Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.] [1,0,1,0]=>[1,2]=>[2,1]=>[[.,.],.] [1,1,0,0]=>[2,1]=>[1,2]=>[.,[.,.]] [1,0,1,0,1,0]=>[1,2,3]=>[3,2,1]=>[[[.,.],.],.] [1,0,1,1,0,0]=>[1,3,2]=>[2,3,1]=>[[.,.],[.,.]] [1,1,0,0,1,0]=>[2,1,3]=>[3,1,2]=>[[.,[.,.]],.] [1,1,0,1,0,0]=>[2,3,1]=>[1,3,2]=>[.,[[.,.],.]] [1,1,1,0,0,0]=>[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[4,3,2,1]=>[[[[.,.],.],.],.] [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[3,4,2,1]=>[[[.,.],.],[.,.]] [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,3,1]=>[[.,.],[[.,.],.]] [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[2,3,4,1]=>[[.,.],[.,[.,.]]] [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[4,3,1,2]=>[[[.,[.,.]],.],.] [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,4,1,2]=>[[.,[.,.]],[.,.]] [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[4,1,3,2]=>[[.,[[.,.],.]],.] [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[1,4,3,2]=>[.,[[[.,.],.],.]] [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[1,3,4,2]=>[.,[[.,.],[.,.]]] [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[4,1,2,3]=>[[.,[.,[.,.]]],.] [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[1,4,2,3]=>[.,[[.,[.,.]],.]] [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]] [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.] [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[[[.,.],.],[[.,.],.]] [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.] [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]] [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.] [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,5,4,3,1]=>[[.,.],[[[.,.],.],.]] [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[2,4,5,3,1]=>[[.,.],[[.,.],[.,.]]] [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.] [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[2,5,3,4,1]=>[[.,.],[[.,[.,.]],.]] [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[2,3,5,4,1]=>[[.,.],[.,[[.,.],.]]] [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.] [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]] [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[5,3,4,1,2]=>[[[.,[.,.]],[.,.]],.] [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,5,4,1,2]=>[[.,[.,.]],[[.,.],.]] [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[[[.,[[.,.],.]],.],.] [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,5,1,3,2]=>[[.,[[.,.],.]],[.,.]] [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[[.,[[[.,.],.],.]],.] [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]] [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[1,4,5,3,2]=>[.,[[[.,.],.],[.,.]]] [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[5,1,3,4,2]=>[[.,[[.,.],[.,.]]],.] [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]] [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[1,3,5,4,2]=>[.,[[.,.],[[.,.],.]]] [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.] [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[5,1,4,2,3]=>[[.,[[.,[.,.]],.]],.] [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[.,[[[.,[.,.]],.],.]] [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]] [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.] [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]] [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]] [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]] [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.] [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]] [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]] [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[[[[.,.],.],.],[[.,.],.]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],.] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[[[.,.],.],[[[.,.],.],.]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[[[.,.],.],[[.,[.,.]],.]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>[[[.,.],.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[[[.,.],[.,.]],[[.,.],.]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[[[.,.],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],.] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,.]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>[[.,.],[[[[.,.],.],.],.]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>[[.,.],[[[.,.],.],[.,.]]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[6,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],.] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>[[.,.],[[[.,.],[.,.]],.]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>[[.,.],[[.,.],[[.,.],.]]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>[[.,.],[[.,.],[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[6,2,5,3,4,1]=>[[[.,.],[[.,[.,.]],.]],.] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],.]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[[.,.],[[.,[.,.]],[.,.]]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>[[.,.],[[.,[[.,.],.]],.]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>[[.,.],[.,[[[.,.],.],.]]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>[[.,.],[.,[[.,.],[.,.]]]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],.]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>[[.,.],[.,[[.,[.,.]],.]]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>[[.,.],[.,[.,[[.,.],.]]]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],.] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>[[[.,[.,.]],.],[[.,.],.]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],.] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],.] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],.]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],.] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[3,4,6,5,1,2]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],.] [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,.]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],.] [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>[[.,[[.,.],.]],[.,[.,.]]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],.] [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,.]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],.] [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>[.,[[[[.,.],.],.],[.,.]]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],.] [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],.]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[1,4,6,5,3,2]=>[.,[[[.,.],.],[[.,.],.]]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>[.,[[[.,.],.],[.,[.,.]]]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],.] [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],.] [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],.]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>[.,[[[.,.],[.,.]],[.,.]]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[6,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],.] [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[1,3,6,5,4,2]=>[.,[[.,.],[[[.,.],.],.]]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[1,3,5,6,4,2]=>[.,[[.,.],[[.,.],[.,.]]]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[1,3,6,4,5,2]=>[.,[[.,.],[[.,[.,.]],.]]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>[.,[[.,.],[.,[[.,.],.]]]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.] [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],.] [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],.] [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,.]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],.] [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],.]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],.] [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],.]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>[.,[[.,[.,.]],[[.,.],.]]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],.] [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,.]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],.] [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],.]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>[.,[[.,[[.,.],.]],[.,.]]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],.] [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],.]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>[.,[.,[[[.,.],.],[.,.]]]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[6,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],.] [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],.]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>[.,[.,[[.,.],[[.,.],.]]]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.] [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],.] [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],.]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],.] [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],.]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[.,[.,[[[.,[.,.]],.],.]]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.] [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],.]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[.,[.,[[.,[[.,.],.]],.]]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[[[[[.,.],.],.],[[.,.],.]],.] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[4,7,5,6,3,2,1]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[4,5,7,6,3,2,1]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[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]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[[[[.,.],.],[[[.,.],.],.]],.] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>[[[.,.],.],[[[[.,.],.],.],.]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[3,6,7,5,4,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[7,3,5,6,4,2,1]=>[[[[.,.],.],[[.,.],[.,.]]],.] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[3,7,5,6,4,2,1]=>[[[.,.],.],[[[.,.],[.,.]],.]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[7,3,6,4,5,2,1]=>[[[[.,.],.],[[.,[.,.]],.]],.] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[3,7,6,4,5,2,1]=>[[[.,.],.],[[[.,[.,.]],.],.]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[3,6,7,4,5,2,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[7,3,4,6,5,2,1]=>[[[[.,.],.],[.,[[.,.],.]]],.] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[3,7,4,6,5,2,1]=>[[[.,.],.],[[.,[[.,.],.]],.]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[3,4,6,7,5,2,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[3,7,4,5,6,2,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[3,4,7,5,6,2,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[3,4,5,7,6,2,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[[.,.],.]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[4,6,7,5,2,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[4,7,5,6,2,3,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[4,5,7,6,2,3,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[[[[[.,.],[[.,.],.]],.],.],.] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],[.,.]] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[5,6,7,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[[[[.,.],[[[.,.],.],.]],.],.] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],[.,.]] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>[[.,.],[[[[[.,.],.],.],.],.]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[2,6,7,5,4,3,1]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[7,2,5,6,4,3,1]=>[[[.,.],[[[.,.],.],[.,.]]],.] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[2,7,5,6,4,3,1]=>[[.,.],[[[[.,.],.],[.,.]],.]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[2,5,7,6,4,3,1]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[2,5,6,7,4,3,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[7,6,2,4,5,3,1]=>[[[[.,.],[[.,.],[.,.]]],.],.] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[6,7,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[7,2,6,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[2,7,6,4,5,3,1]=>[[.,.],[[[[.,.],[.,.]],.],.]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[2,6,7,4,5,3,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[7,2,4,6,5,3,1]=>[[[.,.],[[.,.],[[.,.],.]]],.] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[2,7,4,6,5,3,1]=>[[.,.],[[[.,.],[[.,.],.]],.]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[2,4,7,6,5,3,1]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[7,2,4,5,6,3,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[2,7,4,5,6,3,1]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[2,4,7,5,6,3,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[2,4,5,7,6,3,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[2,4,5,6,7,3,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[5,7,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[7,6,2,5,3,4,1]=>[[[[.,.],[[.,[.,.]],.]],.],.] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[6,7,2,5,3,4,1]=>[[[.,.],[[.,[.,.]],.]],[.,.]] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[7,2,6,5,3,4,1]=>[[[.,.],[[[.,[.,.]],.],.]],.] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[2,7,6,5,3,4,1]=>[[.,.],[[[[.,[.,.]],.],.],.]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[2,6,7,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[7,2,5,6,3,4,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[2,7,5,6,3,4,1]=>[[.,.],[[[.,[.,.]],[.,.]],.]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[2,5,7,6,3,4,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[2,5,6,7,3,4,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[7,6,2,3,5,4,1]=>[[[[.,.],[.,[[.,.],.]]],.],.] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[6,7,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[7,2,6,3,5,4,1]=>[[[.,.],[[.,[[.,.],.]],.]],.] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[2,7,6,3,5,4,1]=>[[.,.],[[[.,[[.,.],.]],.],.]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[2,6,7,3,5,4,1]=>[[.,.],[[.,[[.,.],.]],[.,.]]] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[7,2,3,6,5,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[2,7,3,6,5,4,1]=>[[.,.],[[.,[[[.,.],.],.]],.]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[2,3,7,6,5,4,1]=>[[.,.],[.,[[[[.,.],.],.],.]]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[2,3,6,7,5,4,1]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[7,2,3,5,6,4,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[2,7,3,5,6,4,1]=>[[.,.],[[.,[[.,.],[.,.]]],.]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[2,3,7,5,6,4,1]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[2,3,5,7,6,4,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[2,3,5,6,7,4,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[7,2,6,3,4,5,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[2,7,6,3,4,5,1]=>[[.,.],[[[.,[.,[.,.]]],.],.]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[2,6,7,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[7,2,3,6,4,5,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[2,7,3,6,4,5,1]=>[[.,.],[[.,[[.,[.,.]],.]],.]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[2,3,7,6,4,5,1]=>[[.,.],[.,[[[.,[.,.]],.],.]]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[2,3,6,7,4,5,1]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[7,2,3,4,6,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[2,7,3,4,6,5,1]=>[[.,.],[[.,[.,[[.,.],.]]],.]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[2,3,7,4,6,5,1]=>[[.,.],[.,[[.,[[.,.],.]],.]]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[2,3,4,7,6,5,1]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[2,3,4,6,7,5,1]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[2,7,3,4,5,6,1]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[2,3,7,4,5,6,1]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[2,3,4,7,5,6,1]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[2,3,4,5,7,6,1]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[5,7,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[[.,.],.]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[7,4,6,5,3,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],.] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[4,7,6,5,3,1,2]=>[[[.,[.,.]],.],[[[.,.],.],.]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[4,6,7,5,3,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[4,7,5,6,3,1,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[4,5,7,6,3,1,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],.] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[5,7,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[7,6,3,5,4,1,2]=>[[[[.,[.,.]],[[.,.],.]],.],.] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[7,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],.] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[3,7,6,5,4,1,2]=>[[.,[.,.]],[[[[.,.],.],.],.]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[3,6,7,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[7,3,5,6,4,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],.] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[3,7,5,6,4,1,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[3,5,7,6,4,1,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[3,5,6,7,4,1,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[7,3,6,4,5,1,2]=>[[[.,[.,.]],[[.,[.,.]],.]],.] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[3,7,6,4,5,1,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[3,6,7,4,5,1,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[7,3,4,6,5,1,2]=>[[[.,[.,.]],[.,[[.,.],.]]],.] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[3,7,4,6,5,1,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[3,4,7,6,5,1,2]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[3,4,6,7,5,1,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[3,7,4,5,6,1,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[3,4,7,5,6,1,2]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[3,4,5,7,6,1,2]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],.] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[6,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[7,5,6,4,1,3,2]=>[[[[.,[[.,.],.]],.],[.,.]],.] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[5,6,7,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[7,6,4,5,1,3,2]=>[[[[.,[[.,.],.]],[.,.]],.],.] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[7,4,6,5,1,3,2]=>[[[.,[[.,.],.]],[[.,.],.]],.] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[4,7,6,5,1,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[4,6,7,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[7,4,5,6,1,3,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[4,7,5,6,1,3,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[4,5,7,6,1,3,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[4,5,6,7,1,3,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],.] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[7,5,6,1,4,3,2]=>[[[.,[[[.,.],.],.]],[.,.]],.] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[5,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[5,6,7,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[[[.,[[[[.,.],.],.],.]],.],.] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[6,7,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],.] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[1,6,7,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,.]]] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[7,1,5,6,4,3,2]=>[[.,[[[[.,.],.],.],[.,.]]],.] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[1,7,5,6,4,3,2]=>[.,[[[[[.,.],.],.],[.,.]],.]] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[1,5,7,6,4,3,2]=>[.,[[[[.,.],.],.],[[.,.],.]]] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[7,6,1,4,5,3,2]=>[[[.,[[[.,.],.],[.,.]]],.],.] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[6,7,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[7,1,6,4,5,3,2]=>[[.,[[[[.,.],.],[.,.]],.]],.] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[1,6,7,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[7,1,4,6,5,3,2]=>[[.,[[[.,.],.],[[.,.],.]]],.] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[1,7,4,6,5,3,2]=>[.,[[[[.,.],.],[[.,.],.]],.]] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[1,4,7,6,5,3,2]=>[.,[[[.,.],.],[[[.,.],.],.]]] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[1,4,6,7,5,3,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[7,1,4,5,6,3,2]=>[[.,[[[.,.],.],[.,[.,.]]]],.] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[1,7,4,5,6,3,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[1,4,7,5,6,3,2]=>[.,[[[.,.],.],[[.,[.,.]],.]]] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[1,4,5,7,6,3,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[1,4,5,6,7,3,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[7,6,5,1,3,4,2]=>[[[[.,[[.,.],[.,.]]],.],.],.] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[6,7,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[7,5,6,1,3,4,2]=>[[[.,[[.,.],[.,.]]],[.,.]],.] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[5,7,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[5,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[7,6,1,5,3,4,2]=>[[[.,[[[.,.],[.,.]],.]],.],.] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[6,7,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[7,1,6,5,3,4,2]=>[[.,[[[[.,.],[.,.]],.],.]],.] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[1,7,6,5,3,4,2]=>[.,[[[[[.,.],[.,.]],.],.],.]] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[1,6,7,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],[.,.]]] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[7,1,5,6,3,4,2]=>[[.,[[[.,.],[.,.]],[.,.]]],.] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[1,7,5,6,3,4,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[1,5,7,6,3,4,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[1,5,6,7,3,4,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[7,6,1,3,5,4,2]=>[[[.,[[.,.],[[.,.],.]]],.],.] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[6,7,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[7,1,6,3,5,4,2]=>[[.,[[[.,.],[[.,.],.]],.]],.] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[1,7,6,3,5,4,2]=>[.,[[[[.,.],[[.,.],.]],.],.]] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[1,6,7,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[7,1,3,6,5,4,2]=>[[.,[[.,.],[[[.,.],.],.]]],.] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[1,7,3,6,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[1,3,7,6,5,4,2]=>[.,[[.,.],[[[[.,.],.],.],.]]] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[1,3,6,7,5,4,2]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[7,1,3,5,6,4,2]=>[[.,[[.,.],[[.,.],[.,.]]]],.] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[1,7,3,5,6,4,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[1,3,7,5,6,4,2]=>[.,[[.,.],[[[.,.],[.,.]],.]]] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[1,3,5,7,6,4,2]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[1,3,5,6,7,4,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[7,6,1,3,4,5,2]=>[[[.,[[.,.],[.,[.,.]]]],.],.] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[6,7,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[7,1,6,3,4,5,2]=>[[.,[[[.,.],[.,[.,.]]],.]],.] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[1,7,6,3,4,5,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[1,6,7,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[7,1,3,6,4,5,2]=>[[.,[[.,.],[[.,[.,.]],.]]],.] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[1,7,3,6,4,5,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[1,3,7,6,4,5,2]=>[.,[[.,.],[[[.,[.,.]],.],.]]] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[1,3,6,7,4,5,2]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[7,1,3,4,6,5,2]=>[[.,[[.,.],[.,[[.,.],.]]]],.] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[1,7,3,4,6,5,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[1,3,7,4,6,5,2]=>[.,[[.,.],[[.,[[.,.],.]],.]]] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[1,3,4,7,6,5,2]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[1,3,4,6,7,5,2]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[7,1,3,4,5,6,2]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[1,3,7,4,5,6,2]=>[.,[[.,.],[[.,[.,[.,.]]],.]]] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[1,3,4,7,5,6,2]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[1,3,4,5,7,6,2]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[1,3,4,5,6,7,2]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[5,7,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[7,4,6,5,1,2,3]=>[[[.,[.,[.,.]]],[[.,.],.]],.] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[4,7,6,5,1,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[4,6,7,5,1,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[4,7,5,6,1,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[4,5,7,6,1,2,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>[[[[.,[[.,[.,.]],.]],.],.],.] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[6,7,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[7,5,6,1,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],.] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[5,7,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[5,6,7,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>[[[.,[[[.,[.,.]],.],.]],.],.] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[6,7,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],[.,.]] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>[[.,[[[[.,[.,.]],.],.],.]],.] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>[.,[[[[[.,[.,.]],.],.],.],.]] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[1,6,7,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[7,1,5,6,4,2,3]=>[[.,[[[.,[.,.]],.],[.,.]]],.] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[1,7,5,6,4,2,3]=>[.,[[[[.,[.,.]],.],[.,.]],.]] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[1,5,7,6,4,2,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[1,5,6,7,4,2,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[7,6,1,4,5,2,3]=>[[[.,[[.,[.,.]],[.,.]]],.],.] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[6,7,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[7,1,6,4,5,2,3]=>[[.,[[[.,[.,.]],[.,.]],.]],.] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[1,7,6,4,5,2,3]=>[.,[[[[.,[.,.]],[.,.]],.],.]] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[7,1,4,6,5,2,3]=>[[.,[[.,[.,.]],[[.,.],.]]],.] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[1,7,4,6,5,2,3]=>[.,[[[.,[.,.]],[[.,.],.]],.]] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[1,4,7,6,5,2,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[1,4,6,7,5,2,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[7,1,4,5,6,2,3]=>[[.,[[.,[.,.]],[.,[.,.]]]],.] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[1,7,4,5,6,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],.]] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[1,4,7,5,6,2,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[1,4,5,7,6,2,3]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>[[[[.,[.,[[.,.],.]]],.],.],.] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[6,7,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[7,5,6,1,2,4,3]=>[[[.,[.,[[.,.],.]]],[.,.]],.] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[5,7,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[5,6,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>[[[.,[[.,[[.,.],.]],.]],.],.] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[6,7,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],[.,.]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>[[.,[[[.,[[.,.],.]],.],.]],.] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>[.,[[[[.,[[.,.],.]],.],.],.]] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[1,6,7,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],[.,.]]] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[7,1,5,6,2,4,3]=>[[.,[[.,[[.,.],.]],[.,.]]],.] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[1,7,5,6,2,4,3]=>[.,[[[.,[[.,.],.]],[.,.]],.]] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[1,5,7,6,2,4,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[1,5,6,7,2,4,3]=>[.,[[.,[[.,.],.]],[.,[.,.]]]] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>[[[.,[.,[[[.,.],.],.]]],.],.] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[6,7,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>[[.,[[.,[[[.,.],.],.]],.]],.] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>[.,[[[.,[[[.,.],.],.]],.],.]] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[1,6,7,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],[.,.]]] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>[[.,[.,[[[[.,.],.],.],.]]],.] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>[.,[[.,[[[[.,.],.],.],.]],.]] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[1,2,6,7,5,4,3]=>[.,[.,[[[[.,.],.],.],[.,.]]]] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[7,1,2,5,6,4,3]=>[[.,[.,[[[.,.],.],[.,.]]]],.] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[1,7,2,5,6,4,3]=>[.,[[.,[[[.,.],.],[.,.]]],.]] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[1,2,7,5,6,4,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[1,2,5,7,6,4,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[1,2,5,6,7,4,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[7,6,1,2,4,5,3]=>[[[.,[.,[[.,.],[.,.]]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[6,7,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[7,1,6,2,4,5,3]=>[[.,[[.,[[.,.],[.,.]]],.]],.] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[1,7,6,2,4,5,3]=>[.,[[[.,[[.,.],[.,.]]],.],.]] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[1,6,7,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[7,1,2,6,4,5,3]=>[[.,[.,[[[.,.],[.,.]],.]]],.] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[1,7,2,6,4,5,3]=>[.,[[.,[[[.,.],[.,.]],.]],.]] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[1,2,7,6,4,5,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[1,2,6,7,4,5,3]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[7,1,2,4,6,5,3]=>[[.,[.,[[.,.],[[.,.],.]]]],.] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[1,7,2,4,6,5,3]=>[.,[[.,[[.,.],[[.,.],.]]],.]] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[1,2,7,4,6,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[1,2,4,7,6,5,3]=>[.,[.,[[.,.],[[[.,.],.],.]]]] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[1,2,4,6,7,5,3]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[7,1,2,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[1,7,2,4,5,6,3]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[1,2,4,7,5,6,3]=>[.,[.,[[.,.],[[.,[.,.]],.]]]] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[5,7,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>[[[.,[[.,[.,[.,.]]],.]],.],.] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[6,7,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>[[.,[[[.,[.,[.,.]]],.],.]],.] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>[.,[[[[.,[.,[.,.]]],.],.],.]] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[1,6,7,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,.]]] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[7,1,5,6,2,3,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],.] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[1,7,5,6,2,3,4]=>[.,[[[.,[.,[.,.]]],[.,.]],.]] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[1,5,7,6,2,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>[[[.,[.,[[.,[.,.]],.]]],.],.] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[6,7,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>[[.,[[.,[[.,[.,.]],.]],.]],.] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>[.,[[[.,[[.,[.,.]],.]],.],.]] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[1,6,7,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>[[.,[.,[[[.,[.,.]],.],.]]],.] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>[.,[[.,[[[.,[.,.]],.],.]],.]] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>[.,[.,[[[[.,[.,.]],.],.],.]]] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[7,1,2,5,6,3,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],.] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[1,7,2,5,6,3,4]=>[.,[[.,[[.,[.,.]],[.,.]]],.]] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[1,2,7,5,6,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],.]]] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[1,2,5,7,6,3,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[1,2,5,6,7,3,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>[[[.,[.,[.,[[.,.],.]]]],.],.] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[6,7,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>[[.,[[.,[.,[[.,.],.]]],.]],.] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>[.,[[[.,[.,[[.,.],.]]],.],.]] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],[.,.]]] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>[[.,[.,[[.,[[.,.],.]],.]]],.] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>[.,[[.,[[.,[[.,.],.]],.]],.]] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>[.,[.,[[[.,[[.,.],.]],.],.]]] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[1,2,6,7,3,5,4]=>[.,[.,[[.,[[.,.],.]],[.,.]]]] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>[[.,[.,[.,[[[.,.],.],.]]]],.] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>[.,[[.,[.,[[[.,.],.],.]]],.]] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>[.,[.,[[.,[[[.,.],.],.]],.]]] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[7,1,2,3,5,6,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],.] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[1,7,2,3,5,6,4]=>[.,[[.,[.,[[.,.],[.,.]]]],.]] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[1,2,7,3,5,6,4]=>[.,[.,[[.,[[.,.],[.,.]]],.]]] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],.]],.] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>[.,[[[.,[.,[.,[.,.]]]],.],.]] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>[[.,[.,[[.,[.,[.,.]]],.]]],.] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>[.,[[.,[[.,[.,[.,.]]],.]],.]] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>[.,[.,[[[.,[.,[.,.]]],.],.]]] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[1,2,6,7,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>[[.,[.,[.,[[.,[.,.]],.]]]],.] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>[.,[[.,[.,[[.,[.,.]],.]]],.]] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>[.,[.,[[.,[[.,[.,.]],.]],.]]] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],.]]]] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],.] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>[.,[[.,[.,[.,[[.,.],.]]]],.]] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,[.,[[.,.],.]]],.]]] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,[[.,.],.]],.]]]] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.] [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.] [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.] [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.] [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[3,4,5,6,7,8,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]] [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[5,8,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[5,7,8,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[5,6,8,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[7,8,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
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.