Identifier
Mp00017: Binary trees to 312-avoiding permutationPermutations
Mp00064: Permutations reversePermutations
Mp00108: Permutations cycle type Integer partitions
Images
=>
Cc0010;cc-rep-0Cc0002;cc-rep-3
[.,.]=>[1]=>[1]=>[1] [.,[.,.]]=>[2,1]=>[1,2]=>[1,1] [[.,.],.]=>[1,2]=>[2,1]=>[2] [.,[.,[.,.]]]=>[3,2,1]=>[1,2,3]=>[1,1,1] [.,[[.,.],.]]=>[2,3,1]=>[1,3,2]=>[2,1] [[.,.],[.,.]]=>[1,3,2]=>[2,3,1]=>[3] [[.,[.,.]],.]=>[2,1,3]=>[3,1,2]=>[3] [[[.,.],.],.]=>[1,2,3]=>[3,2,1]=>[2,1] [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>[1,1,1,1] [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,2,4,3]=>[2,1,1] [.,[[.,.],[.,.]]]=>[2,4,3,1]=>[1,3,4,2]=>[3,1] [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,4,2,3]=>[3,1] [.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,4,3,2]=>[2,1,1] [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[2,3,4,1]=>[4] [[.,.],[[.,.],.]]=>[1,3,4,2]=>[2,4,3,1]=>[3,1] [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[3,4,1,2]=>[2,2] [[[.,.],.],[.,.]]=>[1,2,4,3]=>[3,4,2,1]=>[4] [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,1,2,3]=>[4] [[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,1,3,2]=>[3,1] [[[.,.],[.,.]],.]=>[1,3,2,4]=>[4,2,3,1]=>[2,1,1] [[[.,[.,.]],.],.]=>[2,1,3,4]=>[4,3,1,2]=>[4] [[[[.,.],.],.],.]=>[1,2,3,4]=>[4,3,2,1]=>[2,2] [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[1,1,1,1,1] [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[2,1,1,1] [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[1,2,4,5,3]=>[3,1,1] [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[3,1,1] [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[2,1,1,1] [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[1,3,4,5,2]=>[4,1] [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[1,3,5,4,2]=>[3,1,1] [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[1,4,5,2,3]=>[2,2,1] [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[1,4,5,3,2]=>[4,1] [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[4,1] [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[3,1,1] [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[1,5,3,4,2]=>[2,1,1,1] [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[4,1] [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[2,2,1] [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[2,3,4,5,1]=>[5] [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[2,3,5,4,1]=>[4,1] [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[2,4,5,3,1]=>[5] [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[2,5,3,4,1]=>[3,1,1] [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[2,5,4,3,1]=>[3,2] [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[3,4,5,1,2]=>[5] [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,5,4,1,2]=>[3,2] [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[3,2] [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[5] [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[4,5,1,2,3]=>[5] [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[4,5,1,3,2]=>[3,2] [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[5] [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[2,2,1] [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[4,1] [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[5] [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[5,1,2,4,3]=>[4,1] [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[5,1,3,4,2]=>[3,1,1] [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[5,1,4,2,3]=>[5] [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[3,2] [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[2,1,1,1] [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[5,2,4,3,1]=>[2,2,1] [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[5,3,4,1,2]=>[5] [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[3,2] [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[3,2] [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[5] [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[3,2] [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[4,1] [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[2,2,1] [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[1,1,1,1,1,1] [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[2,1,1,1,1] [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>[3,1,1,1] [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[3,1,1,1] [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[2,1,1,1,1] [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>[4,1,1] [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>[3,1,1,1] [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>[2,2,1,1] [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>[4,1,1] [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[4,1,1] [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[3,1,1,1] [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>[2,1,1,1,1] [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[4,1,1] [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[2,2,1,1] [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>[5,1] [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>[4,1,1] [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[1,3,5,6,4,2]=>[5,1] [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[1,3,6,4,5,2]=>[3,1,1,1] [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[1,3,6,5,4,2]=>[3,2,1] [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>[5,1] [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>[3,2,1] [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>[3,2,1] [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[1,4,6,5,3,2]=>[5,1] [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>[5,1] [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>[3,2,1] [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>[5,1] [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>[2,2,1,1] [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>[4,1,1] [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[5,1] [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[4,1,1] [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>[3,1,1,1] [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[5,1] [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[3,2,1] [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>[2,1,1,1,1] [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[1,6,3,5,4,2]=>[2,2,1,1] [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>[5,1] [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>[3,2,1] [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[3,2,1] [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[5,1] [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>[3,2,1] [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[4,1,1] [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[2,2,1,1] [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[6] [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>[5,1] [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>[6] [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>[4,1,1] [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>[4,2] [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>[4,2] [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>[6] [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[6] [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>[5,1] [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>[3,1,1,1] [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>[3,2,1] [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>[3,3] [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>[3,3] [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>[3,2,1] [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>[3,3] [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[3,4,6,5,1,2]=>[6] [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>[5,1] [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>[4,2] [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>[3,2,1] [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[6] [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>[3,3] [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[3,2,1] [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[6] [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[5,1] [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[2,2,2] [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>[4,2] [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>[4,2] [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>[2,2,2] [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[6] [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[4,2] [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[6] [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>[4,2] [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[4,2] [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[6] [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>[3,3] [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>[6] [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>[4,2] [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>[5,1] [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>[3,2,1] [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[6] [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[5,1] [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[2,2,1,1] [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[4,1,1] [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[6] [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>[4,2] [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[6] [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[2,2,2] [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[4,2] [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[6] [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>[5,1] [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[6,1,2,4,5,3]=>[4,1,1] [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[6] [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[4,2] [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>[3,1,1,1] [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[6,1,3,5,4,2]=>[3,2,1] [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>[6] [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>[3,3] [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[4,2] [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[6] [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>[3,3] [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[5,1] [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[3,2,1] [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[2,1,1,1,1] [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[6,2,3,5,4,1]=>[2,2,1,1] [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[6,2,4,5,3,1]=>[3,2,1] [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[6,2,5,3,4,1]=>[3,2,1] [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>[2,2,1,1] [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>[6] [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>[5,1] [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>[4,2] [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[3,2,1] [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>[6] [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>[4,2] [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[2,2,2] [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>[6] [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[4,2] [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[6] [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[3,3] [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>[6] [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[3,2,1] [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[5,1] [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>[4,2] [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[3,2,1] [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>[4,1,1] [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[2,2,1,1] [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[4,2] [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[6] [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[4,2] [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[4,2] [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[2,2,2] [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1] [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>[2,1,1,1,1,1] [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5]=>[3,1,1,1,1] [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>[3,1,1,1,1] [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>[2,1,1,1,1,1] [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4]=>[4,1,1,1] [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4]=>[3,1,1,1,1] [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5]=>[2,2,1,1,1] [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4]=>[4,1,1,1] [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>[4,1,1,1] [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>[3,1,1,1,1] [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4]=>[2,1,1,1,1,1] [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>[4,1,1,1] [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[2,2,1,1,1] [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[1,2,4,5,6,7,3]=>[5,1,1] [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[1,2,4,5,7,6,3]=>[4,1,1,1] [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[1,2,4,6,7,5,3]=>[5,1,1] [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[1,2,4,7,5,6,3]=>[3,1,1,1,1] [.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[1,2,4,7,6,5,3]=>[3,2,1,1] [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[1,2,5,6,7,3,4]=>[5,1,1] [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[1,2,5,7,6,3,4]=>[3,2,1,1] [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[1,2,5,6,7,4,3]=>[3,2,1,1] [.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[1,2,5,7,6,4,3]=>[5,1,1] [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[1,2,6,7,3,4,5]=>[5,1,1] [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[1,2,6,7,3,5,4]=>[3,2,1,1] [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[1,2,6,7,4,5,3]=>[5,1,1] [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[1,2,6,7,5,3,4]=>[2,2,1,1,1] [.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[1,2,6,7,5,4,3]=>[4,1,1,1] [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>[5,1,1] [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>[4,1,1,1] [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[1,2,7,3,5,6,4]=>[3,1,1,1,1] [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>[5,1,1] [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>[3,2,1,1] [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[1,2,7,4,5,6,3]=>[2,1,1,1,1,1] [.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[1,2,7,4,6,5,3]=>[2,2,1,1,1] [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[1,2,7,5,6,3,4]=>[5,1,1] [.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[1,2,7,5,6,4,3]=>[3,2,1,1] [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>[3,2,1,1] [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>[5,1,1] [.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[1,2,7,6,4,5,3]=>[3,2,1,1] [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>[4,1,1,1] [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>[2,2,1,1,1] [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[1,3,4,5,6,7,2]=>[6,1] [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[1,3,4,5,7,6,2]=>[5,1,1] [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[1,3,4,6,7,5,2]=>[6,1] [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[1,3,4,7,5,6,2]=>[4,1,1,1] [.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[1,3,4,7,6,5,2]=>[4,2,1] [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[1,3,5,6,7,4,2]=>[4,2,1] [.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[1,3,5,7,6,4,2]=>[6,1] [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[1,3,6,7,4,5,2]=>[6,1] [.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[1,3,6,7,5,4,2]=>[5,1,1] [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[1,3,7,4,5,6,2]=>[3,1,1,1,1] [.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[1,3,7,4,6,5,2]=>[3,2,1,1] [.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[1,3,7,5,6,4,2]=>[3,3,1] [.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[1,3,7,6,4,5,2]=>[3,3,1] [.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[1,3,7,6,5,4,2]=>[3,2,1,1] [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3]=>[3,3,1] [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[1,4,5,7,6,2,3]=>[6,1] [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[1,4,6,7,5,2,3]=>[5,1,1] [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[1,4,7,5,6,2,3]=>[4,2,1] [.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[1,4,7,6,5,2,3]=>[3,2,1,1] [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[1,4,5,6,7,3,2]=>[6,1] [.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[1,4,5,7,6,3,2]=>[3,3,1] [.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[1,4,6,7,5,3,2]=>[3,2,1,1] [.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[1,4,7,5,6,3,2]=>[6,1] [.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[1,4,7,6,5,3,2]=>[5,1,1] [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4]=>[2,2,2,1] [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[1,5,7,6,2,3,4]=>[4,2,1] [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[1,5,6,7,2,4,3]=>[4,2,1] [.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[1,5,7,6,2,4,3]=>[2,2,2,1] [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[1,5,6,7,3,4,2]=>[6,1] [.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[1,5,7,6,3,4,2]=>[4,2,1] [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[1,5,6,7,4,2,3]=>[6,1] [.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[1,5,7,6,4,2,3]=>[4,2,1] [.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2]=>[4,2,1] [.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[1,5,7,6,4,3,2]=>[6,1] [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5]=>[3,3,1] [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4]=>[6,1] [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[1,6,7,2,4,5,3]=>[4,2,1] [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[1,6,7,2,5,3,4]=>[5,1,1] [.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[1,6,7,2,5,4,3]=>[3,2,1,1] [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[1,6,7,3,4,5,2]=>[6,1] [.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[1,6,7,3,5,4,2]=>[5,1,1] [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3]=>[2,2,1,1,1] [.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[1,6,7,4,5,3,2]=>[4,1,1,1] [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[1,6,7,5,2,3,4]=>[6,1] [.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[1,6,7,5,2,4,3]=>[4,2,1] [.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[1,6,7,5,3,4,2]=>[6,1] [.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[1,6,7,5,4,2,3]=>[2,2,2,1] [.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[1,6,7,5,4,3,2]=>[4,2,1] [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>[6,1] [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>[5,1,1] [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[1,7,2,3,5,6,4]=>[4,1,1,1] [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>[6,1] [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>[4,2,1] [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[1,7,2,4,5,6,3]=>[3,1,1,1,1] [.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[1,7,2,4,6,5,3]=>[3,2,1,1] [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[1,7,2,5,6,3,4]=>[6,1] [.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[1,7,2,5,6,4,3]=>[3,3,1] [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>[4,2,1] [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>[6,1] [.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[1,7,2,6,4,5,3]=>[3,3,1] [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>[5,1,1] [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>[3,2,1,1] [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[1,7,3,4,5,6,2]=>[2,1,1,1,1,1] [.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[1,7,3,4,6,5,2]=>[2,2,1,1,1] [.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[1,7,3,5,6,4,2]=>[3,2,1,1] [.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[1,7,3,6,4,5,2]=>[3,2,1,1] [.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[1,7,3,6,5,4,2]=>[2,2,1,1,1] [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[1,7,4,5,6,2,3]=>[6,1] [.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[1,7,4,6,5,2,3]=>[5,1,1] [.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[1,7,4,5,6,3,2]=>[4,2,1] [.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[1,7,4,6,5,3,2]=>[3,2,1,1] [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[1,7,5,6,2,3,4]=>[6,1] [.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[1,7,5,6,2,4,3]=>[4,2,1] [.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[1,7,5,6,3,4,2]=>[2,2,2,1] [.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[1,7,5,6,4,2,3]=>[6,1] [.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[1,7,5,6,4,3,2]=>[4,2,1] [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>[6,1] [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>[3,3,1] [.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[1,7,6,2,4,5,3]=>[6,1] [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>[3,2,1,1] [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>[5,1,1] [.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[1,7,6,3,4,5,2]=>[4,2,1] [.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[1,7,6,3,5,4,2]=>[3,2,1,1] [.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[1,7,6,4,5,2,3]=>[4,1,1,1] [.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2]=>[2,2,1,1,1] [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>[4,2,1] [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>[6,1] [.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[1,7,6,5,3,4,2]=>[4,2,1] [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>[4,2,1] [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[2,2,2,1] [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>[7] [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[2,3,4,5,7,6,1]=>[6,1] [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[2,3,4,6,7,5,1]=>[7] [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[2,3,4,7,5,6,1]=>[5,1,1] [[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[2,3,4,7,6,5,1]=>[5,2] [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[2,3,5,6,7,4,1]=>[5,2] [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[2,3,5,7,6,4,1]=>[7] [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[2,3,6,7,4,5,1]=>[7] [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[2,3,6,7,5,4,1]=>[6,1] [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[2,3,7,4,5,6,1]=>[4,1,1,1] [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[2,3,7,4,6,5,1]=>[4,2,1] [[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[2,3,7,5,6,4,1]=>[4,3] [[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[2,3,7,6,4,5,1]=>[4,3] [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[2,3,7,6,5,4,1]=>[4,2,1] [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[2,4,5,6,7,3,1]=>[7] [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[2,4,5,7,6,3,1]=>[4,3] [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1]=>[4,2,1] [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[2,4,7,5,6,3,1]=>[7] [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[2,4,7,6,5,3,1]=>[6,1] [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[2,5,6,7,3,4,1]=>[7] [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[2,5,7,6,3,4,1]=>[5,2] [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[2,5,6,7,4,3,1]=>[5,2] [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[2,5,7,6,4,3,1]=>[7] [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[2,6,7,3,4,5,1]=>[7] [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[2,6,7,3,5,4,1]=>[6,1] [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[2,6,7,4,5,3,1]=>[5,1,1] [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[2,6,7,5,3,4,1]=>[7] [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[2,6,7,5,4,3,1]=>[5,2] [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[2,7,3,4,5,6,1]=>[3,1,1,1,1] [[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[2,7,3,4,6,5,1]=>[3,2,1,1] [[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[2,7,3,5,6,4,1]=>[3,3,1] [[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[2,7,3,6,4,5,1]=>[3,3,1] [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[2,7,3,6,5,4,1]=>[3,2,1,1] [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[2,7,4,5,6,3,1]=>[4,3] [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[2,7,4,6,5,3,1]=>[3,3,1] [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[2,7,5,6,3,4,1]=>[3,2,2] [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[2,7,5,6,4,3,1]=>[4,3] [[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[2,7,6,3,4,5,1]=>[4,3] [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[2,7,6,3,5,4,1]=>[3,3,1] [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[2,7,6,4,5,3,1]=>[3,2,1,1] [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[2,7,6,5,3,4,1]=>[4,3] [[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>[3,2,2] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>[7] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[3,4,5,7,6,1,2]=>[4,3] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[3,4,6,7,5,1,2]=>[3,3,1] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[3,4,7,5,6,1,2]=>[7] [[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[3,4,7,6,5,1,2]=>[6,1] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[3,5,6,7,4,1,2]=>[4,3] [[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[3,5,7,6,4,1,2]=>[7] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[3,6,7,4,5,1,2]=>[5,1,1] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[3,6,7,5,4,1,2]=>[5,2] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[3,7,4,5,6,1,2]=>[5,2] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[3,7,4,6,5,1,2]=>[4,2,1] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[3,7,5,6,4,1,2]=>[5,2] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[3,7,6,4,5,1,2]=>[3,2,1,1] [[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[3,7,6,5,4,1,2]=>[3,2,2] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>[4,3] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[3,4,5,7,6,2,1]=>[7] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[3,4,6,7,5,2,1]=>[6,1] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[3,4,7,5,6,2,1]=>[4,3] [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1]=>[3,3,1] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1]=>[7] [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1]=>[4,3] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[3,6,7,4,5,2,1]=>[3,2,1,1] [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[3,6,7,5,4,2,1]=>[3,2,2] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[3,7,4,5,6,2,1]=>[7] [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[3,7,4,6,5,2,1]=>[6,1] [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[3,7,5,6,4,2,1]=>[7] [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[3,7,6,4,5,2,1]=>[5,1,1] [[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>[5,2] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>[7] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[4,5,7,6,1,2,3]=>[5,2] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[4,6,7,5,1,2,3]=>[3,2,2] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[4,7,5,6,1,2,3]=>[7] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,7,6,5,1,2,3]=>[4,3] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[4,5,6,7,1,3,2]=>[5,2] [[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[4,5,7,6,1,3,2]=>[7] [[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[4,6,7,5,1,3,2]=>[4,3] [[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[4,7,5,6,1,3,2]=>[5,2] [[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[4,7,6,5,1,3,2]=>[3,2,2] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>[3,2,2] [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[4,5,7,6,2,3,1]=>[5,2] [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[4,6,7,5,2,3,1]=>[7] [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[4,7,5,6,2,3,1]=>[7] [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>[5,2] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>[7] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[4,5,7,6,3,1,2]=>[4,3] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[4,6,7,5,3,1,2]=>[7] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[4,7,5,6,3,1,2]=>[3,2,2] [[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[4,7,6,5,3,1,2]=>[5,2] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[4,3] [[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[4,5,7,6,3,2,1]=>[7] [[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1]=>[5,2] [[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[4,7,5,6,3,2,1]=>[5,2] [[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[7] [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>[7] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[5,7,6,1,2,3,4]=>[5,2] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[5,6,7,1,2,4,3]=>[5,2] [[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[5,7,6,1,2,4,3]=>[7] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[5,6,7,1,3,4,2]=>[7] [[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[5,7,6,1,3,4,2]=>[5,2] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[5,6,7,1,4,2,3]=>[3,2,2] [[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[5,7,6,1,4,2,3]=>[4,3] [[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[5,6,7,1,4,3,2]=>[4,3] [[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[5,7,6,1,4,3,2]=>[3,2,2] [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>[4,3] [[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[5,7,6,2,3,4,1]=>[7] [[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[5,6,7,2,4,3,1]=>[7] [[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>[5,2] [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>[7] [[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[5,7,6,3,4,1,2]=>[5,2] [[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>[5,2] [[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[7] [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[2,2,2,1] [[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[5,7,6,4,1,2,3]=>[4,2,1] [[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[5,6,7,4,1,3,2]=>[4,2,1] [[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[5,7,6,4,1,3,2]=>[2,2,2,1] [[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>[6,1] [[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[4,2,1] [[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>[6,1] [[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[5,7,6,4,3,1,2]=>[4,2,1] [[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>[4,2,1] [[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[6,1] [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>[7] [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[6,7,1,2,3,5,4]=>[4,3] [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[6,7,1,2,4,5,3]=>[7] [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[6,7,1,2,5,3,4]=>[3,3,1] [[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[6,7,1,2,5,4,3]=>[6,1] [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[6,7,1,3,4,5,2]=>[5,2] [[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[6,7,1,3,5,4,2]=>[4,2,1] [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[6,7,1,4,5,2,3]=>[5,1,1] [[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[6,7,1,4,5,3,2]=>[3,2,1,1] [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[6,7,1,5,2,3,4]=>[4,3] [[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[6,7,1,5,2,4,3]=>[7] [[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[6,7,1,5,3,4,2]=>[5,2] [[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[6,7,1,5,4,2,3]=>[5,2] [[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[6,7,1,5,4,3,2]=>[3,2,2] [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>[7] [[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[6,7,2,3,5,4,1]=>[6,1] [[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[6,7,2,4,5,3,1]=>[5,1,1] [[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[6,7,2,5,3,4,1]=>[7] [[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>[5,2] [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[2,2,1,1,1] [[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[6,7,3,5,4,1,2]=>[2,2,2,1] [[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>[4,1,1,1] [[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[4,2,1] [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>[7] [[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2]=>[5,2] [[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[7] [[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>[3,2,2] [[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[4,3] [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>[7] [[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[6,7,5,1,2,4,3]=>[4,3] [[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[6,7,5,1,3,4,2]=>[3,2,2] [[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[6,7,5,1,4,2,3]=>[7] [[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2]=>[5,2] [[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>[5,2] [[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[7] [[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>[3,2,2] [[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[4,3] [[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>[6,1] [[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[6,7,5,4,1,3,2]=>[4,2,1] [[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[6,1] [[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[2,2,2,1] [[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[4,2,1] [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[7] [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>[6,1] [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[7,1,2,3,5,6,4]=>[5,1,1] [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>[7] [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>[5,2] [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[7,1,2,4,5,6,3]=>[4,1,1,1] [[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[7,1,2,4,6,5,3]=>[4,2,1] [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[7,1,2,5,6,3,4]=>[7] [[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[7,1,2,5,6,4,3]=>[4,3] [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>[5,2] [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>[7] [[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[7,1,2,6,4,5,3]=>[4,3] [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>[6,1] [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>[4,2,1] [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[7,1,3,4,5,6,2]=>[3,1,1,1,1] [[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[7,1,3,4,6,5,2]=>[3,2,1,1] [[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[7,1,3,5,6,4,2]=>[3,3,1] [[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[7,1,3,6,4,5,2]=>[3,3,1] [[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[7,1,3,6,5,4,2]=>[3,2,1,1] [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[7,1,4,5,6,2,3]=>[7] [[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[7,1,4,6,5,2,3]=>[6,1] [[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[7,1,4,5,6,3,2]=>[4,3] [[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[7,1,4,6,5,3,2]=>[3,3,1] [[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[7,1,5,6,2,3,4]=>[7] [[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[7,1,5,6,2,4,3]=>[5,2] [[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[7,1,5,6,3,4,2]=>[3,2,2] [[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[7,1,5,6,4,2,3]=>[7] [[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[7,1,5,6,4,3,2]=>[4,3] [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>[7] [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>[4,3] [[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[7,1,6,2,4,5,3]=>[7] [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>[4,2,1] [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>[6,1] [[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[7,1,6,3,4,5,2]=>[4,3] [[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[7,1,6,3,5,4,2]=>[3,3,1] [[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[7,1,6,4,5,2,3]=>[5,1,1] [[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[7,1,6,4,5,3,2]=>[3,2,1,1] [[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>[5,2] [[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>[7] [[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[7,1,6,5,3,4,2]=>[4,3] [[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>[5,2] [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[3,2,2] [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[2,1,1,1,1,1] [[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[7,2,3,4,6,5,1]=>[2,2,1,1,1] [[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[7,2,3,5,6,4,1]=>[3,2,1,1] [[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[7,2,3,6,4,5,1]=>[3,2,1,1] [[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[7,2,3,6,5,4,1]=>[2,2,1,1,1] [[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[7,2,4,5,6,3,1]=>[4,2,1] [[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[7,2,4,6,5,3,1]=>[3,2,1,1] [[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[7,2,5,6,3,4,1]=>[2,2,2,1] [[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[7,2,5,6,4,3,1]=>[4,2,1] [[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[7,2,6,3,4,5,1]=>[4,2,1] [[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[7,2,6,3,5,4,1]=>[3,2,1,1] [[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[7,2,6,4,5,3,1]=>[2,2,1,1,1] [[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[7,2,6,5,3,4,1]=>[4,2,1] [[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>[2,2,2,1] [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>[7] [[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[7,3,4,6,5,1,2]=>[6,1] [[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[7,3,5,6,4,1,2]=>[7] [[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[7,3,6,4,5,1,2]=>[5,1,1] [[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[7,3,6,5,4,1,2]=>[5,2] [[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>[5,2] [[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[7,3,4,6,5,2,1]=>[4,2,1] [[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[7,3,5,6,4,2,1]=>[5,2] [[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[7,3,6,4,5,2,1]=>[3,2,1,1] [[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[3,2,2] [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>[4,3] [[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[7,4,6,5,1,2,3]=>[7] [[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[7,4,5,6,1,3,2]=>[7] [[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[7,4,6,5,1,3,2]=>[5,2] [[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>[5,2] [[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[3,2,2] [[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>[5,2] [[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[7,4,6,5,3,1,2]=>[7] [[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>[3,2,2] [[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[5,2] [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>[3,2,2] [[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[7,5,6,1,2,4,3]=>[5,2] [[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[7,5,6,1,3,4,2]=>[7] [[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[7,5,6,1,4,2,3]=>[7] [[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[7,5,6,1,4,3,2]=>[5,2] [[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>[5,2] [[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[3,2,2] [[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>[7] [[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[5,2] [[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>[6,1] [[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[7,5,6,4,1,3,2]=>[4,2,1] [[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[2,2,2,1] [[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>[6,1] [[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[4,2,1] [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[4,3] [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>[7] [[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[7,6,1,2,4,5,3]=>[4,3] [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>[6,1] [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>[3,3,1] [[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[7,6,1,3,4,5,2]=>[7] [[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[7,6,1,3,5,4,2]=>[6,1] [[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[7,6,1,4,5,2,3]=>[3,2,1,1] [[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[7,6,1,4,5,3,2]=>[5,1,1] [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>[7] [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>[4,3] [[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[7,6,1,5,3,4,2]=>[7] [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>[3,2,2] [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[5,2] [[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>[5,2] [[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[7,6,2,3,5,4,1]=>[4,2,1] [[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[7,6,2,4,5,3,1]=>[3,2,1,1] [[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[7,6,2,5,3,4,1]=>[5,2] [[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[3,2,2] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>[4,1,1,1] [[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[7,6,3,5,4,1,2]=>[4,2,1] [[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[2,2,1,1,1] [[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[2,2,2,1] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>[5,2] [[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[7,6,4,5,1,3,2]=>[7] [[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[5,2] [[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>[4,3] [[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[3,2,2] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[4,3] [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>[7] [[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[7,6,5,1,3,4,2]=>[5,2] [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>[5,2] [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[7] [[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>[3,2,2] [[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[5,2] [[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>[4,3] [[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[3,2,2] [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[4,2,1] [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[6,1] [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[4,2,1] [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[4,2,1] [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[2,2,2,1] [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1] [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[3,4,5,6,7,8,1,2]=>[4,4] [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[2,2,2,2] [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[5,6,8,7,1,2,4,3]=>[2,2,2,2] [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[5,8,6,7,1,3,4,2]=>[2,2,2,2] [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[5,7,8,6,1,4,2,3]=>[2,2,2,2] [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[5,8,7,6,1,4,3,2]=>[2,2,2,2] [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[5,6,7,8,3,4,1,2]=>[4,4] [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>[2,2,2,2] [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[6,8,7,5,4,1,3,2]=>[2,2,2,2] [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[7,8,1,2,3,4,5,6]=>[4,4] [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>[2,2,1,1,1,1] [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[7,8,5,6,1,2,3,4]=>[4,4] [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2] [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>[2,2,2,2] [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[2,2,2,2] [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>[2,2,2,2] [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[2,2,2,2] [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[2,2,2,2] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[2,2,2,2]
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
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
cycle type
Description
The cycle type of a permutation as a partition.