Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
St000246: Permutations ⟶ ℤ (values match St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.)
Values
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>0
[.,[.,.]]=>[2,1]=>0
[[.,.],.]=>[1,2]=>1
[.,[.,[.,.]]]=>[3,2,1]=>0
[.,[[.,.],.]]=>[2,3,1]=>1
[[.,.],[.,.]]=>[3,1,2]=>1
[[.,[.,.]],.]=>[2,1,3]=>2
[[[.,.],.],.]=>[1,2,3]=>3
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>0
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>1
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>1
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>2
[.,[[[.,.],.],.]]=>[2,3,4,1]=>3
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>1
[[.,.],[[.,.],.]]=>[3,4,1,2]=>2
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>2
[[[.,.],.],[.,.]]=>[4,1,2,3]=>3
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>3
[[.,[[.,.],.]],.]=>[2,3,1,4]=>4
[[[.,.],[.,.]],.]=>[3,1,2,4]=>4
[[[.,[.,.]],.],.]=>[2,1,3,4]=>5
[[[[.,.],.],.],.]=>[1,2,3,4]=>6
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>0
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>1
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>1
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>2
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>3
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>1
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>2
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>2
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>3
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>3
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>4
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>4
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>5
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>6
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>1
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>2
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>2
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>3
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>4
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>2
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>3
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>3
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>4
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>3
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>4
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>4
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>5
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>6
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>4
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>5
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>5
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>6
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>7
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>5
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>6
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>6
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>7
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>7
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>8
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>8
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>9
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>10
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>0
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>1
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>1
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>2
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>3
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>1
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>2
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>2
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>3
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>3
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>4
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>4
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>5
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>6
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>1
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>2
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>2
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>3
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>4
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>2
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>3
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>3
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>4
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>3
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>4
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>4
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>5
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>6
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>4
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>5
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>5
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>6
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>7
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>5
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>6
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>6
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>7
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>7
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>8
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>8
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>9
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>10
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>1
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>2
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>2
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>3
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>4
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>2
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>3
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>3
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>4
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>4
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>5
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>5
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>6
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>7
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>2
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>3
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>3
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>4
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>5
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>3
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>4
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>4
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>5
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>6
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>3
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>4
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>4
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>5
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>4
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>5
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>5
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>6
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>6
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>7
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>4
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>5
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>5
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>6
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>7
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>5
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>6
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>6
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>7
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>7
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>8
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>8
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>9
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>10
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>5
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>6
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>6
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>7
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>8
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>6
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>7
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>7
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>8
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>8
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>9
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>9
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>10
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>11
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>6
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>7
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>7
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>8
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>9
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>7
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>8
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>8
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>9
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>8
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>9
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>9
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>10
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>11
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>9
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>10
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>10
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>11
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>12
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>10
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>11
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>11
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>12
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>12
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>13
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>13
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>14
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>15
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>0
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>11
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>11
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>11
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>12
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>11
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>11
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>12
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>12
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>13
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>13
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>14
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>15
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>1
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>2
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>4
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>11
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>3
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>4
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>5
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>6
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>7
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>8
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>6
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>7
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>9
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>7
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>10
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>11
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>11
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>11
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>11
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>12
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>11
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>11
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>12
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>12
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>13
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>13
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>14
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>15
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>6
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>7
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>8
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>9
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>7
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>8
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>9
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>9
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>10
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>9
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>10
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>10
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>16
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>9
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>12
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>13
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>16
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>11
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>17
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>17
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>15
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>18
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>17
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>18
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>18
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>19
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>19
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>20
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>21
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>0
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>2
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>2
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>2
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>2
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>4
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>6
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>2
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>2
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>2
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>6
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>2
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>2
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>2
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>2
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>4
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>6
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>6
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>10
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>6
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>8
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>10
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>12
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>18
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>18
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>18
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>19
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>19
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>20
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>21
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>1
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>2
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>2
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>2
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>2
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>2
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>3
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>4
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>8
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>8
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>16
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>2
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>4
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>3
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>6
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>6
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>5
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>6
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>7
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>9
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>6
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>8
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>8
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>10
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>6
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>7
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>8
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>9
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>12
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>4
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>6
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>10
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>11
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>13
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>8
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>9
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>15
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>16
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>6
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>7
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>9
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>8
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>10
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>12
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>18
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>18
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>18
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>19
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>19
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>20
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>21
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>7
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>8
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>9
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>10
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>8
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>10
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>9
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>9
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>10
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>10
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>9
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>11
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>13
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>22
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>16
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>18
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>22
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>13
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>23
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>16
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>19
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>23
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>18
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>24
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>24
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>22
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>24
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>25
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>27
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>28
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>0
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>28
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>36
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>0
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>36
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>45
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>8
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>9
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>5
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>28
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>36
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>27
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>27
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>45
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>35
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>26
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>26
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>26
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>26
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>35
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>45
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>22
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>18
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>16
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>21
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>29
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>24
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>21
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>20
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>1
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>9
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>10
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>10
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>10
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>3
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>15
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>21
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>26
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>30
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>33
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>35
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>17
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>24
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>30
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>35
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>39
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>42
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>44
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>54
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>29
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>30
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>37
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>30
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>29
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>37
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>3
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>28
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>15
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>10
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>6
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>21
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>15
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>10
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>6
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>32
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Description
The number of non-inversions of a permutation.
For a permutation of $\{1,\ldots,n\}$, this is given by $\operatorname{noninv}(\pi) = \binom{n}{2}-\operatorname{inv}(\pi)$.
For a permutation of $\{1,\ldots,n\}$, this is given by $\operatorname{noninv}(\pi) = \binom{n}{2}-\operatorname{inv}(\pi)$.
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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