Identifier
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.] [1,0,1,0]=>[2,1]=>[2,1]=>[[.,.],.] [1,1,0,0]=>[1,2]=>[1,2]=>[.,[.,.]] [1,0,1,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]] [1,0,1,1,0,0]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.] [1,1,0,0,1,0]=>[3,1,2]=>[3,1,2]=>[[.,[.,.]],.] [1,1,0,1,0,0]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]] [1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,0,1,0,1,0]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]] [1,0,1,0,1,1,0,0]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],[.,.]],.] [1,0,1,1,0,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [1,0,1,1,0,1,0,0]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [1,1,0,0,1,0,1,0]=>[3,1,4,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]] [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[4,1,3,2]=>[[.,[[.,.],.]],.] [1,1,0,1,0,0,1,0]=>[3,1,2,4]=>[3,1,2,4]=>[[.,[.,.]],[.,.]] [1,1,0,1,0,1,0,0]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]] [1,1,0,1,1,0,0,0]=>[1,3,4,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]] [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[4,1,2,3]=>[[.,[.,[.,.]]],.] [1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[1,4,2,3]=>[.,[[.,[.,.]],.]] [1,1,1,0,1,0,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]] [1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]] [1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]] [1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]] [1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>[5,2,1,4,3]=>[[[.,.],[[.,.],.]],.] [1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>[2,1,5,3,4]=>[[.,.],[[.,[.,.]],.]] [1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.] [1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]] [1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]] [1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[5,2,3,1,4]=>[[[.,.],[.,[.,.]]],.] [1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]] [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.] [1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,[[.,.],.]],[.,.]] [1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]] [1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]] [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[[.,[[.,.],[.,.]]],.] [1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]=>[3,5,1,2,4]=>[[.,[.,.]],[[.,.],.]] [1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,[[.,.],[.,.]]],.] [1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>[3,1,2,5,4]=>[[.,[.,.]],[[.,.],.]] [1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]] [1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[1,5,3,2,4]=>[.,[[[.,.],[.,.]],.]] [1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]] [1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]] [1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]] [1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>[4,5,2,1,3]=>[[[.,.],[.,.]],[.,.]] [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.] [1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]=>[4,1,5,2,3]=>[[.,[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]] [1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]] [1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]] [1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]] [1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]] [1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]] [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.] [1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,4]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]] [1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]] [1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]] [1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>[[[.,.],[.,.]],[[.,.],.]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>[[.,.],[[[.,.],[.,.]],.]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>[4,2,6,1,3,5]=>[[[.,.],[.,.]],[[.,.],.]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],.] [1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[5,2,1,4,3,6]=>[[[.,.],[[.,.],.]],[.,.]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>[6,2,1,4,5,3]=>[[[.,.],[[.,.],[.,.]]],.] [1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[5,2,1,6,3,4]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>[[.,.],[[.,[[.,.],.]],.]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>[5,2,6,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[[[.,.],[.,[[.,.],.]]],.] [1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[[.,.],[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>[6,2,3,1,5,4]=>[[[.,.],[.,[[.,.],.]]],.] [1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.] [1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[[.,.],[.,[[.,[.,.]],.]]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>[[[.,.],.],[[.,[.,.]],.]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],.] [1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],.] [1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>[[.,[[.,.],.]],[[.,.],.]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>[3,6,1,4,2,5]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>[4,6,3,1,2,5]=>[[[.,[.,.]],.],[[.,.],.]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,[[.,.],.]],[.,[.,.]]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>[5,1,3,6,2,4]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>[3,6,1,2,5,4]=>[[.,[.,.]],[[[.,.],.],.]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>[5,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[[.,[[.,.],[[.,.],.]]],.] [1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>[3,5,1,2,4,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>[.,[[[.,.],[.,.]],[.,.]]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[.,[[[.,.],[.,.]],[.,.]]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>[1,6,3,2,5,4]=>[.,[[[.,.],[[.,.],.]],.]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[3,6,1,2,4,5]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[.,[[.,.],[[.,[.,.]],.]]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>[.,[[[.,.],[.,[.,.]]],.]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>[1,6,3,4,2,5]=>[.,[[[.,.],[.,[.,.]]],.]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>[5,1,6,4,2,3]=>[[.,[[.,[.,.]],.]],[.,.]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>[4,6,2,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>[5,6,2,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],.] [1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]=>[4,5,2,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,[.,[[.,.],.]]],[.,.]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[4,1,5,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[1,5,2,4,3,6]=>[.,[[.,[[.,.],.]],[.,.]]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>[4,1,6,2,5,3]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[.,[[.,[.,.]],[[.,.],.]]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>[1,6,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],.]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>[4,6,2,1,3,5]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],.] [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>[4,1,6,2,3,5]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>[1,4,6,2,3,5]=>[.,[[.,[.,.]],[[.,.],.]]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>[1,6,2,4,3,5]=>[.,[[.,[[.,.],[.,.]]],.]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[.,[[.,[.,.]],[[.,.],.]]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>[.,[.,[[[.,.],[.,.]],.]]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>[5,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.] [1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]=>[5,1,6,3,2,4]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>[1,5,6,3,2,4]=>[.,[[[.,.],[.,.]],[.,.]]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>[1,6,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],.]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>[5,1,2,6,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>[1,5,2,6,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>[1,2,6,3,5,4]=>[.,[.,[[.,[[.,.],.]],.]]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]=>[4,2,6,1,3,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[2,1,6,4,7,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>[4,2,6,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>[6,2,1,4,7,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>[2,1,7,4,3,6,5]=>[[.,.],[[[.,.],[[.,.],.]],.]] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>[4,2,7,1,3,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[6,2,7,4,3,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[7,2,1,4,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],.] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]=>[4,2,7,1,3,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>[4,2,5,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>[5,2,1,4,3,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>[2,1,7,4,5,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>[4,2,7,1,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>[5,2,7,4,1,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[7,2,1,4,5,3,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>[5,2,1,4,3,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>[4,2,6,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>[5,2,6,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>[6,2,1,4,5,3,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>[4,2,7,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>[5,2,7,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>[6,2,7,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]=>[7,2,1,4,5,6,3]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[5,2,1,6,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]=>[2,1,6,3,5,4,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>[5,2,6,3,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[2,1,5,7,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]=>[5,2,1,7,3,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[2,1,6,7,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>[6,2,1,7,5,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>[2,1,7,3,5,6,4]=>[[.,.],[[.,[[.,.],[.,.]]],.]] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]=>[5,2,7,3,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[6,2,7,3,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[7,2,1,3,5,6,4]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>[2,1,5,7,3,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>[5,2,1,7,3,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>[2,1,7,3,5,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],.]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>[5,2,7,3,1,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>[5,2,3,1,4,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>[5,2,3,7,1,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[7,2,3,1,5,4,6]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>[5,2,3,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>[6,2,3,1,5,4,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>[5,2,3,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>[6,2,3,7,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>[7,2,3,1,5,6,4]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>[2,1,6,7,4,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>[6,2,1,7,4,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>[2,1,7,3,4,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],.]] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]=>[6,2,7,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>[2,1,6,3,7,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[6,2,1,3,7,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>[3,2,1,6,7,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>[6,2,3,1,7,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>[2,1,3,7,4,6,5]=>[[.,.],[.,[[.,[[.,.],.]],.]]] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>[3,2,1,7,4,6,5]=>[[[.,.],.],[[.,[[.,.],.]],.]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[6,2,3,7,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[7,2,3,1,4,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>[6,2,3,4,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>[7,2,3,4,1,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>[4,2,3,1,7,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[4,1,3,2,6,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>[3,6,1,4,2,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]=>[4,6,3,1,2,5,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[3,4,1,2,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]=>[4,1,3,2,7,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[3,6,1,4,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>[4,6,3,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]=>[6,1,3,4,7,2,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>[3,7,1,4,2,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>[4,7,3,1,2,6,5]=>[[[.,[.,.]],.],[[[.,.],.],.]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[6,7,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[7,1,3,4,2,6,5]=>[[.,[[.,.],[.,[[.,.],.]]]],.] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]=>[3,4,1,2,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]=>[4,1,3,2,7,5,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>[3,7,1,4,2,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]=>[4,7,3,1,2,5,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[4,1,3,2,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[3,5,1,4,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>[4,5,3,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>[5,1,3,4,2,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[3,7,1,4,5,2,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>[4,7,3,1,5,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>[5,7,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[7,1,3,4,5,2,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>[3,5,1,4,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]=>[3,6,1,4,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>[4,6,3,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>[3,7,1,4,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]=>[4,7,3,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]=>[5,7,3,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7]=>[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[5,1,3,6,2,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>[3,6,1,2,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>[5,6,3,2,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[3,5,1,7,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>[5,1,3,7,2,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[3,6,1,7,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>[5,6,3,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>[6,1,3,7,5,2,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>[3,7,1,2,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>[5,7,3,2,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[6,7,3,2,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[7,1,3,2,5,6,4]=>[[.,[[.,.],[[.,.],[.,.]]]],.] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>[3,5,1,7,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>[5,1,3,7,2,4,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>[3,7,1,2,5,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>[5,7,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],.] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>[3,5,1,2,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[5,1,3,2,4,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]=>[.,[[.,.],[[[.,.],[.,.]],.]]] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>[1,5,3,7,2,4,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[1,7,3,2,5,4,6]=>[.,[[[.,.],[[.,.],[.,.]]],.]] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[3,5,1,2,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>[1,6,3,2,5,4,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>[3,1,2,7,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>[1,7,3,2,5,6,4]=>[.,[[[.,.],[[.,.],[.,.]]],.]] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>[3,6,1,7,4,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>[6,1,3,7,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>[3,7,1,2,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>[6,7,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>[[.,[[.,.],[.,[[.,.],.]]]],.] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>[3,6,1,2,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>[6,1,3,2,7,4,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[3,1,2,6,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>[1,6,3,2,7,4,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>[3,1,2,7,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>[1,3,2,7,4,6,5]=>[.,[[.,.],[[.,[[.,.],.]],.]]] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[1,6,3,7,4,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[1,7,3,2,4,6,5]=>[.,[[[.,.],[.,[[.,.],.]]],.]] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>[3,6,1,2,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>[1,6,3,4,2,5,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>[1,7,3,4,2,6,5]=>[.,[[[.,.],[.,[[.,.],.]]],.]] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],.]]] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]=>[.,[[[.,.],.],[[.,[.,.]],.]]] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[1,7,3,4,2,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>[1,7,3,4,5,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[5,1,6,4,2,3,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]=>[4,6,2,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>[5,6,2,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[4,5,7,1,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>[5,1,7,4,2,6,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[4,6,7,1,5,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>[6,1,7,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>[4,7,2,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>[5,7,2,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[6,7,2,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]=>[5,1,7,4,2,3,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>[4,7,2,1,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>[5,7,2,4,1,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>[4,5,2,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[5,1,2,4,3,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[4,1,5,2,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>[1,5,2,4,3,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[4,1,7,2,5,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>[1,4,7,2,5,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>[1,5,7,4,2,3,6]=>[.,[[[.,[.,.]],.],[[.,.],.]]] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[1,7,2,4,5,3,6]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[4,5,2,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>[4,1,5,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>[1,5,2,4,3,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>[4,1,6,2,5,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>[1,6,2,4,5,3,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]=>[4,1,7,2,5,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>[1,7,2,4,5,6,3]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>[4,6,7,1,3,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>[6,1,7,4,3,2,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]=>[4,7,2,1,3,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>[6,7,2,4,3,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>[[.,[.,[[.,.],[[.,.],.]]]],.] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>[4,6,2,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>[6,1,2,4,7,3,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[4,1,6,2,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>[1,6,2,4,7,3,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]=>[4,1,7,2,3,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>[1,4,7,2,3,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[1,6,7,4,3,2,5]=>[.,[[[[.,.],.],[.,.]],[.,.]]] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[1,7,2,4,3,6,5]=>[.,[[.,[[.,.],[[.,.],.]]],.]] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>[4,6,2,1,3,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>[4,1,6,2,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>[1,4,6,2,3,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>[1,2,7,4,3,6,5]=>[.,[.,[[[.,.],[[.,.],.]],.]]] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>[4,7,2,1,3,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>[4,1,7,2,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>[1,4,7,2,3,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>[1,7,2,4,3,5,6]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>[.,[.,[[.,.],[[.,[.,.]],.]]]] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>[1,2,7,4,5,3,6]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]=>[5,6,7,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>[6,1,7,3,5,2,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]=>[5,7,2,3,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>[6,7,2,3,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],.] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4]=>[5,6,2,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>[6,1,2,7,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[5,1,6,7,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>[1,6,2,7,5,3,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>[5,1,7,3,2,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>[1,5,7,3,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[1,6,7,3,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[1,7,2,3,5,6,4]=>[.,[[.,[.,[[.,.],[.,.]]]],.]] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>[5,6,2,3,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>[5,1,6,3,2,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>[1,5,6,3,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>[1,6,2,3,5,4,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>[5,1,2,6,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>[1,5,2,6,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>[1,2,6,3,5,4,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>[5,1,2,7,3,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]=>[1,5,2,7,3,6,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>[1,2,7,3,5,6,4]=>[.,[.,[[.,[[.,.],[.,.]]],.]]] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>[5,7,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>[[.,[.,[.,[[.,.],[.,.]]]]],.] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>[5,1,7,3,2,4,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>[1,5,7,3,2,4,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>[1,7,2,3,5,4,6]=>[.,[[.,[.,[[.,.],[.,.]]]],.]] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>[5,1,2,7,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[1,5,2,7,3,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>[1,2,5,7,3,4,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[1,2,7,3,5,4,6]=>[.,[.,[[.,[[.,.],[.,.]]],.]]] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]=>[.,[.,[.,[[[.,.],[.,.]],.]]]] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]=>[6,7,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],.] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5]=>[6,1,7,3,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>[1,6,7,3,4,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>[1,7,2,3,4,6,5]=>[.,[[.,[.,[.,[[.,.],.]]]],.]] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>[6,1,2,7,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[1,6,2,7,4,3,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[1,2,6,7,4,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,[.,[[.,.],.]]],.]]] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[6,1,2,3,7,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[1,6,2,3,7,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>[1,2,6,3,7,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,[[.,.],.]],.]]]] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,8,4]=>[5,2,3,8,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]] [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,2]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5]=>[3,6,1,7,8,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]] [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7]=>[4,5,6,1,2,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6]=>[4,5,7,1,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5]=>[4,6,7,1,8,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,3,8,4,6,7]=>[5,1,2,8,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
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.