.,.],.],.],.] [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[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]=>[1,5,4,3,2]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[2,5,4,3,1]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[2,1,5,4,3]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]] [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[3,5,4,2,1]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[3,1,5,4,2]=>[2,4,5,1,3]=>[[.,.],[[.,.],[.,.]]] [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[3,2,5,4,1]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[3,2,1,5,4]=>[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]] [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]] [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[2,3,5,4,1]=>[1,4,5,3,2]=>[.,[[[.,.],.],[.,.]]] [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[2,3,1,5,4]=>[4,5,1,3,2]=>[[.,[[.,.],.]],[.,.]] [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]] [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]] [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[4,1,5,3,2]=>[2,3,5,1,4]=>[[.,.],[.,[[.,.],.]]] [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[4,2,5,3,1]=>[1,3,5,2,4]=>[.,[[.,.],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[4,2,1,5,3]=>[3,5,1,2,4]=>[[.,[.,.]],[[.,.],.]] [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[1,4,2,5,3]=>[3,5,2,4,1]=>[[[.,.],.],[[.,.],.]] [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]] [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[4,3,1,5,2]=>[2,5,1,3,4]=>[[.,.],[[.,[.,.]],.]] [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]] [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[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]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.] [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[2,4,3,5,1]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]] [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[2,4,3,1,5]=>[5,1,3,4,2]=>[[.,[[.,.],[.,.]]],.] [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[2,1,4,3,5]=>[5,3,4,1,2]=>[[[.,[.,.]],[.,.]],.] [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.] [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]] [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[3,4,1,5,2]=>[2,5,1,4,3]=>[[.,.],[[[.,.],.],.]] [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]] [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[3,4,2,1,5]=>[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.] [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[3,1,4,2,5]=>[5,2,4,1,3]=>[[[.,.],[[.,.],.]],.] [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[.,[[[.,[.,.]],.],.]] [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[3,2,4,1,5]=>[5,1,4,2,3]=>[[.,[[.,[.,.]],.]],.] [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[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]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.] [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]] [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[[.,[[[.,.],.],.]],.] [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[[[.,[[.,.],.]],.],.] [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[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]=>[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]=>[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]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[3,1,6,5,4,2]=>[2,4,5,6,1,3]=>[[.,.],[[.,.],[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[[[.,.],[.,.]],[.,[.,.]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>[.,[[[.,.],.],[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>[[.,[[.,.],.]],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[[[.,[.,.]],.],[.,[.,.]]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[4,1,6,5,3,2]=>[2,3,5,6,1,4]=>[[.,.],[.,[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[4,2,6,5,3,1]=>[1,3,5,6,2,4]=>[.,[[.,.],[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>[[.,[.,.]],[[.,.],[.,.]]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[1,4,2,6,5,3]=>[3,5,6,2,4,1]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[4,3,1,6,5,2]=>[2,5,6,1,3,4]=>[[.,.],[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>[.,[[[.,.],[.,.]],[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,.]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>[.,[.,[[[.,.],.],[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[3,4,1,6,5,2]=>[2,5,6,1,4,3]=>[[.,.],[[[.,.],.],[.,.]]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>[.,[[.,[[.,.],.]],[.,.]]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,.]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[3,1,4,2,6,5]=>[5,6,2,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,.]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>[.,[[[[.,.],.],.],[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,.]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,.]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[5,1,6,4,3,2]=>[2,3,4,6,1,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[5,2,6,4,3,1]=>[1,3,4,6,2,5]=>[.,[[.,.],[.,[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[5,2,1,6,4,3]=>[3,4,6,1,2,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[1,5,2,6,4,3]=>[3,4,6,2,5,1]=>[[[.,.],.],[.,[[.,.],.]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[5,3,6,4,2,1]=>[1,2,4,6,3,5]=>[.,[.,[[.,.],[[.,.],.]]]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[5,3,1,6,4,2]=>[2,4,6,1,3,5]=>[[.,.],[[.,.],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[5,3,2,6,4,1]=>[1,4,6,2,3,5]=>[.,[[.,[.,.]],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[5,3,2,1,6,4]=>[4,6,1,2,3,5]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[1,5,3,2,6,4]=>[4,6,2,3,5,1]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[2,5,3,6,4,1]=>[1,4,6,3,5,2]=>[.,[[[.,.],.],[[.,.],.]]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[2,5,3,1,6,4]=>[4,6,1,3,5,2]=>[[.,[[.,.],.]],[[.,.],.]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[2,1,5,3,6,4]=>[4,6,3,5,1,2]=>[[[.,[.,.]],.],[[.,.],.]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[[[[.,.],.],.],[[.,.],.]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[5,4,1,6,3,2]=>[2,3,6,1,4,5]=>[[.,.],[.,[[.,[.,.]],.]]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[5,4,2,6,3,1]=>[1,3,6,2,4,5]=>[.,[[.,.],[[.,[.,.]],.]]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[5,4,2,1,6,3]=>[3,6,1,2,4,5]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[1,5,4,2,6,3]=>[3,6,2,4,5,1]=>[[[.,.],.],[[.,[.,.]],.]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[5,4,3,1,6,2]=>[2,6,1,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[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]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],.] [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[3,5,4,1,6,2]=>[2,6,1,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],.]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[3,5,4,2,1,6]=>[6,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],.] [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[3,1,5,4,2,6]=>[6,2,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],.] [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],.]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],.] [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],.]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],.] [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],.] [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],.] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.] [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[4,5,1,6,3,2]=>[2,3,6,1,5,4]=>[[.,.],[.,[[[.,.],.],.]]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[4,5,2,6,3,1]=>[1,3,6,2,5,4]=>[.,[[.,.],[[[.,.],.],.]]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[4,5,2,1,6,3]=>[3,6,1,2,5,4]=>[[.,[.,.]],[[[.,.],.],.]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>[[[.,.],.],[[[.,.],.],.]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[.,[.,[[.,[[.,.],.]],.]]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[4,5,3,1,6,2]=>[2,6,1,3,5,4]=>[[.,.],[[.,[[.,.],.]],.]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],.]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.] [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[4,1,5,3,2,6]=>[6,2,3,5,1,4]=>[[[.,.],[.,[[.,.],.]]],.] [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[4,2,5,3,6,1]=>[1,6,3,5,2,4]=>[.,[[[.,.],[[.,.],.]],.]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[4,2,5,3,1,6]=>[6,1,3,5,2,4]=>[[.,[[.,.],[[.,.],.]]],.] [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[4,2,1,5,3,6]=>[6,3,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],.] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[[[[.,.],.],[[.,.],.]],.] [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[.,[.,[[[.,[.,.]],.],.]]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[4,3,5,1,6,2]=>[2,6,1,5,3,4]=>[[.,.],[[[.,[.,.]],.],.]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],.]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],.] [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[4,3,1,5,2,6]=>[6,2,5,1,3,4]=>[[[.,.],[[.,[.,.]],.]],.] [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],.]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],.] [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[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]=>[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],.]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],.] [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],.] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],.] [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[3,4,5,1,6,2]=>[2,6,1,5,4,3]=>[[.,.],[[[[.,.],.],.],.]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],.]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],.] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[3,4,1,5,2,6]=>[6,2,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],.] [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],.]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],.] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],.] [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[3,1,4,2,5,6]=>[6,5,2,4,1,3]=>[[[[.,.],[[.,.],.]],.],.] [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],.]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],.] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],.] [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[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]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.] [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],.] [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],.] [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],.] [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[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]=>[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]=>[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]=>[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[2,7,6,5,4,3,1]=>[1,3,4,5,6,7,2]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[3,7,6,5,4,2,1]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[3,1,7,6,5,4,2]=>[2,4,5,6,7,1,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[2,3,7,6,5,4,1]=>[1,4,5,6,7,3,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[2,3,1,7,6,5,4]=>[4,5,6,7,1,3,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [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]=>[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]=>[4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[4,1,7,6,5,3,2]=>[2,3,5,6,7,1,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[4,2,7,6,5,3,1]=>[1,3,5,6,7,2,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[4,2,1,7,6,5,3]=>[3,5,6,7,1,2,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[1,4,2,7,6,5,3]=>[3,5,6,7,2,4,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>[1,2,5,6,7,3,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[4,3,1,7,6,5,2]=>[2,5,6,7,1,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[2,4,3,7,6,5,1]=>[1,5,6,7,3,4,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[2,4,3,1,7,6,5]=>[5,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>[1,2,5,6,7,4,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[3,4,1,7,6,5,2]=>[2,5,6,7,1,4,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[3,4,2,7,6,5,1]=>[1,5,6,7,2,4,3]=>[.,[[.,[[.,.],.]],[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[3,4,2,1,7,6,5]=>[5,6,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[3,1,4,2,7,6,5]=>[5,6,7,2,4,1,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[3,2,4,7,6,5,1]=>[1,5,6,7,4,2,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[3,2,4,1,7,6,5]=>[5,6,7,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[2,3,4,1,7,6,5]=>[5,6,7,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[2,3,1,4,7,6,5]=>[5,6,7,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[5,1,7,6,4,3,2]=>[2,3,4,6,7,1,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[5,2,7,6,4,3,1]=>[1,3,4,6,7,2,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[5,2,1,7,6,4,3]=>[3,4,6,7,1,2,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[1,5,2,7,6,4,3]=>[3,4,6,7,2,5,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[5,3,7,6,4,2,1]=>[1,2,4,6,7,3,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[5,3,1,7,6,4,2]=>[2,4,6,7,1,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[5,3,2,7,6,4,1]=>[1,4,6,7,2,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[5,3,2,1,7,6,4]=>[4,6,7,1,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[1,5,3,2,7,6,4]=>[4,6,7,2,3,5,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[2,5,3,7,6,4,1]=>[1,4,6,7,3,5,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[2,5,3,1,7,6,4]=>[4,6,7,1,3,5,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[2,1,5,3,7,6,4]=>[4,6,7,3,5,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[1,2,5,3,7,6,4]=>[4,6,7,3,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[5,4,1,7,6,3,2]=>[2,3,6,7,1,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[5,4,2,7,6,3,1]=>[1,3,6,7,2,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[5,4,2,1,7,6,3]=>[3,6,7,1,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[1,5,4,2,7,6,3]=>[3,6,7,2,4,5,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[5,4,3,7,6,2,1]=>[1,2,6,7,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[5,4,3,1,7,6,2]=>[2,6,7,1,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[2,5,4,3,7,6,1]=>[1,6,7,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[2,5,4,3,1,7,6]=>[6,7,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[3,5,4,7,6,2,1]=>[1,2,6,7,4,5,3]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[3,5,4,1,7,6,2]=>[2,6,7,1,4,5,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>[1,6,7,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[3,5,4,2,1,7,6]=>[6,7,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[3,1,5,4,2,7,6]=>[6,7,2,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[3,2,5,4,1,7,6]=>[6,7,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[2,3,5,4,7,6,1]=>[1,6,7,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[2,3,5,4,1,7,6]=>[6,7,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[4,5,1,7,6,3,2]=>[2,3,6,7,1,5,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[4,5,2,7,6,3,1]=>[1,3,6,7,2,5,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[4,5,2,1,7,6,3]=>[3,6,7,1,2,5,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[4,1,5,2,7,6,3]=>[3,6,7,2,5,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[4,5,3,7,6,2,1]=>[1,2,6,7,3,5,4]=>[.,[.,[[.,[[.,.],.]],[.,.]]]] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[4,5,3,1,7,6,2]=>[2,6,7,1,3,5,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],[.,.]]] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[4,5,3,2,1,7,6]=>[6,7,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[4,1,5,3,2,7,6]=>[6,7,2,3,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[4,2,5,3,7,6,1]=>[1,6,7,3,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[4,2,5,3,1,7,6]=>[6,7,1,3,5,2,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[4,2,1,5,3,7,6]=>[6,7,3,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[4,3,5,7,6,2,1]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[4,3,5,1,7,6,2]=>[2,6,7,1,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[4,3,5,2,7,6,1]=>[1,6,7,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[4,3,5,2,1,7,6]=>[6,7,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[4,3,1,5,2,7,6]=>[6,7,2,5,1,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>[1,6,7,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,.]]] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[4,3,2,5,1,7,6]=>[6,7,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,.]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[2,4,3,5,7,6,1]=>[1,6,7,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],[.,.]]] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[2,4,3,5,1,7,6]=>[6,7,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[2,4,3,1,5,7,6]=>[6,7,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[3,4,5,7,6,2,1]=>[1,2,6,7,5,4,3]=>[.,[.,[[[[.,.],.],.],[.,.]]]] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[3,4,5,1,7,6,2]=>[2,6,7,1,5,4,3]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[3,4,5,2,7,6,1]=>[1,6,7,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[3,4,5,2,1,7,6]=>[6,7,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,.]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[3,4,1,5,2,7,6]=>[6,7,2,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[.,.]] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[3,4,2,5,7,6,1]=>[1,6,7,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],[.,.]]] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[3,4,2,5,1,7,6]=>[6,7,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],[.,.]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[3,4,2,1,5,7,6]=>[6,7,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[3,1,4,2,5,7,6]=>[6,7,5,2,4,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[3,2,4,5,7,6,1]=>[1,6,7,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[3,2,4,5,1,7,6]=>[6,7,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],[.,.]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[3,2,4,1,5,7,6]=>[6,7,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[2,3,4,5,7,6,1]=>[1,6,7,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,.]]] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[2,3,4,5,1,7,6]=>[6,7,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[2,3,1,4,5,7,6]=>[6,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[6,1,7,5,4,3,2]=>[2,3,4,5,7,1,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[6,2,7,5,4,3,1]=>[1,3,4,5,7,2,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[6,2,1,7,5,4,3]=>[3,4,5,7,1,2,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[1,6,2,7,5,4,3]=>[3,4,5,7,2,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[6,3,7,5,4,2,1]=>[1,2,4,5,7,3,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[6,3,1,7,5,4,2]=>[2,4,5,7,1,3,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[6,3,2,7,5,4,1]=>[1,4,5,7,2,3,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[6,3,2,1,7,5,4]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[1,6,3,2,7,5,4]=>[4,5,7,2,3,6,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[2,6,3,7,5,4,1]=>[1,4,5,7,3,6,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[2,6,3,1,7,5,4]=>[4,5,7,1,3,6,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[2,1,6,3,7,5,4]=>[4,5,7,3,6,1,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[1,2,6,3,7,5,4]=>[4,5,7,3,6,2,1]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[6,4,7,5,3,2,1]=>[1,2,3,5,7,4,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[6,4,1,7,5,3,2]=>[2,3,5,7,1,4,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[6,4,2,7,5,3,1]=>[1,3,5,7,2,4,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[6,4,2,1,7,5,3]=>[3,5,7,1,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[1,6,4,2,7,5,3]=>[3,5,7,2,4,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[6,4,3,7,5,2,1]=>[1,2,5,7,3,4,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[6,4,3,1,7,5,2]=>[2,5,7,1,3,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[6,4,3,2,7,5,1]=>[1,5,7,2,3,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[6,4,3,2,1,7,5]=>[5,7,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[1,6,4,3,2,7,5]=>[5,7,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[2,6,4,3,7,5,1]=>[1,5,7,3,4,6,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[2,6,4,3,1,7,5]=>[5,7,1,3,4,6,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[2,1,6,4,3,7,5]=>[5,7,3,4,6,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[1,2,6,4,3,7,5]=>[5,7,3,4,6,2,1]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[3,6,4,7,5,2,1]=>[1,2,5,7,4,6,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[3,6,4,1,7,5,2]=>[2,5,7,1,4,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[3,6,4,2,7,5,1]=>[1,5,7,2,4,6,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[3,6,4,2,1,7,5]=>[5,7,1,2,4,6,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[3,1,6,4,2,7,5]=>[5,7,2,4,6,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[3,2,6,4,7,5,1]=>[1,5,7,4,6,2,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[3,2,6,4,1,7,5]=>[5,7,1,4,6,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[3,2,1,6,4,7,5]=>[5,7,4,6,1,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1]=>[[[[.,.],[.,.]],.],[[.,.],.]] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[2,3,6,4,7,5,1]=>[1,5,7,4,6,3,2]=>[.,[[[[.,.],.],.],[[.,.],.]]] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[2,3,6,4,1,7,5]=>[5,7,1,4,6,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[2,3,1,6,4,7,5]=>[5,7,4,6,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[2,1,3,6,4,7,5]=>[5,7,4,6,3,1,2]=>[[[[.,[.,.]],.],.],[[.,.],.]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[6,5,1,7,4,3,2]=>[2,3,4,7,1,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[6,5,2,7,4,3,1]=>[1,3,4,7,2,5,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[6,5,2,1,7,4,3]=>[3,4,7,1,2,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[1,6,5,2,7,4,3]=>[3,4,7,2,5,6,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[6,5,3,7,4,2,1]=>[1,2,4,7,3,5,6]=>[.,[.,[[.,.],[[.,[.,.]],.]]]] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[6,5,3,1,7,4,2]=>[2,4,7,1,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[6,5,3,2,7,4,1]=>[1,4,7,2,3,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[6,5,3,2,1,7,4]=>[4,7,1,2,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[1,6,5,3,2,7,4]=>[4,7,2,3,5,6,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[2,6,5,3,7,4,1]=>[1,4,7,3,5,6,2]=>[.,[[[.,.],.],[[.,[.,.]],.]]] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[2,6,5,3,1,7,4]=>[4,7,1,3,5,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[2,1,6,5,3,7,4]=>[4,7,3,5,6,1,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[1,2,6,5,3,7,4]=>[4,7,3,5,6,2,1]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[6,5,4,1,7,3,2]=>[2,3,7,1,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[6,5,4,2,7,3,1]=>[1,3,7,2,4,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],.]]] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[6,5,4,2,1,7,3]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[1,6,5,4,2,7,3]=>[3,7,2,4,5,6,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[6,5,4,3,1,7,2]=>[2,7,1,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[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]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[2,6,5,4,3,7,1]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[2,6,5,4,3,1,7]=>[7,1,3,4,5,6,2]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[3,6,5,4,7,2,1]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[3,6,5,4,1,7,2]=>[2,7,1,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[3,6,5,4,2,7,1]=>[1,7,2,4,5,6,3]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>[7,1,2,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[3,1,6,5,4,2,7]=>[7,2,4,5,6,1,3]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[3,2,6,5,4,7,1]=>[1,7,4,5,6,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],.]] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[3,2,6,5,4,1,7]=>[7,1,4,5,6,2,3]=>[[.,[[.,[.,.]],[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[2,3,6,5,4,7,1]=>[1,7,4,5,6,3,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[2,3,6,5,4,1,7]=>[7,1,4,5,6,3,2]=>[[.,[[[.,.],.],[.,[.,.]]]],.] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[2,3,1,6,5,4,7]=>[7,4,5,6,1,3,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[4,6,5,1,7,3,2]=>[2,3,7,1,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[4,6,5,2,7,3,1]=>[1,3,7,2,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[4,6,5,2,1,7,3]=>[3,7,1,2,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[4,1,6,5,2,7,3]=>[3,7,2,5,6,1,4]=>[[[.,.],.],[[[.,.],[.,.]],.]] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[4,6,5,3,7,2,1]=>[1,2,7,3,5,6,4]=>[.,[.,[[.,[[.,.],[.,.]]],.]]] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[4,6,5,3,1,7,2]=>[2,7,1,3,5,6,4]=>[[.,.],[[.,[[.,.],[.,.]]],.]] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[4,6,5,3,2,7,1]=>[1,7,2,3,5,6,4]=>[.,[[.,[.,[[.,.],[.,.]]]],.]] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[4,6,5,3,2,1,7]=>[7,1,2,3,5,6,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],.] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[4,1,6,5,3,2,7]=>[7,2,3,5,6,1,4]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[4,2,6,5,3,7,1]=>[1,7,3,5,6,2,4]=>[.,[[[.,.],[[.,.],[.,.]]],.]] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[4,2,6,5,3,1,7]=>[7,1,3,5,6,2,4]=>[[.,[[.,.],[[.,.],[.,.]]]],.] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[4,2,1,6,5,3,7]=>[7,3,5,6,1,2,4]=>[[[.,[.,.]],[[.,.],[.,.]]],.] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[1,4,2,6,5,3,7]=>[7,3,5,6,2,4,1]=>[[[[.,.],.],[[.,.],[.,.]]],.] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[4,3,6,5,7,2,1]=>[1,2,7,5,6,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],.]]] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[4,3,6,5,1,7,2]=>[2,7,1,5,6,3,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[4,3,6,5,2,7,1]=>[1,7,2,5,6,3,4]=>[.,[[.,[[.,[.,.]],[.,.]]],.]] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[4,3,6,5,2,1,7]=>[7,1,2,5,6,3,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],.] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[4,3,1,6,5,2,7]=>[7,2,5,6,1,3,4]=>[[[.,.],[[.,[.,.]],[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[4,3,2,6,5,7,1]=>[1,7,5,6,2,3,4]=>[.,[[[.,[.,[.,.]]],[.,.]],.]] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>[7,1,5,6,2,3,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[2,4,3,6,5,7,1]=>[1,7,5,6,3,4,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[2,4,3,6,5,1,7]=>[7,1,5,6,3,4,2]=>[[.,[[[.,.],[.,.]],[.,.]]],.] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[2,4,3,1,6,5,7]=>[7,5,6,1,3,4,2]=>[[[.,[[.,.],[.,.]]],[.,.]],.] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[3,4,6,5,7,2,1]=>[1,2,7,5,6,4,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[3,4,6,5,1,7,2]=>[2,7,1,5,6,4,3]=>[[.,.],[[[[.,.],.],[.,.]],.]] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[3,4,6,5,2,7,1]=>[1,7,2,5,6,4,3]=>[.,[[.,[[[.,.],.],[.,.]]],.]] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[3,4,6,5,2,1,7]=>[7,1,2,5,6,4,3]=>[[.,[.,[[[.,.],.],[.,.]]]],.] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[3,4,1,6,5,2,7]=>[7,2,5,6,1,4,3]=>[[[.,.],[[[.,.],.],[.,.]]],.] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[3,4,2,6,5,7,1]=>[1,7,5,6,2,4,3]=>[.,[[[.,[[.,.],.]],[.,.]],.]] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[3,4,2,6,5,1,7]=>[7,1,5,6,2,4,3]=>[[.,[[.,[[.,.],.]],[.,.]]],.] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[3,4,2,1,6,5,7]=>[7,5,6,1,2,4,3]=>[[[.,[.,[[.,.],.]]],[.,.]],.] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[3,1,4,2,6,5,7]=>[7,5,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],.] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[3,2,4,6,5,7,1]=>[1,7,5,6,4,2,3]=>[.,[[[[.,[.,.]],.],[.,.]],.]] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[3,2,4,6,5,1,7]=>[7,1,5,6,4,2,3]=>[[.,[[[.,[.,.]],.],[.,.]]],.] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[3,2,4,1,6,5,7]=>[7,5,6,1,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],.] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[2,3,4,6,5,7,1]=>[1,7,5,6,4,3,2]=>[.,[[[[[.,.],.],.],[.,.]],.]] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[2,3,4,6,5,1,7]=>[7,1,5,6,4,3,2]=>[[.,[[[[.,.],.],.],[.,.]]],.] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[2,3,4,1,6,5,7]=>[7,5,6,1,4,3,2]=>[[[.,[[[.,.],.],.]],[.,.]],.] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[2,3,1,4,6,5,7]=>[7,5,6,4,1,3,2]=>[[[[.,[[.,.],.]],.],[.,.]],.] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[5,6,1,7,4,3,2]=>[2,3,4,7,1,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[5,6,2,7,4,3,1]=>[1,3,4,7,2,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[5,6,2,1,7,4,3]=>[3,4,7,1,2,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[5,1,6,2,7,4,3]=>[3,4,7,2,6,1,5]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[5,6,3,7,4,2,1]=>[1,2,4,7,3,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[5,6,3,1,7,4,2]=>[2,4,7,1,3,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[5,6,3,2,7,4,1]=>[1,4,7,2,3,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[5,6,3,2,1,7,4]=>[4,7,1,2,3,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[5,1,6,3,2,7,4]=>[4,7,2,3,6,1,5]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[5,2,6,3,7,4,1]=>[1,4,7,3,6,2,5]=>[.,[[[.,.],.],[[[.,.],.],.]]] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[5,2,6,3,1,7,4]=>[4,7,1,3,6,2,5]=>[[.,[[.,.],.]],[[[.,.],.],.]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[5,2,1,6,3,7,4]=>[4,7,3,6,1,2,5]=>[[[.,[.,.]],.],[[[.,.],.],.]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,[[.,.],.]],.]]]] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[5,6,4,1,7,3,2]=>[2,3,7,1,4,6,5]=>[[.,.],[.,[[.,[[.,.],.]],.]]] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[5,6,4,2,7,3,1]=>[1,3,7,2,4,6,5]=>[.,[[.,.],[[.,[[.,.],.]],.]]] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[5,6,4,2,1,7,3]=>[3,7,1,2,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[5,1,6,4,2,7,3]=>[3,7,2,4,6,1,5]=>[[[.,.],.],[[.,[[.,.],.]],.]] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,[.,[[.,.],.]]],.]]] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[5,6,4,3,1,7,2]=>[2,7,1,3,4,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],.]] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>[.,[[.,[.,[.,[[.,.],.]]]],.]] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],.] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[5,1,6,4,3,2,7]=>[7,2,3,4,6,1,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[5,2,6,4,3,7,1]=>[1,7,3,4,6,2,5]=>[.,[[[.,.],[.,[[.,.],.]]],.]] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[5,2,6,4,3,1,7]=>[7,1,3,4,6,2,5]=>[[.,[[.,.],[.,[[.,.],.]]]],.] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[5,2,1,6,4,3,7]=>[7,3,4,6,1,2,5]=>[[[.,[.,.]],[.,[[.,.],.]]],.] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[1,5,2,6,4,3,7]=>[7,3,4,6,2,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[5,3,6,4,7,2,1]=>[1,2,7,4,6,3,5]=>[.,[.,[[[.,.],[[.,.],.]],.]]] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[5,3,6,4,1,7,2]=>[2,7,1,4,6,3,5]=>[[.,.],[[[.,.],[[.,.],.]],.]] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[5,3,6,4,2,7,1]=>[1,7,2,4,6,3,5]=>[.,[[.,[[.,.],[[.,.],.]]],.]] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[5,3,6,4,2,1,7]=>[7,1,2,4,6,3,5]=>[[.,[.,[[.,.],[[.,.],.]]]],.] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[5,3,1,6,4,2,7]=>[7,2,4,6,1,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],.] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[5,3,2,6,4,7,1]=>[1,7,4,6,2,3,5]=>[.,[[[.,[.,.]],[[.,.],.]],.]] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[5,3,2,6,4,1,7]=>[7,1,4,6,2,3,5]=>[[.,[[.,[.,.]],[[.,.],.]]],.] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[5,3,2,1,6,4,7]=>[7,4,6,1,2,3,5]=>[[[.,[.,[.,.]]],[[.,.],.]],.] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[1,5,3,2,6,4,7]=>[7,4,6,2,3,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[2,5,3,6,4,7,1]=>[1,7,4,6,3,5,2]=>[.,[[[[.,.],.],[[.,.],.]],.]] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[2,5,3,6,4,1,7]=>[7,1,4,6,3,5,2]=>[[.,[[[.,.],.],[[.,.],.]]],.] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[2,5,3,1,6,4,7]=>[7,4,6,1,3,5,2]=>[[[.,[[.,.],.]],[[.,.],.]],.] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[2,1,5,3,6,4,7]=>[7,4,6,3,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],.] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[[[[[.,.],.],.],[[.,.],.]],.] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],.]]]] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[5,4,6,1,7,3,2]=>[2,3,7,1,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],.]]] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[5,4,6,2,7,3,1]=>[1,3,7,2,6,4,5]=>[.,[[.,.],[[[.,[.,.]],.],.]]] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[5,4,6,2,1,7,3]=>[3,7,1,2,6,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[5,4,1,6,2,7,3]=>[3,7,2,6,1,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>[.,[.,[[.,[[.,[.,.]],.]],.]]] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[5,4,6,3,1,7,2]=>[2,7,1,3,6,4,5]=>[[.,.],[[.,[[.,[.,.]],.]],.]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>[.,[[.,[.,[[.,[.,.]],.]]],.]] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>[[.,[.,[.,[[.,[.,.]],.]]]],.] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[5,4,1,6,3,2,7]=>[7,2,3,6,1,4,5]=>[[[.,.],[.,[[.,[.,.]],.]]],.] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[5,4,2,6,3,7,1]=>[1,7,3,6,2,4,5]=>[.,[[[.,.],[[.,[.,.]],.]],.]] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[5,4,2,6,3,1,7]=>[7,1,3,6,2,4,5]=>[[.,[[.,.],[[.,[.,.]],.]]],.] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[5,4,2,1,6,3,7]=>[7,3,6,1,2,4,5]=>[[[.,[.,.]],[[.,[.,.]],.]],.] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[1,5,4,2,6,3,7]=>[7,3,6,2,4,5,1]=>[[[[.,.],.],[[.,[.,.]],.]],.] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>[.,[.,[[[.,[.,[.,.]]],.],.]]] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[5,4,3,6,1,7,2]=>[2,7,1,6,3,4,5]=>[[.,.],[[[.,[.,[.,.]]],.],.]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>[.,[[.,[[.,[.,[.,.]]],.]],.]] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>[[.,[.,[[.,[.,[.,.]]],.]]],.] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[5,4,3,1,6,2,7]=>[7,2,6,1,3,4,5]=>[[[.,.],[[.,[.,[.,.]]],.]],.] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>[.,[[[.,[.,[.,[.,.]]]],.],.]] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],.]],.] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[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]=>[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[2,5,4,3,6,7,1]=>[1,7,6,3,4,5,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[2,5,4,3,6,1,7]=>[7,1,6,3,4,5,2]=>[[.,[[[.,.],[.,[.,.]]],.]],.] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[2,5,4,3,1,6,7]=>[7,6,1,3,4,5,2]=>[[[.,[[.,.],[.,[.,.]]]],.],.] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[3,5,4,6,7,2,1]=>[1,2,7,6,4,5,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[3,5,4,6,1,7,2]=>[2,7,1,6,4,5,3]=>[[.,.],[[[[.,.],[.,.]],.],.]] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[3,5,4,6,2,7,1]=>[1,7,2,6,4,5,3]=>[.,[[.,[[[.,.],[.,.]],.]],.]] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[3,5,4,6,2,1,7]=>[7,1,2,6,4,5,3]=>[[.,[.,[[[.,.],[.,.]],.]]],.] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[3,5,4,1,6,2,7]=>[7,2,6,1,4,5,3]=>[[[.,.],[[[.,.],[.,.]],.]],.] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[3,5,4,2,6,7,1]=>[1,7,6,2,4,5,3]=>[.,[[[.,[[.,.],[.,.]]],.],.]] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[3,5,4,2,6,1,7]=>[7,1,6,2,4,5,3]=>[[.,[[.,[[.,.],[.,.]]],.]],.] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[3,5,4,2,1,6,7]=>[7,6,1,2,4,5,3]=>[[[.,[.,[[.,.],[.,.]]]],.],.] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[3,1,5,4,2,6,7]=>[7,6,2,4,5,1,3]=>[[[[.,.],[[.,.],[.,.]]],.],.] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[3,2,5,4,6,7,1]=>[1,7,6,4,5,2,3]=>[.,[[[[.,[.,.]],[.,.]],.],.]] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[3,2,5,4,6,1,7]=>[7,1,6,4,5,2,3]=>[[.,[[[.,[.,.]],[.,.]],.]],.] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[3,2,5,4,1,6,7]=>[7,6,1,4,5,2,3]=>[[[.,[[.,[.,.]],[.,.]]],.],.] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[2,3,5,4,6,1,7]=>[7,1,6,4,5,3,2]=>[[.,[[[[.,.],.],[.,.]],.]],.] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[2,3,5,4,1,6,7]=>[7,6,1,4,5,3,2]=>[[[.,[[[.,.],.],[.,.]]],.],.] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[2,3,1,5,4,6,7]=>[7,6,4,5,1,3,2]=>[[[[.,[[.,.],.]],[.,.]],.],.] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[4,5,6,1,7,3,2]=>[2,3,7,1,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[4,5,6,2,7,3,1]=>[1,3,7,2,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[4,5,6,2,1,7,3]=>[3,7,1,2,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[4,5,1,6,2,7,3]=>[3,7,2,6,1,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>[.,[.,[[.,[[[.,.],.],.]],.]]] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[4,5,6,3,1,7,2]=>[2,7,1,3,6,5,4]=>[[.,.],[[.,[[[.,.],.],.]],.]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>[.,[[.,[.,[[[.,.],.],.]]],.]] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>[[.,[.,[.,[[[.,.],.],.]]]],.] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[4,5,1,6,3,2,7]=>[7,2,3,6,1,5,4]=>[[[.,.],[.,[[[.,.],.],.]]],.] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[4,5,2,6,3,7,1]=>[1,7,3,6,2,5,4]=>[.,[[[.,.],[[[.,.],.],.]],.]] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[4,5,2,6,3,1,7]=>[7,1,3,6,2,5,4]=>[[.,[[.,.],[[[.,.],.],.]]],.] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[4,5,2,1,6,3,7]=>[7,3,6,1,2,5,4]=>[[[.,[.,.]],[[[.,.],.],.]],.] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[4,1,5,2,6,3,7]=>[7,3,6,2,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],.] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>[.,[.,[[[.,[[.,.],.]],.],.]]] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[4,5,3,6,1,7,2]=>[2,7,1,6,3,5,4]=>[[.,.],[[[.,[[.,.],.]],.],.]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>[.,[[.,[[.,[[.,.],.]],.]],.]] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>[[.,[.,[[.,[[.,.],.]],.]]],.] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[4,5,3,1,6,2,7]=>[7,2,6,1,3,5,4]=>[[[.,.],[[.,[[.,.],.]],.]],.] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>[.,[[[.,[.,[[.,.],.]]],.],.]] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>[[.,[[.,[.,[[.,.],.]]],.]],.] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>[[[.,[.,[.,[[.,.],.]]]],.],.] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[4,1,5,3,2,6,7]=>[7,6,2,3,5,1,4]=>[[[[.,.],[.,[[.,.],.]]],.],.] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[4,2,5,3,6,7,1]=>[1,7,6,3,5,2,4]=>[.,[[[[.,.],[[.,.],.]],.],.]] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[4,2,5,3,6,1,7]=>[7,1,6,3,5,2,4]=>[[.,[[[.,.],[[.,.],.]],.]],.] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[4,2,5,3,1,6,7]=>[7,6,1,3,5,2,4]=>[[[.,[[.,.],[[.,.],.]]],.],.] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[4,2,1,5,3,6,7]=>[7,6,3,5,1,2,4]=>[[[[.,[.,.]],[[.,.],.]],.],.] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[1,4,2,5,3,6,7]=>[7,6,3,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],.],.] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>[.,[.,[[[[.,[.,.]],.],.],.]]] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[4,3,5,6,1,7,2]=>[2,7,1,6,5,3,4]=>[[.,.],[[[[.,[.,.]],.],.],.]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>[.,[[.,[[[.,[.,.]],.],.]],.]] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>[[.,[.,[[[.,[.,.]],.],.]]],.] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[4,3,5,1,6,2,7]=>[7,2,6,1,5,3,4]=>[[[.,.],[[[.,[.,.]],.],.]],.] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>[.,[[[.,[[.,[.,.]],.]],.],.]] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>[[.,[[.,[[.,[.,.]],.]],.]],.] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>[[[.,[.,[[.,[.,.]],.]]],.],.] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[4,3,1,5,2,6,7]=>[7,6,2,5,1,3,4]=>[[[[.,.],[[.,[.,.]],.]],.],.] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>[.,[[[[.,[.,[.,.]]],.],.],.]] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>[[.,[[[.,[.,[.,.]]],.],.]],.] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>[[[.,[[.,[.,[.,.]]],.]],.],.] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[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]=>[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[2,4,3,5,6,7,1]=>[1,7,6,5,3,4,2]=>[.,[[[[[.,.],[.,.]],.],.],.]] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[2,4,3,5,6,1,7]=>[7,1,6,5,3,4,2]=>[[.,[[[[.,.],[.,.]],.],.]],.] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[2,4,3,5,1,6,7]=>[7,6,1,5,3,4,2]=>[[[.,[[[.,.],[.,.]],.]],.],.] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[2,4,3,1,5,6,7]=>[7,6,5,1,3,4,2]=>[[[[.,[[.,.],[.,.]]],.],.],.] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],.] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[3,4,5,6,1,7,2]=>[2,7,1,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>[.,[[.,[[[[.,.],.],.],.]],.]] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>[[.,[.,[[[[.,.],.],.],.]]],.] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[3,4,5,1,6,2,7]=>[7,2,6,1,5,4,3]=>[[[.,.],[[[[.,.],.],.],.]],.] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>[.,[[[.,[[[.,.],.],.]],.],.]] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>[[.,[[.,[[[.,.],.],.]],.]],.] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>[[[.,[.,[[[.,.],.],.]]],.],.] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[3,4,1,5,2,6,7]=>[7,6,2,5,1,4,3]=>[[[[.,.],[[[.,.],.],.]],.],.] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>[.,[[[[.,[[.,.],.]],.],.],.]] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>[[.,[[[.,[[.,.],.]],.],.]],.] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>[[[.,[[.,[[.,.],.]],.]],.],.] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>[[[[.,[.,[[.,.],.]]],.],.],.] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[7,6,5,2,4,1,3]=>[[[[[.,.],[[.,.],.]],.],.],.] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>[.,[[[[[.,[.,.]],.],.],.],.]] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>[[.,[[[[.,[.,.]],.],.],.]],.] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>[[[.,[[[.,[.,.]],.],.]],.],.] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>[[[[.,[[.,[.,.]],.]],.],.],.] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[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]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],.] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[[[.,[[[[.,.],.],.],.]],.],.] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],.] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],.] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[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]=>[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]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[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
Lehmer-code to major-code bijection
Description
Sends a permutation to the unique permutation such that the Lehmer code is sent to the major code.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation $\sigma$ is given by $L(\sigma) = l_1 \ldots l_n$ with $l_i = \# \{ j > i : \sigma_j < \sigma_i \}$. In particular, $l_i$ is the number of boxes in the $i$-th column of the Rothe diagram. For example, the Lehmer code of $\sigma = [4,3,1,5,2]$ is $32010$. The Lehmer code $L : \mathfrak{S}_n\ \tilde\longrightarrow\ S_n$ is a bijection between permutations of size $n$ and sequences $l_1\ldots l_n \in \mathbf{N}^n$ with $l_i \leq i$.
* The major code $M(\sigma)$ of a permutation $\sigma \in \mathfrak{S}_n$ is a way to encode a permutation as a sequence $m_1 m_2 \ldots m_n$ with $m_i \geq i$. To define $m_i$, let $\operatorname{del}_i(\sigma)$ be the normalized permutation obtained by removing all $\sigma_j < i$ from the one-line notation of $\sigma$. The $i$-th index is then given by
$$m_i = \operatorname{maj}(\operatorname{del}_i(\sigma)) - \operatorname{maj}(\operatorname{del}_{i-1}(\sigma)).$$
For example, the permutation $[9,3,5,7,2,1,4,6,8]$ has major code $[5, 0, 1, 0, 1, 2, 0, 1, 0]$ since
$$\operatorname{maj}([8,2,4,6,1,3,5,7]) = 5, \quad \operatorname{maj}([7,1,3,5,2,4,6]) = 5, \quad \operatorname{maj}([6,2,4,1,3,5]) = 4,$$
$$\operatorname{maj}([5,1,3,2,4]) = 4, \quad \operatorname{maj}([4,2,1,3]) = 3, \quad \operatorname{maj}([3,1,2]) = 1, \quad \operatorname{maj}([2,1]) = 1.$$
Observe that the sum of the major code of $\sigma$ equals the major index of $\sigma$.
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.