Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.] [1,0,1,0]=>[1,2]=>[1,2]=>[.,[.,.]] [1,1,0,0]=>[2,1]=>[2,1]=>[[.,.],.] [1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,1,0,0]=>[1,3,2]=>[3,1,2]=>[[.,.],[.,.]] [1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]] [1,1,0,1,0,0]=>[2,3,1]=>[2,3,1]=>[[.,[.,.]],.] [1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.] [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]] [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]] [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]] [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[4,3,1,2]=>[[[.,.],.],[.,.]] [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]] [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]] [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.] [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.] [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.] [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.] [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]] [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]] [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[5,3,1,4,2]=>[[[.,.],.],[[.,.],.]] [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]] [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]] [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]] [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]] [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]] [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[4,2,1,5,3]=>[[[.,.],.],[[.,.],.]] [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]] [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]] [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]] [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.] [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]] [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.] [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.] [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.] [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]] [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]] [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.] [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.] [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]] [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.] [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.] [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.] [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.] [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.] [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.] [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[6,4,1,2,5,3]=>[[[.,.],.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[5,4,1,2,6,3]=>[[[.,.],.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[5,6,1,2,4,3]=>[[.,[.,.]],[.,[[.,.],.]]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[5,3,1,2,6,4]=>[[[.,.],.],[.,[[.,.],.]]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[6,3,1,4,2,5]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[6,3,1,4,5,2]=>[[[.,.],.],[[.,[.,.]],.]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[5,3,1,4,2,6]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[5,3,1,4,6,2]=>[[[.,.],.],[[.,[.,.]],.]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[5,3,1,6,4,2]=>[[[.,.],.],[[[.,.],.],.]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[6,5,3,1,4,2]=>[[[[.,.],.],.],[[.,.],.]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[4,3,1,5,2,6]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[4,3,1,5,6,2]=>[[[.,.],.],[[.,[.,.]],.]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[6,4,3,1,5,2]=>[[[[.,.],.],.],[[.,.],.]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[4,5,1,3,2,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[4,5,1,3,6,2]=>[[.,[.,.]],[[.,[.,.]],.]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[4,5,1,6,3,2]=>[[.,[.,.]],[[[.,.],.],.]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[6,4,5,1,3,2]=>[[[.,.],[.,.]],[[.,.],.]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[5,4,3,1,6,2]=>[[[[.,.],.],.],[[.,.],.]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[5,4,6,1,3,2]=>[[[.,.],[.,.]],[[.,.],.]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[5,6,4,1,3,2]=>[[[.,[.,.]],.],[[.,.],.]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[5,2,1,3,6,4]=>[[[.,.],.],[.,[[.,.],.]]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[4,2,1,5,3,6]=>[[[.,.],.],[[.,.],[.,.]]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[4,2,1,5,6,3]=>[[[.,.],.],[[.,[.,.]],.]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[6,4,2,1,5,3]=>[[[[.,.],.],.],[[.,.],.]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[5,4,2,1,6,3]=>[[[[.,.],.],.],[[.,.],.]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[5,6,2,1,4,3]=>[[[.,[.,.]],.],[[.,.],.]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[6,2,3,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[5,2,3,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[5,2,3,1,6,4]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[6,5,2,3,1,4]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[5,2,3,6,4,1]=>[[[.,.],[.,[[.,.],.]]],.] [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[6,4,2,3,1,5]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[4,2,5,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[4,2,5,3,6,1]=>[[[.,.],[[.,.],[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[4,2,5,6,3,1]=>[[[.,.],[[.,[.,.]],.]],.] [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,4,2,5,3,1]=>[[[[.,.],.],[[.,.],.]],.] [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[5,4,2,6,3,1]=>[[[[.,.],.],[[.,.],.]],.] [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[5,6,2,4,3,1]=>[[[.,[.,.]],[[.,.],.]],.] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.] [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[5,3,2,1,6,4]=>[[[[.,.],.],.],[[.,.],.]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[5,3,2,6,4,1]=>[[[[.,.],.],[[.,.],.]],.] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,5,3,2,4,1]=>[[[[[.,.],.],.],[.,.]],.] [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[6,3,4,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.] [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.] [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[5,3,4,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[5,3,6,4,2,1]=>[[[[.,.],[[.,.],.]],.],.] [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.] [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,4,3,5,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>[[[[.,[.,.]],.],.],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>[[[[.,[.,.]],[.,.]],.],.] [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.] [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.] [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.] [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.] [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.] [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[5,1,2,3,6,7,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[7,5,1,2,3,6,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[6,5,1,2,3,7,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[6,7,1,2,3,5,4]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[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]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[6,4,1,2,3,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[7,4,1,2,5,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[4,1,2,5,6,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[4,1,2,5,6,7,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[7,4,1,2,5,6,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[6,4,1,2,5,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[6,4,1,2,5,7,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[6,4,1,2,7,5,3]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,5,3]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[5,4,1,2,6,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[5,4,1,2,6,7,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[7,5,4,1,2,6,3]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[5,6,1,2,4,3,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[5,6,1,2,4,7,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[5,6,1,2,7,4,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[7,5,6,1,2,4,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[6,5,4,1,2,7,3]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[6,5,7,1,2,4,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[6,7,5,1,2,4,3]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[6,3,1,2,4,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[5,3,1,2,6,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[5,3,1,2,6,7,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[7,5,3,1,2,6,4]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[6,5,3,1,2,7,4]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[6,7,3,1,2,5,4]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[7,3,1,4,2,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[6,3,1,4,2,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[6,3,1,4,2,7,5]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[7,6,3,1,4,2,5]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[3,1,4,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[7,3,1,4,5,2,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[3,1,4,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[3,1,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[7,3,1,4,5,6,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[6,3,1,4,5,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[6,3,1,4,5,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[6,3,1,4,7,5,2]=>[[[.,.],.],[[.,[[.,.],.]],.]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[7,6,3,1,4,5,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[5,3,1,4,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[7,5,3,1,4,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[5,3,1,4,6,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[5,3,1,4,6,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[7,5,3,1,4,6,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[5,3,1,6,4,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[5,3,1,6,4,7,2]=>[[[.,.],.],[[[.,.],[.,.]],.]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[5,3,1,6,7,4,2]=>[[[.,.],.],[[[.,[.,.]],.],.]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[7,5,3,1,6,4,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[6,5,3,1,4,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[6,5,3,1,4,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[6,5,3,1,7,4,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[6,7,3,1,5,4,2]=>[[[.,[.,.]],.],[[[.,.],.],.]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[7,6,5,3,1,4,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[6,4,3,1,2,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[4,3,1,5,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[7,4,3,1,5,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[4,3,1,5,6,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[4,3,1,5,6,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[7,4,3,1,5,6,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[6,4,3,1,5,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[6,4,3,1,5,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[6,4,3,1,7,5,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[7,6,4,3,1,5,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[4,5,1,3,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[7,4,5,1,3,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[4,5,1,3,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[4,5,1,3,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[7,4,5,1,3,6,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[4,5,1,6,3,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[4,5,1,6,3,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[4,5,1,6,7,3,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[7,4,5,1,6,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[6,4,5,1,3,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[6,4,5,1,3,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[6,4,5,1,7,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[6,4,7,1,5,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[7,6,4,5,1,3,2]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[5,4,3,1,6,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[5,4,3,1,6,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[7,5,4,3,1,6,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[5,4,6,1,3,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[5,4,6,1,3,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[5,4,6,1,7,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[7,5,4,6,1,3,2]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[5,6,4,1,3,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[5,6,4,1,3,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[5,6,4,1,7,3,2]=>[[[.,[.,.]],.],[[[.,.],.],.]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[5,6,7,1,4,3,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[7,5,6,4,1,3,2]=>[[[[.,.],[.,.]],.],[[.,.],.]] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[6,5,4,3,1,7,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[6,5,4,7,1,3,2]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[6,5,7,4,1,3,2]=>[[[[.,.],[.,.]],.],[[.,.],.]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[6,7,5,4,1,3,2]=>[[[[.,[.,.]],.],.],[[.,.],.]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[6,2,1,3,4,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[5,2,1,3,6,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[5,2,1,3,6,7,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[7,5,2,1,3,6,4]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[6,5,2,1,3,7,4]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[6,7,2,1,3,5,4]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[6,4,2,1,3,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[4,2,1,5,3,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[7,4,2,1,5,3,6]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[4,2,1,5,6,3,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[4,2,1,5,6,7,3]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[7,4,2,1,5,6,3]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[6,4,2,1,5,3,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[6,4,2,1,5,7,3]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[6,4,2,1,7,5,3]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[7,6,4,2,1,5,3]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[5,4,2,1,6,3,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[5,4,2,1,6,7,3]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[7,5,4,2,1,6,3]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[5,6,2,1,4,3,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[5,6,2,1,4,7,3]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[5,6,2,1,7,4,3]=>[[[.,[.,.]],.],[[[.,.],.],.]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[7,5,6,2,1,4,3]=>[[[[.,.],[.,.]],.],[[.,.],.]] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[6,5,4,2,1,7,3]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[6,5,7,2,1,4,3]=>[[[[.,.],[.,.]],.],[[.,.],.]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[6,7,5,2,1,4,3]=>[[[[.,[.,.]],.],.],[[.,.],.]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[6,2,3,1,4,7,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[7,6,2,3,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[7,5,2,3,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[5,2,3,1,6,4,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[5,2,3,1,6,7,4]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[7,5,2,3,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[6,5,2,3,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[6,5,2,3,1,7,4]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[6,7,2,3,1,5,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[7,6,5,2,3,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[6,2,3,4,1,7,5]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[7,6,2,3,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[6,2,3,4,7,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,6,2,3,4,5,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[7,5,2,3,4,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,5,2,3,4,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[5,2,3,6,4,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[5,2,3,6,4,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[5,2,3,6,7,4,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,5,2,3,6,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[6,5,2,3,4,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[6,5,2,3,7,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[6,7,2,3,5,4,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,6,5,2,3,4,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[7,4,2,3,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[6,4,2,3,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[6,4,2,3,1,7,5]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[7,6,4,2,3,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[7,4,2,3,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,4,2,3,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,4,2,3,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[6,4,2,3,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[6,4,2,3,7,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,6,4,2,3,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[4,2,5,3,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[7,4,2,5,3,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[4,2,5,3,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[4,2,5,3,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,4,2,5,3,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[4,2,5,6,3,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[4,2,5,6,3,7,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[4,2,5,6,7,3,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,4,2,5,6,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,4,2,5,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[6,4,2,5,3,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[6,4,2,5,7,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[6,4,2,7,5,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,6,4,2,5,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[7,5,4,2,3,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[5,4,2,3,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[5,4,2,3,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,5,4,2,3,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[5,4,2,6,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[5,4,2,6,3,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[5,4,2,6,7,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,5,4,2,6,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[5,6,2,4,3,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[5,6,2,4,3,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[5,6,2,4,7,3,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[5,6,2,7,4,3,1]=>[[[.,[.,.]],[[[.,.],.],.]],.] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,5,6,2,4,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,5,4,2,3,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[6,5,4,2,3,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[6,5,4,2,7,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[6,5,7,2,4,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[6,7,5,2,4,3,1]=>[[[[.,[.,.]],.],[[.,.],.]],.] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[6,3,2,1,4,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[5,3,2,1,6,4,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[5,3,2,1,6,7,4]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[7,5,3,2,1,6,4]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[6,5,3,2,1,7,4]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[6,7,3,2,1,5,4]=>[[[[.,[.,.]],.],.],[[.,.],.]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[6,3,2,4,1,7,5]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[6,3,2,4,7,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,6,3,2,4,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,5,3,2,4,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[5,3,2,6,4,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[5,3,2,6,4,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[5,3,2,6,7,4,1]=>[[[[.,.],.],[[.,[.,.]],.]],.] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,5,3,2,6,4,1]=>[[[[[.,.],.],.],[[.,.],.]],.] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[6,5,3,2,4,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[6,5,3,2,7,4,1]=>[[[[[.,.],.],.],[[.,.],.]],.] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[6,7,3,2,5,4,1]=>[[[[.,[.,.]],.],[[.,.],.]],.] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[7,3,4,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[6,3,4,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[6,3,4,2,1,7,5]=>[[[[.,.],[.,.]],.],[[.,.],.]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[7,3,4,2,5,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,3,4,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[6,3,4,2,5,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[6,3,4,2,7,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[7,3,4,5,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,3,4,5,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,7,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,3,4,5,6,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[6,3,4,5,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[6,3,4,5,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[6,3,4,7,5,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[5,3,4,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[5,3,4,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[5,3,4,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[5,3,4,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[5,3,4,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[5,3,6,4,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[5,3,6,4,2,7,1]=>[[[[.,.],[[.,.],.]],[.,.]],.] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[5,3,6,4,7,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[5,3,6,7,4,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,5,3,6,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[6,5,3,7,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[6,7,3,5,4,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[6,4,3,2,1,7,5]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[6,4,3,2,7,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[7,4,3,5,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,4,3,5,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[4,3,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[6,4,3,7,5,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[7,4,5,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,4,5,3,2,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[4,5,3,6,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,4,5,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,7,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,4,5,6,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,4,5,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[6,4,5,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[6,4,5,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[6,4,5,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[6,4,7,5,3,2,1]=>[[[[[.,.],[[.,.],.]],.],.],.] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,7,1]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
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.