Identifier
Mp00025: Dyck paths to 132-avoiding permutationPermutations
Mp00064: Permutations reversePermutations
Mp00238: Permutations Clarke-Steingrimsson-ZengPermutations
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]=>[1,2]=>[1,2]=>[.,[.,.]] [1,1,0,0]=>[1,2]=>[2,1]=>[2,1]=>[[.,.],.] [1,0,1,0,1,0]=>[3,2,1]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,1,0,0]=>[2,3,1]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]] [1,1,0,0,1,0]=>[3,1,2]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]] [1,1,0,1,0,0]=>[2,1,3]=>[3,1,2]=>[3,1,2]=>[[.,[.,.]],.] [1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]=>[2,3,1]=>[[.,.],[.,.]] [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]] [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[1,4,2,3]=>[1,4,2,3]=>[.,[[.,[.,.]],.]] [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[1,4,3,2]=>[1,3,4,2]=>[.,[[.,.],[.,.]]] [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]] [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[3,1,2,4]=>[3,1,2,4]=>[[.,[.,.]],[.,.]] [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[4,1,2,3]=>[4,1,2,3]=>[[.,[.,[.,.]]],.] [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[4,1,3,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]] [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[3,2,1,4]=>[2,3,1,4]=>[[.,.],[.,[.,.]]] [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[4,2,1,3]=>[2,4,1,3]=>[[.,.],[[.,.],.]] [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[4,3,1,2]=>[3,1,4,2]=>[[.,[.,.]],[.,.]] [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[4,3,2,1]=>[2,3,4,1]=>[[.,.],[.,[.,.]]] [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[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]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]] [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]] [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[1,3,2,4,5]=>[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]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]] [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[1,4,2,3,5]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]] [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]] [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,3,4,2,5]=>[.,[[.,.],[.,[.,.]]]] [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[1,5,3,2,4]=>[1,3,5,2,4]=>[.,[[.,.],[[.,.],.]]] [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[1,4,2,5,3]=>[.,[[.,[.,.]],[.,.]]] [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]] [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[2,1,3,4,5]=>[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]=>[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]=>[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]=>[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]=>[2,1,4,5,3]=>[[.,.],[[.,.],[.,.]]] [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[3,1,2,4,5]=>[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]=>[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]=>[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]=>[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]=>[4,1,5,2,3]=>[[.,[.,[.,.]]],[.,.]] [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[4,1,3,2,5]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[5,1,3,2,4]=>[3,5,1,2,4]=>[[.,[.,.]],[[.,.],.]] [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[5,1,4,2,3]=>[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]] [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]] [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[3,2,1,5,4]=>[2,3,1,5,4]=>[[.,.],[.,[[.,.],.]]] [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,.],[[.,.],[.,.]]] [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,.],[[.,[.,.]],.]] [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[5,2,1,4,3]=>[2,4,5,1,3]=>[[.,.],[[.,.],[.,.]]] [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,[.,.]],[[.,.],.]] [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,[.,[.,.]]],[.,.]] [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[3,4,1,5,2]=>[[.,[.,.]],[.,[.,.]]] [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[.,.],[.,[[.,.],.]]] [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[.,.],[[.,.],[.,.]]] [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[.,[.,.]],[.,[.,.]]] [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]] [1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>[1,2,4,6,3,5]=>[.,[.,[[.,.],[[.,.],.]]]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[1,2,5,3,6,4]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[.,[[.,.],[[.,[.,.]],.]]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,.],[.,.]]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[.,[[.,[.,.]],[[.,.],.]]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[1,5,2,6,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>[1,4,6,2,3,5]=>[.,[[.,[.,.]],[[.,.],.]]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[1,5,6,2,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[1,4,5,6,2,3]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[.,[[.,.],[.,[[.,.],.]]]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>[1,3,5,2,4,6]=>[.,[[.,.],[[.,.],[.,.]]]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>[1,3,6,2,4,5]=>[.,[[.,.],[[.,[.,.]],.]]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>[1,3,5,6,2,4]=>[.,[[.,.],[[.,.],[.,.]]]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>[1,4,2,5,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>[1,4,2,6,3,5]=>[.,[[.,[.,.]],[[.,.],.]]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[1,5,2,3,6,4]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[1,4,5,2,6,3]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[1,3,4,6,2,5]=>[.,[[.,.],[.,[[.,.],.]]]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>[1,3,5,2,6,4]=>[.,[[.,.],[[.,.],[.,.]]]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[1,4,2,5,6,3]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>[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]=>[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]=>[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]=>[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]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[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]=>[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]=>[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]=>[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]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>[2,1,4,6,3,5]=>[[.,.],[[.,.],[[.,.],.]]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>[2,1,5,3,6,4]=>[[.,.],[[.,[.,.]],[.,.]]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>[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]=>[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]=>[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]=>[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]=>[3,1,2,5,6,4]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>[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]=>[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]=>[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]=>[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]=>[5,1,2,6,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>[4,1,5,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>[4,1,6,2,3,5]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[5,1,6,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[4,1,5,6,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>[3,5,1,2,4,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>[3,6,1,2,4,5]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>[4,5,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>[4,6,1,2,3,5]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[3,4,5,1,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>[3,4,6,1,2,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>[3,5,6,1,2,4]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[4,5,1,6,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>[2,3,1,6,4,5]=>[[.,.],[.,[[.,[.,.]],.]]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>[2,4,1,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[[.,.],[[.,[.,.]],[.,.]]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>[2,5,1,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>[2,4,5,1,3,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>[2,4,6,1,3,5]=>[[.,.],[[.,.],[[.,.],.]]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>[2,5,6,1,3,4]=>[[.,.],[[.,[.,.]],[.,.]]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>[2,4,5,6,1,3]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>[3,1,4,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>[3,1,5,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[4,1,5,2,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>[3,4,1,5,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>[3,4,1,6,2,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>[3,5,1,2,6,4]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[4,5,1,2,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[3,4,5,1,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[[.,.],[.,[[.,[.,.]],.]]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>[2,3,5,6,1,4]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[[.,.],[[.,.],[[.,.],.]]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[[.,.],[[.,[.,.]],[.,.]]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>[2,4,5,1,6,3]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[3,4,1,5,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]] [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]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [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]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [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]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [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]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]] [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]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [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]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [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]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [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]=>[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [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]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]] [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]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [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]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [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]=>[1,2,3,5,7,4,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [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]=>[1,2,3,6,4,7,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [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]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [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]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [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]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [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]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [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]=>[1,2,4,3,7,5,6]=>[.,[.,[[.,.],[[.,[.,.]],.]]]] [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]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [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]=>[1,2,5,3,4,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [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]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [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]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [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]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]] [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]=>[1,2,6,3,7,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [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]=>[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [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]=>[1,2,5,7,3,4,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [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]=>[1,2,6,7,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [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]=>[1,2,5,6,7,3,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [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]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [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]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [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]=>[1,2,4,6,3,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [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]=>[1,2,4,7,3,5,6]=>[.,[.,[[.,.],[[.,[.,.]],.]]]] [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]=>[1,2,4,6,7,3,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [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]=>[1,2,5,3,6,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [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]=>[1,2,5,3,7,4,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [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]=>[1,2,6,3,4,7,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [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]=>[1,2,5,6,3,7,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [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]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [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]=>[1,2,4,5,7,3,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [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]=>[1,2,4,6,3,7,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [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]=>[1,2,5,3,6,7,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [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]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [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]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [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]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [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]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [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]=>[1,3,2,4,7,5,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [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]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [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]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [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]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [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]=>[1,3,2,6,4,5,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [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]=>[1,3,2,7,4,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],.]]] [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]=>[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [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]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [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]=>[1,3,2,5,7,4,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [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]=>[1,3,2,6,4,7,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [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]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [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]=>[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [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]=>[1,4,2,3,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [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]=>[1,4,2,3,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [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]=>[1,4,2,3,7,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [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]=>[1,4,2,3,6,7,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [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]=>[1,5,2,3,4,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [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]=>[1,5,2,3,4,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [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]=>[1,6,2,3,4,5,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [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]=>[1,7,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]] [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]=>[1,6,2,3,7,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [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]=>[1,5,2,6,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [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]=>[1,5,2,7,3,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [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]=>[1,6,2,7,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [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]=>[1,5,2,6,7,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [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]=>[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [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]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [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]=>[1,4,6,2,3,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [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]=>[1,4,7,2,3,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [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]=>[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [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]=>[1,5,6,2,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [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]=>[1,5,7,2,3,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [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]=>[1,6,7,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [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]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [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]=>[1,4,5,6,2,3,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [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]=>[1,4,5,7,2,3,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [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]=>[1,4,6,7,2,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [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]=>[1,5,6,2,7,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [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]=>[1,4,5,6,7,2,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [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]=>[1,3,4,2,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [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]=>[1,3,4,2,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [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]=>[1,3,4,2,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [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]=>[1,3,4,2,7,5,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [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]=>[1,3,4,2,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [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]=>[1,3,5,2,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [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]=>[1,3,5,2,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [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]=>[1,3,6,2,4,5,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [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]=>[1,3,7,2,4,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],.]]] [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]=>[1,3,6,2,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [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]=>[1,3,5,6,2,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [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]=>[1,3,5,7,2,4,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [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]=>[1,3,6,7,2,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [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]=>[1,3,5,6,7,2,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [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]=>[1,4,2,5,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [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]=>[1,4,2,5,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [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]=>[1,4,2,6,3,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [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]=>[1,4,2,7,3,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [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]=>[1,4,2,6,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [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]=>[1,5,2,3,6,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [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]=>[1,5,2,3,7,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [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]=>[1,6,2,3,4,7,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [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]=>[1,5,2,6,3,7,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [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]=>[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [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]=>[1,4,5,2,7,3,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [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]=>[1,4,6,2,3,7,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [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]=>[1,5,6,2,3,7,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [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]=>[1,4,5,6,2,7,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [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]=>[1,3,4,5,2,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [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]=>[1,3,4,5,2,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [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]=>[1,3,4,6,2,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [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]=>[1,3,4,7,2,5,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [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]=>[1,3,4,6,7,2,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [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]=>[1,3,5,2,6,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [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]=>[1,3,5,2,7,4,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [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]=>[1,3,6,2,4,7,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [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]=>[1,3,5,6,2,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [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]=>[1,4,2,5,6,3,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [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]=>[1,4,2,5,7,3,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [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]=>[1,4,2,6,3,7,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [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]=>[1,5,2,3,6,7,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [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]=>[1,4,5,2,6,7,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [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]=>[1,3,4,5,6,2,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [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]=>[1,3,4,5,7,2,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [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]=>[1,3,4,6,2,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [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]=>[1,3,5,2,6,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [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]=>[1,4,2,5,6,7,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [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]=>[1,3,4,5,6,7,2]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [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]=>[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]=>[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]=>[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]=>[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]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [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]=>[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]=>[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]=>[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]=>[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]=>[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [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]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[2,1,3,5,7,4,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [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]=>[2,1,3,6,4,7,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [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]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[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]=>[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]=>[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]=>[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]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[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]=>[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]=>[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]=>[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]=>[2,1,6,3,7,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [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]=>[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,1,5,7,3,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [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]=>[2,1,6,7,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [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]=>[2,1,5,6,7,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [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]=>[2,1,4,6,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,1,4,7,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [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]=>[2,1,4,6,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,1,5,3,6,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,1,5,3,7,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [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]=>[2,1,6,3,4,7,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [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]=>[2,1,5,6,3,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[2,1,4,5,7,3,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [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]=>[2,1,4,6,3,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,1,5,3,6,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[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]=>[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]=>[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]=>[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]=>[3,1,2,4,6,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[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]=>[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]=>[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]=>[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]=>[3,1,2,6,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[3,1,2,5,6,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[3,1,2,5,7,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [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]=>[3,1,2,6,4,7,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[3,1,2,5,6,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[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]=>[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]=>[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]=>[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]=>[4,1,2,3,6,7,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[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]=>[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]=>[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]=>[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]=>[6,1,2,3,7,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [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]=>[5,1,2,6,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[5,1,2,7,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [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]=>[6,1,2,7,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [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]=>[5,1,2,6,7,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[4,1,5,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[4,1,5,2,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [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]=>[4,1,6,2,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[4,1,7,2,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [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]=>[4,1,6,2,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[5,1,6,2,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[5,1,7,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [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]=>[6,1,7,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [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]=>[5,1,6,7,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[4,1,5,6,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[4,1,5,7,2,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [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]=>[4,1,6,7,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[5,1,6,2,7,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[4,1,5,6,7,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [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]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,4,1,2,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [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]=>[3,4,1,2,6,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,5,1,2,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[3,5,1,2,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [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]=>[3,6,1,2,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [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]=>[3,6,1,2,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[3,5,1,7,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [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]=>[3,6,1,7,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[3,5,1,6,7,2,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[4,5,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[4,5,1,2,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [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]=>[4,6,1,2,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[4,7,1,2,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [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]=>[4,6,1,2,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[5,6,1,2,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[5,7,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [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]=>[6,7,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [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]=>[5,6,1,7,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [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]=>[4,6,7,1,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[3,4,5,1,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[3,4,5,1,2,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [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]=>[3,4,6,1,2,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,4,7,1,2,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [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]=>[3,4,6,1,7,2,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,5,6,1,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[3,5,7,1,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [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]=>[3,6,7,1,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[3,5,6,7,1,2,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[4,5,1,6,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[4,5,1,7,2,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [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]=>[4,6,1,7,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[5,6,1,2,7,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[4,5,6,1,7,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[3,4,5,6,1,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[3,4,5,7,1,2,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [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]=>[3,4,6,7,1,2,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,5,6,1,7,2,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[4,5,1,6,7,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[3,4,5,6,7,1,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [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]=>[2,3,1,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [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]=>[2,3,1,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [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]=>[2,3,1,4,7,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [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]=>[2,3,1,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [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]=>[2,3,1,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[2,3,1,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [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]=>[2,3,1,6,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [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]=>[2,3,1,7,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [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]=>[2,3,1,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [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]=>[2,3,1,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[2,3,1,5,7,4,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [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]=>[2,3,1,6,4,7,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [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]=>[2,3,1,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[2,4,1,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[2,4,1,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [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]=>[2,4,1,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,4,1,3,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [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]=>[2,4,1,3,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,5,1,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,5,1,3,4,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [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]=>[2,6,1,3,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [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]=>[2,7,1,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [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]=>[2,6,1,3,7,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [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]=>[2,5,1,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,5,1,7,3,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [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]=>[2,6,1,7,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [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]=>[2,5,1,6,7,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,4,5,1,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[2,4,5,1,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [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]=>[2,4,6,1,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,4,7,1,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [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]=>[2,4,6,1,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,5,6,1,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,5,7,1,3,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [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]=>[2,6,7,1,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [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]=>[2,5,6,7,1,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,4,5,6,1,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[2,4,5,7,1,3,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [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]=>[2,4,6,7,1,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,5,6,1,7,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,4,5,6,7,1,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[3,1,4,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[3,1,4,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [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]=>[3,1,4,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,1,4,2,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [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]=>[3,1,4,2,6,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,1,5,2,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[3,1,5,2,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [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]=>[3,1,6,2,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[3,1,7,2,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [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]=>[3,1,6,2,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[3,1,5,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[3,1,5,7,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [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]=>[3,1,6,7,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[3,1,5,6,7,2,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[4,1,2,5,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[4,1,2,5,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [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]=>[4,1,2,6,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[4,1,2,7,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [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]=>[4,1,2,6,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[5,1,2,3,6,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[5,1,2,3,7,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [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]=>[6,1,2,3,4,7,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [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]=>[5,1,2,6,3,7,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[4,1,5,2,6,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[4,1,5,2,7,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [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]=>[4,1,6,2,3,7,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[5,1,6,2,3,7,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[4,1,5,6,2,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[3,4,1,5,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[3,4,1,5,2,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [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]=>[3,4,1,6,2,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,4,1,7,2,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [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]=>[3,4,1,6,7,2,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,5,1,2,6,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[3,5,1,2,7,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [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]=>[3,6,1,2,4,7,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[3,5,1,6,2,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[4,5,1,2,6,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[4,5,1,2,7,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [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]=>[4,6,1,2,3,7,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[5,6,1,2,3,7,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[4,5,6,1,2,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[3,4,5,1,6,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[3,4,5,1,7,2,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [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]=>[3,4,6,1,2,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,5,6,1,2,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[4,5,1,6,2,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[3,4,5,6,1,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [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]=>[2,3,4,1,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [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]=>[2,3,4,1,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [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]=>[2,3,4,1,7,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [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]=>[2,3,4,1,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [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]=>[2,3,5,1,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[2,3,5,1,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [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]=>[2,3,6,1,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [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]=>[2,3,7,1,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [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]=>[2,3,6,1,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [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]=>[2,3,5,6,1,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[2,3,5,7,1,4,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [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]=>[2,3,6,7,1,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [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]=>[2,3,5,6,7,1,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[2,4,1,5,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[2,4,1,5,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [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]=>[2,4,1,6,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,4,1,7,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [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]=>[2,4,1,6,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,5,1,3,6,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,5,1,3,7,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [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]=>[2,6,1,3,4,7,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [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]=>[2,5,1,6,3,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,4,5,1,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[2,4,5,1,7,3,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [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]=>[2,4,6,1,3,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,5,6,1,3,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,4,5,6,1,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[3,1,4,5,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[3,1,4,5,2,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [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]=>[3,1,4,6,2,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,1,4,7,2,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [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]=>[3,1,4,6,7,2,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,1,5,2,6,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[3,1,5,2,7,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [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]=>[3,1,6,2,4,7,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[3,1,5,6,2,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[4,1,2,5,6,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[4,1,2,5,7,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [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]=>[4,1,2,6,3,7,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[5,1,2,3,6,7,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[4,1,5,2,6,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[3,4,1,5,6,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[3,4,1,5,7,2,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [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]=>[3,4,1,6,2,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,5,1,2,6,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[4,5,1,2,6,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[3,4,5,1,6,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [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]=>[2,3,4,5,1,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [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]=>[2,3,4,6,1,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [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]=>[2,3,4,7,1,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [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]=>[2,3,4,6,7,1,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [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]=>[2,3,5,1,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[2,3,5,1,7,4,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [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]=>[2,3,6,1,4,7,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [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]=>[2,3,5,6,1,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[2,4,1,5,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[2,4,1,5,7,3,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [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]=>[2,4,1,6,3,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[2,5,1,3,6,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[2,4,5,1,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[3,1,4,5,6,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[3,1,4,5,7,2,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [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]=>[3,1,4,6,2,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,1,5,2,6,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[4,1,2,5,6,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[3,4,1,5,6,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [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]=>[2,3,4,5,7,1,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [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]=>[2,3,4,6,1,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [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]=>[2,3,5,1,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[2,4,1,5,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[3,1,4,5,6,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [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]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [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]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] [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]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] [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]=>[1,4,2,3,7,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] [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]=>[1,3,4,2,6,7,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] [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]=>[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]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [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]=>[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]=>[4,1,2,3,8,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] [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]=>[2,3,1,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] [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]=>[2,3,4,1,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
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
Clarke-Steingrimsson-Zeng
Description
The Clarke-Steingrimsson-Zeng map sending descents to excedances.
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
  • $des$ is the number of descents, St000021The number of descents of a permutation.,
  • $exc$ is the number of (strict) excedances, St000155The number of exceedances (also excedences) of a permutation.,
  • $Dbot$ is the sum of the descent bottoms, St000154The sum of the descent bottoms of a permutation.,
  • $Ebot$ is the sum of the excedance bottoms,
  • $Ddif$ is the sum of the descent differences, St000030The sum of the descent differences of a permutations.,
  • $Edif$ is the sum of the excedance differences (or depth), St000029The depth of a permutation.,
  • $Res$ is the sum of the (right) embracing numbers,
  • $Ine$ is the sum of the side numbers.
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.