Identifier
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-4
[1,0]=>[1]=>[1]=>[1]=>[.,.] [1,0,1,0]=>[2,1]=>[1,2]=>[2,1]=>[[.,.],.] [1,1,0,0]=>[1,2]=>[2,1]=>[1,2]=>[.,[.,.]] [1,0,1,0,1,0]=>[3,2,1]=>[1,2,3]=>[3,2,1]=>[[[.,.],.],.] [1,0,1,1,0,0]=>[2,3,1]=>[1,3,2]=>[3,1,2]=>[[.,.],[.,.]] [1,1,0,0,1,0]=>[3,1,2]=>[2,1,3]=>[2,3,1]=>[[.,[.,.]],.] [1,1,0,1,0,0]=>[2,1,3]=>[3,1,2]=>[1,3,2]=>[.,[[.,.],.]] [1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[1,2,3,4]=>[4,3,2,1]=>[[[[.,.],.],.],.] [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[1,2,4,3]=>[4,3,1,2]=>[[[.,.],.],[.,.]] [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[1,3,2,4]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[1,4,2,3]=>[4,1,3,2]=>[[.,.],[[.,.],.]] [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[1,4,3,2]=>[4,1,2,3]=>[[.,.],[.,[.,.]]] [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[2,1,3,4]=>[3,4,2,1]=>[[[.,[.,.]],.],.] [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,1,4,3]=>[3,4,1,2]=>[[.,[.,.]],[.,.]] [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[3,1,2,4]=>[2,4,3,1]=>[[.,[[.,.],.]],.] [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[4,1,2,3]=>[1,4,3,2]=>[.,[[[.,.],.],.]] [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[4,1,3,2]=>[1,4,2,3]=>[.,[[.,.],[.,.]]] [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[3,2,1,4]=>[2,3,4,1]=>[[.,[.,[.,.]]],.] [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[4,2,1,3]=>[1,3,4,2]=>[.,[[.,[.,.]],.]] [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[4,3,1,2]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]] [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.] [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[[[.,.],.],[[.,.],.]] [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.] [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[1,3,2,5,4]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]] [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.] [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]] [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[5,1,4,2,3]=>[[.,.],[[.,.],[.,.]]] [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.] [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[1,5,3,2,4]=>[5,1,3,4,2]=>[[.,.],[[.,[.,.]],.]] [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]] [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.] [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]] [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.] [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[2,1,5,3,4]=>[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]] [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[2,1,5,4,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.] [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[3,1,2,5,4]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]] [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.] [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]] [1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[5,1,2,4,3]=>[1,5,4,2,3]=>[.,[[[.,.],.],[.,.]]] [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[4,1,3,2,5]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.] [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[5,1,3,2,4]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]] [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[5,1,4,2,3]=>[1,5,2,4,3]=>[.,[[.,.],[[.,.],.]]] [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.] [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[3,2,1,5,4]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.] [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[.,[[[.,[.,.]],.],.]] [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[5,2,1,4,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]] [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.] [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]] [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]] [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]] [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[4,3,2,1,5]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.] [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[5,3,2,1,4]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]] [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[5,4,2,1,3]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]] [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.] [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[[[[.,.],.],.],[[.,.],.]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[[[[.,.],.],[.,.]],[.,.]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[[[[.,.],.],[[.,.],.]],.] [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[[[.,.],.],[[[.,.],.],.]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[[[.,.],.],[[.,[.,.]],.]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[[[.,.],.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.] [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[[[[.,.],[.,.]],.],[.,.]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[[[.,.],[.,.]],[[.,.],.]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[[[[.,.],[[.,.],.]],.],.] [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[[[.,.],[[.,.],.]],[.,.]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.] [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[[.,.],[[[[.,.],.],.],.]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[[.,.],[[[.,.],.],[.,.]]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[[[.,.],[[.,.],[.,.]]],.] [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[[.,.],[[[.,.],[.,.]],.]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[[.,.],[[.,.],[[.,.],.]]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[[[.,.],[[.,[.,.]],.]],.] [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[[.,.],[[[.,[.,.]],.],.]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>[[.,.],[[.,[.,.]],[.,.]]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.] [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[[.,.],[[.,[[.,.],.]],.]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>[[.,.],[.,[[.,.],[.,.]]]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>[[.,.],[[.,[.,[.,.]]],.]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.] [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[[[[.,[.,.]],.],[.,.]],.] [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[[[.,[.,.]],.],[[.,.],.]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[[[[.,[.,.]],[.,.]],.],.] [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[[[.,[.,.]],[[.,.],.]],.] [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[[.,[.,.]],[[[.,.],.],.]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[[[.,[.,.]],[.,[.,.]]],.] [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[[[[.,[[.,.],.]],.],.],.] [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[[[.,[[.,.],.]],.],[.,.]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[[[.,[[.,.],.]],[.,.]],.] [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>[[.,[[.,.],.]],[.,[.,.]]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[[[.,[[[.,.],.],.]],.],.] [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>[[.,[[[.,.],.],.]],[.,.]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[[.,[[[[.,.],.],.],.]],.] [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>[1,6,5,4,2,3]=>[.,[[[[.,.],.],.],[.,.]]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>[2,6,5,3,4,1]=>[[.,[[[.,.],.],[.,.]]],.] [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>[.,[[[[.,.],.],[.,.]],.]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[1,6,5,2,4,3]=>[.,[[[.,.],.],[[.,.],.]]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[1,6,5,2,3,4]=>[.,[[[.,.],.],[.,[.,.]]]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>[[[.,[[.,.],[.,.]]],.],.] [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>[3,6,4,5,1,2]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>[2,6,4,5,3,1]=>[[.,[[[.,.],[.,.]],.]],.] [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>[1,6,4,5,3,2]=>[.,[[[[.,.],[.,.]],.],.]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>[.,[[[.,.],[.,.]],[.,.]]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>[2,6,3,5,4,1]=>[[.,[[.,.],[[.,.],.]]],.] [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>[.,[[.,.],[[[.,.],.],.]]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[1,6,2,5,3,4]=>[.,[[.,.],[[.,.],[.,.]]]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[2,6,3,4,5,1]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>[1,6,2,4,5,3]=>[.,[[.,.],[[.,[.,.]],.]]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[1,6,2,3,5,4]=>[.,[[.,.],[.,[[.,.],.]]]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[1,6,2,3,4,5]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.] [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[[[.,[.,[.,.]]],.],[.,.]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[[[.,[.,[.,.]]],[.,.]],.] [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[[[.,[[.,[.,.]],.]],.],.] [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>[3,5,6,4,1,2]=>[[.,[[.,[.,.]],.]],[.,.]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[[.,[[[.,[.,.]],.],.]],.] [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[.,[[[[.,[.,.]],.],.],.]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>[2,5,6,3,4,1]=>[[.,[[.,[.,.]],[.,.]]],.] [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>[1,5,6,3,4,2]=>[.,[[[.,[.,.]],[.,.]],.]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>[1,5,6,2,4,3]=>[.,[[.,[.,.]],[[.,.],.]]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>[1,5,6,2,3,4]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[[[.,[.,[[.,.],.]]],.],.] [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>[3,4,6,5,1,2]=>[[.,[.,[[.,.],.]]],[.,.]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[[.,[[.,[[.,.],.]],.]],.] [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[.,[[[.,[[.,.],.]],.],.]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>[1,4,6,5,2,3]=>[.,[[.,[[.,.],.]],[.,.]]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.] [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[.,[[.,[[[.,.],.],.]],.]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[1,2,6,5,3,4]=>[.,[.,[[[.,.],.],[.,.]]]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>[2,3,6,4,5,1]=>[[.,[.,[[.,.],[.,.]]]],.] [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>[1,3,6,4,5,2]=>[.,[[.,[[.,.],[.,.]]],.]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[1,2,6,3,5,4]=>[.,[.,[[.,.],[[.,.],.]]]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[1,2,6,3,4,5]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.] [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>[[.,[[.,[.,[.,.]]],.]],.] [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>[.,[[[.,[.,[.,.]]],.],.]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>[1,4,5,6,2,3]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>[[.,[.,[[.,[.,.]],.]]],.] [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>[.,[[.,[[.,[.,.]],.]],.]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[.,[.,[[[.,[.,.]],.],.]]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.] [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[.,[[.,[.,[[.,.],.]]],.]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[.,[.,[[.,[[.,.],.]],.]]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[[[[.,.],.],[[.,.],[.,.]]],.] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[[[.,.],.],[[[.,.],[.,.]],.]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[[[.,.],.],[[[.,[.,.]],.],.]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[[[.,.],.],[[.,[[.,.],.]],.]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[[[[.,.],[.,.]],.],[[.,.],.]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[[[[[.,.],[[.,.],.]],.],.],.] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[[[[.,.],[[.,.],.]],.],[.,.]] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[[[.,.],[[[.,.],.],.]],[.,.]] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[[[.,.],[[[.,.],.],[.,.]]],.] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[[.,.],[[[[.,.],.],[.,.]],.]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[[[.,.],[[.,.],[[.,.],.]]],.] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[[[.,.],[[.,[.,.]],.]],[.,.]] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[[[.,.],[[[.,[.,.]],.],.]],.] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[[.,.],[[[[.,[.,.]],.],.],.]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[[[.,.],[[.,[[.,.],.]],.]],.] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[[.,.],[[[.,[[.,.],.]],.],.]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[[.,.],[[.,[[.,.],.]],[.,.]]] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[[.,.],[[.,[[[.,.],.],.]],.]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[[.,.],[[.,[[.,[.,.]],.]],.]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[[.,.],[.,[[.,[[.,.],.]],.]]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>[6,7,5,4,2,3,1]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>[6,7,5,4,1,3,2]=>[[[[.,[.,.]],.],.],[[.,.],.]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>[6,7,5,4,1,2,3]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>[6,7,5,3,4,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>[6,7,5,2,4,3,1]=>[[[[.,[.,.]],.],[[.,.],.]],.] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>[6,7,5,1,4,3,2]=>[[[.,[.,.]],.],[[[.,.],.],.]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>[6,7,5,1,4,2,3]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>[6,7,5,2,3,4,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>[6,7,5,1,3,4,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>[6,7,5,1,2,4,3]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>[6,7,5,1,2,3,4]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>[6,7,4,5,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>[6,7,4,5,2,3,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>[6,7,4,5,1,3,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>[6,7,4,5,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>[6,7,3,5,4,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>[6,7,2,5,4,3,1]=>[[[.,[.,.]],[[[.,.],.],.]],.] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>[6,7,1,5,4,3,2]=>[[.,[.,.]],[[[[.,.],.],.],.]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>[6,7,1,5,4,2,3]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>[6,7,2,5,3,4,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>[6,7,1,5,3,4,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>[6,7,1,5,2,4,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>[6,7,1,5,2,3,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>[6,7,3,4,5,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>[6,7,2,4,5,3,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>[6,7,1,4,5,3,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>[6,7,1,4,5,2,3]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>[6,7,2,3,5,4,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>[6,7,1,3,5,4,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>[6,7,1,2,5,4,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>[6,7,1,2,5,3,4]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>[6,7,2,3,4,5,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>[6,7,1,3,4,5,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>[6,7,1,2,4,5,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>[6,7,1,2,3,5,4]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>[[[[[.,[[.,.],.]],.],.],.],.] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>[5,7,6,4,3,1,2]=>[[[[.,[[.,.],.]],.],.],[.,.]] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>[5,7,6,4,2,3,1]=>[[[[.,[[.,.],.]],.],[.,.]],.] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>[5,7,6,4,1,2,3]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>[5,7,6,3,4,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>[5,7,6,3,4,1,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>[5,7,6,2,4,3,1]=>[[[.,[[.,.],.]],[[.,.],.]],.] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>[5,7,6,1,4,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>[5,7,6,1,4,2,3]=>[[.,[[.,.],.]],[[.,.],[.,.]]] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>[5,7,6,2,3,4,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>[5,7,6,1,3,4,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>[5,7,6,1,2,4,3]=>[[.,[[.,.],.]],[.,[[.,.],.]]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>[5,7,6,1,2,3,4]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>[[[[.,[[[.,.],.],.]],.],.],.] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>[4,7,6,5,3,1,2]=>[[[.,[[[.,.],.],.]],.],[.,.]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>[4,7,6,5,2,3,1]=>[[[.,[[[.,.],.],.]],[.,.]],.] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>[4,7,6,5,1,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>[4,7,6,5,1,2,3]=>[[.,[[[.,.],.],.]],[.,[.,.]]] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>[[[.,[[[[.,.],.],.],.]],.],.] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>[3,7,6,5,4,1,2]=>[[.,[[[[.,.],.],.],.]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>[[.,[[[[[.,.],.],.],.],.]],.] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>[1,7,6,5,4,2,3]=>[.,[[[[[.,.],.],.],.],[.,.]]] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>[2,7,6,5,3,4,1]=>[[.,[[[[.,.],.],.],[.,.]]],.] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>[1,7,6,5,3,4,2]=>[.,[[[[[.,.],.],.],[.,.]],.]] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>[1,7,6,5,2,4,3]=>[.,[[[[.,.],.],.],[[.,.],.]]] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>[1,7,6,5,2,3,4]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>[3,7,6,4,5,2,1]=>[[[.,[[[.,.],.],[.,.]]],.],.] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>[3,7,6,4,5,1,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>[2,7,6,4,5,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>[1,7,6,4,5,2,3]=>[.,[[[[.,.],.],[.,.]],[.,.]]] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>[2,7,6,3,5,4,1]=>[[.,[[[.,.],.],[[.,.],.]]],.] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>[.,[[[[.,.],.],[[.,.],.]],.]] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>[1,7,6,2,5,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>[1,7,6,2,5,3,4]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>[2,7,6,3,4,5,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>[1,7,6,3,4,5,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>[1,7,6,2,4,5,3]=>[.,[[[.,.],.],[[.,[.,.]],.]]] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>[1,7,6,2,3,5,4]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>[1,7,6,2,3,4,5]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>[4,7,5,6,3,2,1]=>[[[[.,[[.,.],[.,.]]],.],.],.] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>[4,7,5,6,3,1,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>[4,7,5,6,2,3,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>[4,7,5,6,1,3,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>[4,7,5,6,1,2,3]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>[3,7,5,6,4,2,1]=>[[[.,[[[.,.],[.,.]],.]],.],.] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>[3,7,5,6,4,1,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>[2,7,5,6,4,3,1]=>[[.,[[[[.,.],[.,.]],.],.]],.] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>[1,7,5,6,4,3,2]=>[.,[[[[[.,.],[.,.]],.],.],.]] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>[.,[[[[.,.],[.,.]],.],[.,.]]] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>[2,7,5,6,3,4,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>[1,7,5,6,3,4,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>[1,7,5,6,2,4,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>[1,7,5,6,2,3,4]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>[3,7,4,6,5,2,1]=>[[[.,[[.,.],[[.,.],.]]],.],.] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>[3,7,4,6,5,1,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>[2,7,4,6,5,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>[1,7,4,6,5,3,2]=>[.,[[[[.,.],[[.,.],.]],.],.]] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>[1,7,4,6,5,2,3]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>[2,7,3,6,5,4,1]=>[[.,[[.,.],[[[.,.],.],.]]],.] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>[1,7,3,6,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>[.,[[.,.],[[[[.,.],.],.],.]]] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>[1,7,2,6,5,3,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>[2,7,3,6,4,5,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>[1,7,3,6,4,5,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>[1,7,2,6,4,5,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>[1,7,2,6,3,4,5]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>[3,7,4,5,6,2,1]=>[[[.,[[.,.],[.,[.,.]]]],.],.] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>[3,7,4,5,6,1,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>[2,7,4,5,6,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>[1,7,4,5,6,3,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>[1,7,4,5,6,2,3]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>[2,7,3,5,6,4,1]=>[[.,[[.,.],[[.,[.,.]],.]]],.] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>[1,7,3,5,6,4,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>[1,7,2,5,6,4,3]=>[.,[[.,.],[[[.,[.,.]],.],.]]] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>[1,7,2,5,6,3,4]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>[2,7,3,4,6,5,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>[1,7,3,4,6,5,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>[.,[[.,.],[[.,[[.,.],.]],.]]] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>[1,7,2,3,6,5,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>[1,7,2,3,6,4,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>[2,7,3,4,5,6,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>[1,7,2,4,5,6,3]=>[.,[[.,.],[[.,[.,[.,.]]],.]]] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>[1,7,2,3,5,6,4]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>[1,7,2,3,4,6,5]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>[5,6,7,4,3,1,2]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>[5,6,7,4,2,3,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>[5,6,7,4,1,3,2]=>[[[.,[.,[.,.]]],.],[[.,.],.]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>[5,6,7,3,4,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>[5,6,7,3,4,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>[5,6,7,2,4,3,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>[5,6,7,1,4,3,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>[5,6,7,1,4,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>[5,6,7,2,3,4,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>[5,6,7,1,3,4,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>[5,6,7,1,2,4,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>[[[[.,[[.,[.,.]],.]],.],.],.] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>[4,6,7,5,3,1,2]=>[[[.,[[.,[.,.]],.]],.],[.,.]] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>[4,6,7,5,2,3,1]=>[[[.,[[.,[.,.]],.]],[.,.]],.] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>[4,6,7,5,1,3,2]=>[[.,[[.,[.,.]],.]],[[.,.],.]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>[4,6,7,5,1,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>[[[.,[[[.,[.,.]],.],.]],.],.] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>[3,6,7,5,4,1,2]=>[[.,[[[.,[.,.]],.],.]],[.,.]] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>[[.,[[[[.,[.,.]],.],.],.]],.] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>[.,[[[[[.,[.,.]],.],.],.],.]] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>[1,6,7,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>[2,6,7,5,3,4,1]=>[[.,[[[.,[.,.]],.],[.,.]]],.] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>[1,6,7,5,3,4,2]=>[.,[[[[.,[.,.]],.],[.,.]],.]] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>[1,6,7,5,2,4,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>[1,6,7,5,2,3,4]=>[.,[[[.,[.,.]],.],[.,[.,.]]]] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>[3,6,7,4,5,2,1]=>[[[.,[[.,[.,.]],[.,.]]],.],.] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>[3,6,7,4,5,1,2]=>[[.,[[.,[.,.]],[.,.]]],[.,.]] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>[2,6,7,4,5,3,1]=>[[.,[[[.,[.,.]],[.,.]],.]],.] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>[1,6,7,4,5,3,2]=>[.,[[[[.,[.,.]],[.,.]],.],.]] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>[2,6,7,3,5,4,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>[1,6,7,3,5,4,2]=>[.,[[[.,[.,.]],[[.,.],.]],.]] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>[1,6,7,2,5,4,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>[1,6,7,2,5,3,4]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>[2,6,7,3,4,5,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>[1,6,7,3,4,5,2]=>[.,[[[.,[.,.]],[.,[.,.]]],.]] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>[1,6,7,2,4,5,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>[1,6,7,2,3,5,4]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>[1,6,7,2,3,4,5]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>[[[[.,[.,[[.,.],.]]],.],.],.] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>[4,5,7,6,3,1,2]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>[4,5,7,6,2,3,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>[4,5,7,6,1,3,2]=>[[.,[.,[[.,.],.]]],[[.,.],.]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>[4,5,7,6,1,2,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>[[[.,[[.,[[.,.],.]],.]],.],.] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>[3,5,7,6,4,1,2]=>[[.,[[.,[[.,.],.]],.]],[.,.]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>[[.,[[[.,[[.,.],.]],.],.]],.] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[.,[[[[.,[[.,.],.]],.],.],.]] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>[1,5,7,6,4,2,3]=>[.,[[[.,[[.,.],.]],.],[.,.]]] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>[2,5,7,6,3,4,1]=>[[.,[[.,[[.,.],.]],[.,.]]],.] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>[1,5,7,6,3,4,2]=>[.,[[[.,[[.,.],.]],[.,.]],.]] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>[1,5,7,6,2,4,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>[1,5,7,6,2,3,4]=>[.,[[.,[[.,.],.]],[.,[.,.]]]] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>[[[.,[.,[[[.,.],.],.]]],.],.] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>[3,4,7,6,5,1,2]=>[[.,[.,[[[.,.],.],.]]],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>[[.,[[.,[[[.,.],.],.]],.]],.] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[.,[[[.,[[[.,.],.],.]],.],.]] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>[1,4,7,6,5,2,3]=>[.,[[.,[[[.,.],.],.]],[.,.]]] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>[[.,[.,[[[[.,.],.],.],.]]],.] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>[.,[[.,[[[[.,.],.],.],.]],.]] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>[1,2,7,6,5,3,4]=>[.,[.,[[[[.,.],.],.],[.,.]]]] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>[2,3,7,6,4,5,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>[1,3,7,6,4,5,2]=>[.,[[.,[[[.,.],.],[.,.]]],.]] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>[1,2,7,6,4,5,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>[1,2,7,6,3,5,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>[1,2,7,6,3,4,5]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>[3,4,7,5,6,2,1]=>[[[.,[.,[[.,.],[.,.]]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>[3,4,7,5,6,1,2]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>[2,4,7,5,6,3,1]=>[[.,[[.,[[.,.],[.,.]]],.]],.] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>[1,4,7,5,6,3,2]=>[.,[[[.,[[.,.],[.,.]]],.],.]] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>[1,4,7,5,6,2,3]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>[2,3,7,5,6,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>[1,3,7,5,6,4,2]=>[.,[[.,[[[.,.],[.,.]],.]],.]] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>[1,2,7,5,6,4,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>[1,2,7,5,6,3,4]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>[2,3,7,4,6,5,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>[1,3,7,4,6,5,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>[1,2,7,4,6,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>[1,2,7,3,6,5,4]=>[.,[.,[[.,.],[[[.,.],.],.]]]] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>[1,2,7,3,6,4,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>[2,3,7,4,5,6,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>[1,3,7,4,5,6,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>[1,2,7,3,5,6,4]=>[.,[.,[[.,.],[[.,[.,.]],.]]]] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>[4,5,6,7,3,1,2]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>[4,5,6,7,2,3,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>[4,5,6,7,1,3,2]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[[[.,[[.,[.,[.,.]]],.]],.],.] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>[3,5,6,7,4,1,2]=>[[.,[[.,[.,[.,.]]],.]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>[[.,[[[.,[.,[.,.]]],.],.]],.] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>[.,[[[[.,[.,[.,.]]],.],.],.]] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>[1,5,6,7,4,2,3]=>[.,[[[.,[.,[.,.]]],.],[.,.]]] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>[2,5,6,7,3,4,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>[1,5,6,7,3,4,2]=>[.,[[[.,[.,[.,.]]],[.,.]],.]] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>[1,5,6,7,2,4,3]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>[[[.,[.,[[.,[.,.]],.]]],.],.] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>[3,4,6,7,5,1,2]=>[[.,[.,[[.,[.,.]],.]]],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[[.,[[.,[[.,[.,.]],.]],.]],.] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>[.,[[[.,[[.,[.,.]],.]],.],.]] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>[1,4,6,7,5,2,3]=>[.,[[.,[[.,[.,.]],.]],[.,.]]] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[[.,[.,[[[.,[.,.]],.],.]]],.] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>[.,[[.,[[[.,[.,.]],.],.]],.]] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[.,[.,[[[[.,[.,.]],.],.],.]]] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>[2,3,6,7,4,5,1]=>[[.,[.,[[.,[.,.]],[.,.]]]],.] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>[1,3,6,7,4,5,2]=>[.,[[.,[[.,[.,.]],[.,.]]],.]] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>[1,2,6,7,4,5,3]=>[.,[.,[[[.,[.,.]],[.,.]],.]]] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>[[[.,[.,[.,[[.,.],.]]]],.],.] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>[3,4,5,7,6,1,2]=>[[.,[.,[.,[[.,.],.]]]],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>[[.,[[.,[.,[[.,.],.]]],.]],.] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[.,[[[.,[.,[[.,.],.]]],.],.]] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>[1,4,5,7,6,2,3]=>[.,[[.,[.,[[.,.],.]]],[.,.]]] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>[[.,[.,[[.,[[.,.],.]],.]]],.] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[.,[[.,[[.,[[.,.],.]],.]],.]] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>[.,[.,[[[.,[[.,.],.]],.],.]]] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>[1,2,5,7,6,3,4]=>[.,[.,[[.,[[.,.],.]],[.,.]]]] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[.,[[.,[.,[[[.,.],.],.]]],.]] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[.,[.,[[.,[[[.,.],.],.]],.]]] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>[1,2,3,7,6,4,5]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>[2,3,4,7,5,6,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>[1,3,4,7,5,6,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>[1,2,4,7,5,6,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>[3,4,5,6,7,1,2]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>[[.,[[.,[.,[.,[.,.]]]],.]],.] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>[.,[[[.,[.,[.,[.,.]]]],.],.]] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>[1,4,5,6,7,2,3]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>[[.,[.,[[.,[.,[.,.]]],.]]],.] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>[.,[[.,[[.,[.,[.,.]]],.]],.]] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>[.,[.,[[[.,[.,[.,.]]],.],.]]] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>[1,2,5,6,7,3,4]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>[[.,[.,[.,[[.,[.,.]],.]]]],.] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>[.,[[.,[.,[[.,[.,.]],.]]],.]] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[.,[.,[[.,[[.,[.,.]],.]],.]]] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>[.,[.,[.,[[[.,[.,.]],.],.]]]] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[.,[[.,[.,[.,[[.,.],.]]]],.]] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,[.,[[.,.],.]]],.]]] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,[[.,.],.]],.]]]] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[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]=>[8,7,6,5,4,3,2,1]=>[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]=>[8,7,5,6,3,4,2,1]=>[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]=>[8,6,7,5,4,2,3,1]=>[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]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.] [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[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]=>[7,8,6,5,4,3,1,2]=>[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]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>[7,8,1,2,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]] [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>[5,8,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>[5,7,8,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>[5,6,8,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>[3,4,5,6,7,8,1,2]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.