Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
St000007: Permutations ⟶ ℤ
Values
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>1
[.,[.,.]]=>[2,1]=>2
[[.,.],.]=>[1,2]=>1
[.,[.,[.,.]]]=>[3,2,1]=>3
[.,[[.,.],.]]=>[2,3,1]=>2
[[.,.],[.,.]]=>[3,1,2]=>2
[[.,[.,.]],.]=>[2,1,3]=>1
[[[.,.],.],.]=>[1,2,3]=>1
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>4
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>3
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>3
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>2
[.,[[[.,.],.],.]]=>[2,3,4,1]=>2
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>3
[[.,.],[[.,.],.]]=>[3,4,1,2]=>2
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>2
[[[.,.],.],[.,.]]=>[4,1,2,3]=>2
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>1
[[.,[[.,.],.]],.]=>[2,3,1,4]=>1
[[[.,.],[.,.]],.]=>[3,1,2,4]=>1
[[[.,[.,.]],.],.]=>[2,1,3,4]=>1
[[[[.,.],.],.],.]=>[1,2,3,4]=>1
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>5
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>4
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>4
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>3
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>3
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>4
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>3
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>3
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>3
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>2
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>2
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>2
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>2
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>2
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>4
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>3
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>3
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>2
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>2
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>3
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>2
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>3
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>2
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>2
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>2
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>2
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>2
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>2
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>1
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>1
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>1
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>1
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>1
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>1
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>1
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>1
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>1
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>1
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>1
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>1
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>1
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>1
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>6
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>5
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>5
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>4
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>4
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>5
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>4
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>4
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>4
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>3
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>3
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>3
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>3
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>3
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>5
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>4
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>4
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>3
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>3
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>4
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>3
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>4
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>3
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>3
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>3
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>3
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>3
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>3
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>2
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>2
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>2
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>2
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>2
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>2
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>2
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>2
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>2
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>2
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>2
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>2
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>2
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>2
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>5
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>4
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>4
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>3
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>3
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>4
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>3
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>3
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>3
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>2
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>2
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>2
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>2
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>2
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>4
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>3
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>3
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>2
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>2
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>4
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>3
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>3
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>2
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>2
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>3
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>2
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>3
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>2
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>3
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>2
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>3
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>2
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>3
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>2
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>2
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>2
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>2
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>2
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>2
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>2
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>2
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>2
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>2
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>2
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>2
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>2
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>2
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>2
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>1
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>1
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>1
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>1
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>1
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>1
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>1
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>1
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>1
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>1
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>1
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>1
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>1
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>1
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>1
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>1
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>1
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>1
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>1
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>1
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>1
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>1
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>1
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>1
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>1
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>1
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>1
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>1
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>1
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>1
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>1
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>1
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>1
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>1
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>1
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>1
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>1
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>1
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>1
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>1
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>1
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>7
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>2
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>2
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>2
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>2
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>2
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>2
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>2
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>2
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>2
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>2
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>2
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>2
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>6
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>5
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>4
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>3
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>2
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>5
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>4
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>3
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>3
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>2
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>2
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>4
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>3
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>2
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>2
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>3
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>2
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>2
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>2
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>2
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>2
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>2
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>2
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>2
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>2
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>2
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>2
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>2
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>2
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>1
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>1
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>1
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>1
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>1
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>1
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>1
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>1
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>1
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>1
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>1
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>1
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>1
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>1
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>1
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>1
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>1
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>1
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>1
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>1
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>1
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>1
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>1
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>1
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>1
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>1
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>1
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>1
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>1
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>8
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>6
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>6
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>6
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>6
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>4
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>4
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>6
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>6
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>6
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>4
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>6
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>6
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>6
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>6
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>4
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>4
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>4
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>3
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>2
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>2
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>2
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>2
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>2
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>2
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>2
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>2
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>2
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>2
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>2
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>7
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>6
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>6
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>6
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>6
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>6
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>5
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>4
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>3
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>3
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>2
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>6
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>4
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>6
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>4
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>4
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>5
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>4
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>4
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>3
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>2
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>2
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>2
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>2
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>2
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>5
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>4
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>3
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>3
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>2
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>4
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>4
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>4
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>3
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>2
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>2
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>2
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>3
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>2
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>2
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>2
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>2
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>2
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>2
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>2
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>2
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>2
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>2
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>2
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>2
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>2
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>2
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>1
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>1
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>1
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>1
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>1
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>1
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>1
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>1
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>1
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>1
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>1
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>1
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>1
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>1
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>1
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>1
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>1
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>1
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>1
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>1
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>1
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>1
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>1
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>1
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>1
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>1
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>1
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>1
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>1
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>1
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>9
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>2
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>1
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>10
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>2
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>1
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>1
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>5
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>2
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>2
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>2
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>2
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>2
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>2
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>2
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>2
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>2
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>2
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>2
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>2
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>2
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>2
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>2
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>3
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>2
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>2
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>2
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>2
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>8
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>1
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>9
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>1
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>1
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>1
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>7
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>1
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>1
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>1
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>1
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>1
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>1
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>1
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>1
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>1
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>1
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>1
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>1
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>1
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>1
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>1
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>1
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>1
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>1
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>1
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>1
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>8
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>3
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>4
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>5
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>6
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>4
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>5
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>6
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>7
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>1
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Description
The number of saliances of the permutation.
A saliance is a right-to-left maximum. This can be described as an occurrence of the mesh pattern $([1], {(1,1)})$, i.e., the upper right quadrant is shaded, see [1].
A saliance is a right-to-left maximum. This can be described as an occurrence of the mesh pattern $([1], {(1,1)})$, i.e., the upper right quadrant is shaded, see [1].
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the Sylvester class.
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 maximal element of the Sylvester class.
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