- FindStat

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Identifier

St001376: Binary trees ⟶ ℤ

Values

=>
                            Cc0010;cc-rep
                            
                            
                            

                        [.,.]=>0
[.,[.,.]]=>1
[[.,.],.]=>1
[.,[.,[.,.]]]=>3
[.,[[.,.],.]]=>3
[[.,.],[.,.]]=>0
[[.,[.,.]],.]=>3
[[[.,.],.],.]=>3
[.,[.,[.,[.,.]]]]=>6
[.,[.,[[.,.],.]]]=>6
[.,[[.,.],[.,.]]]=>3
[.,[[.,[.,.]],.]]=>6
[.,[[[.,.],.],.]]=>6
[[.,.],[.,[.,.]]]=>2
[[.,.],[[.,.],.]]=>2
[[.,[.,.]],[.,.]]=>2
[[[.,.],.],[.,.]]=>2
[[.,[.,[.,.]]],.]=>6
[[.,[[.,.],.]],.]=>6
[[[.,.],[.,.]],.]=>3
[[[.,[.,.]],.],.]=>6
[[[[.,.],.],.],.]=>6
[.,[.,[.,[.,[.,.]]]]]=>10
[.,[.,[.,[[.,.],.]]]]=>10
[.,[.,[[.,.],[.,.]]]]=>7
[.,[.,[[.,[.,.]],.]]]=>10
[.,[.,[[[.,.],.],.]]]=>10
[.,[[.,.],[.,[.,.]]]]=>6
[.,[[.,.],[[.,.],.]]]=>6
[.,[[.,[.,.]],[.,.]]]=>6
[.,[[[.,.],.],[.,.]]]=>6
[.,[[.,[.,[.,.]]],.]]=>10
[.,[[.,[[.,.],.]],.]]=>10
[.,[[[.,.],[.,.]],.]]=>7
[.,[[[.,[.,.]],.],.]]=>10
[.,[[[[.,.],.],.],.]]=>10
[[.,.],[.,[.,[.,.]]]]=>5
[[.,.],[.,[[.,.],.]]]=>5
[[.,.],[[.,.],[.,.]]]=>2
[[.,.],[[.,[.,.]],.]]=>5
[[.,.],[[[.,.],.],.]]=>5
[[.,[.,.]],[.,[.,.]]]=>2
[[.,[.,.]],[[.,.],.]]=>2
[[[.,.],.],[.,[.,.]]]=>2
[[[.,.],.],[[.,.],.]]=>2
[[.,[.,[.,.]]],[.,.]]=>5
[[.,[[.,.],.]],[.,.]]=>5
[[[.,.],[.,.]],[.,.]]=>2
[[[.,[.,.]],.],[.,.]]=>5
[[[[.,.],.],.],[.,.]]=>5
[[.,[.,[.,[.,.]]]],.]=>10
[[.,[.,[[.,.],.]]],.]=>10
[[.,[[.,.],[.,.]]],.]=>7
[[.,[[.,[.,.]],.]],.]=>10
[[.,[[[.,.],.],.]],.]=>10
[[[.,.],[.,[.,.]]],.]=>6
[[[.,.],[[.,.],.]],.]=>6
[[[.,[.,.]],[.,.]],.]=>6
[[[[.,.],.],[.,.]],.]=>6
[[[.,[.,[.,.]]],.],.]=>10
[[[.,[[.,.],.]],.],.]=>10
[[[[.,.],[.,.]],.],.]=>7
[[[[.,[.,.]],.],.],.]=>10
[[[[[.,.],.],.],.],.]=>10
[.,[.,[.,[.,[.,[.,.]]]]]]=>15
[.,[.,[.,[.,[[.,.],.]]]]]=>15
[.,[.,[.,[[.,.],[.,.]]]]]=>12
[.,[.,[.,[[.,[.,.]],.]]]]=>15
[.,[.,[.,[[[.,.],.],.]]]]=>15
[.,[.,[[.,.],[.,[.,.]]]]]=>11
[.,[.,[[.,.],[[.,.],.]]]]=>11
[.,[.,[[.,[.,.]],[.,.]]]]=>11
[.,[.,[[[.,.],.],[.,.]]]]=>11
[.,[.,[[.,[.,[.,.]]],.]]]=>15
[.,[.,[[.,[[.,.],.]],.]]]=>15
[.,[.,[[[.,.],[.,.]],.]]]=>12
[.,[.,[[[.,[.,.]],.],.]]]=>15
[.,[.,[[[[.,.],.],.],.]]]=>15
[.,[[.,.],[.,[.,[.,.]]]]]=>10
[.,[[.,.],[.,[[.,.],.]]]]=>10
[.,[[.,.],[[.,.],[.,.]]]]=>7
[.,[[.,.],[[.,[.,.]],.]]]=>10
[.,[[.,.],[[[.,.],.],.]]]=>10
[.,[[.,[.,.]],[.,[.,.]]]]=>7
[.,[[.,[.,.]],[[.,.],.]]]=>7
[.,[[[.,.],.],[.,[.,.]]]]=>7
[.,[[[.,.],.],[[.,.],.]]]=>7
[.,[[.,[.,[.,.]]],[.,.]]]=>10
[.,[[.,[[.,.],.]],[.,.]]]=>10
[.,[[[.,.],[.,.]],[.,.]]]=>7
[.,[[[.,[.,.]],.],[.,.]]]=>10
[.,[[[[.,.],.],.],[.,.]]]=>10
[.,[[.,[.,[.,[.,.]]]],.]]=>15
[.,[[.,[.,[[.,.],.]]],.]]=>15
[.,[[.,[[.,.],[.,.]]],.]]=>12
[.,[[.,[[.,[.,.]],.]],.]]=>15
[.,[[.,[[[.,.],.],.]],.]]=>15
[.,[[[.,.],[.,[.,.]]],.]]=>11
[.,[[[.,.],[[.,.],.]],.]]=>11
[.,[[[.,[.,.]],[.,.]],.]]=>11
[.,[[[[.,.],.],[.,.]],.]]=>11
[.,[[[.,[.,[.,.]]],.],.]]=>15
[.,[[[.,[[.,.],.]],.],.]]=>15
[.,[[[[.,.],[.,.]],.],.]]=>12
[.,[[[[.,[.,.]],.],.],.]]=>15
[.,[[[[[.,.],.],.],.],.]]=>15
[[.,.],[.,[.,[.,[.,.]]]]]=>9
[[.,.],[.,[.,[[.,.],.]]]]=>9
[[.,.],[.,[[.,.],[.,.]]]]=>6
[[.,.],[.,[[.,[.,.]],.]]]=>9
[[.,.],[.,[[[.,.],.],.]]]=>9
[[.,.],[[.,.],[.,[.,.]]]]=>5
[[.,.],[[.,.],[[.,.],.]]]=>5
[[.,.],[[.,[.,.]],[.,.]]]=>5
[[.,.],[[[.,.],.],[.,.]]]=>5
[[.,.],[[.,[.,[.,.]]],.]]=>9
[[.,.],[[.,[[.,.],.]],.]]=>9
[[.,.],[[[.,.],[.,.]],.]]=>6
[[.,.],[[[.,[.,.]],.],.]]=>9
[[.,.],[[[[.,.],.],.],.]]=>9
[[.,[.,.]],[.,[.,[.,.]]]]=>5
[[.,[.,.]],[.,[[.,.],.]]]=>5
[[.,[.,.]],[[.,.],[.,.]]]=>2
[[.,[.,.]],[[.,[.,.]],.]]=>5
[[.,[.,.]],[[[.,.],.],.]]=>5
[[[.,.],.],[.,[.,[.,.]]]]=>5
[[[.,.],.],[.,[[.,.],.]]]=>5
[[[.,.],.],[[.,.],[.,.]]]=>2
[[[.,.],.],[[.,[.,.]],.]]=>5
[[[.,.],.],[[[.,.],.],.]]=>5
[[.,[.,[.,.]]],[.,[.,.]]]=>5
[[.,[.,[.,.]]],[[.,.],.]]=>5
[[.,[[.,.],.]],[.,[.,.]]]=>5
[[.,[[.,.],.]],[[.,.],.]]=>5
[[[.,.],[.,.]],[.,[.,.]]]=>2
[[[.,.],[.,.]],[[.,.],.]]=>2
[[[.,[.,.]],.],[.,[.,.]]]=>5
[[[.,[.,.]],.],[[.,.],.]]=>5
[[[[.,.],.],.],[.,[.,.]]]=>5
[[[[.,.],.],.],[[.,.],.]]=>5
[[.,[.,[.,[.,.]]]],[.,.]]=>9
[[.,[.,[[.,.],.]]],[.,.]]=>9
[[.,[[.,.],[.,.]]],[.,.]]=>6
[[.,[[.,[.,.]],.]],[.,.]]=>9
[[.,[[[.,.],.],.]],[.,.]]=>9
[[[.,.],[.,[.,.]]],[.,.]]=>5
[[[.,.],[[.,.],.]],[.,.]]=>5
[[[.,[.,.]],[.,.]],[.,.]]=>5
[[[[.,.],.],[.,.]],[.,.]]=>5
[[[.,[.,[.,.]]],.],[.,.]]=>9
[[[.,[[.,.],.]],.],[.,.]]=>9
[[[[.,.],[.,.]],.],[.,.]]=>6
[[[[.,[.,.]],.],.],[.,.]]=>9
[[[[[.,.],.],.],.],[.,.]]=>9
[[.,[.,[.,[.,[.,.]]]]],.]=>15
[[.,[.,[.,[[.,.],.]]]],.]=>15
[[.,[.,[[.,.],[.,.]]]],.]=>12
[[.,[.,[[.,[.,.]],.]]],.]=>15
[[.,[.,[[[.,.],.],.]]],.]=>15
[[.,[[.,.],[.,[.,.]]]],.]=>11
[[.,[[.,.],[[.,.],.]]],.]=>11
[[.,[[.,[.,.]],[.,.]]],.]=>11
[[.,[[[.,.],.],[.,.]]],.]=>11
[[.,[[.,[.,[.,.]]],.]],.]=>15
[[.,[[.,[[.,.],.]],.]],.]=>15
[[.,[[[.,.],[.,.]],.]],.]=>12
[[.,[[[.,[.,.]],.],.]],.]=>15
[[.,[[[[.,.],.],.],.]],.]=>15
[[[.,.],[.,[.,[.,.]]]],.]=>10
[[[.,.],[.,[[.,.],.]]],.]=>10
[[[.,.],[[.,.],[.,.]]],.]=>7
[[[.,.],[[.,[.,.]],.]],.]=>10
[[[.,.],[[[.,.],.],.]],.]=>10
[[[.,[.,.]],[.,[.,.]]],.]=>7
[[[.,[.,.]],[[.,.],.]],.]=>7
[[[[.,.],.],[.,[.,.]]],.]=>7
[[[[.,.],.],[[.,.],.]],.]=>7
[[[.,[.,[.,.]]],[.,.]],.]=>10
[[[.,[[.,.],.]],[.,.]],.]=>10
[[[[.,.],[.,.]],[.,.]],.]=>7
[[[[.,[.,.]],.],[.,.]],.]=>10
[[[[[.,.],.],.],[.,.]],.]=>10
[[[.,[.,[.,[.,.]]]],.],.]=>15
[[[.,[.,[[.,.],.]]],.],.]=>15
[[[.,[[.,.],[.,.]]],.],.]=>12
[[[.,[[.,[.,.]],.]],.],.]=>15
[[[.,[[[.,.],.],.]],.],.]=>15
[[[[.,.],[.,[.,.]]],.],.]=>11
[[[[.,.],[[.,.],.]],.],.]=>11
[[[[.,[.,.]],[.,.]],.],.]=>11
[[[[[.,.],.],[.,.]],.],.]=>11
[[[[.,[.,[.,.]]],.],.],.]=>15
[[[[.,[[.,.],.]],.],.],.]=>15
[[[[[.,.],[.,.]],.],.],.]=>12
[[[[[.,[.,.]],.],.],.],.]=>15
[[[[[[.,.],.],.],.],.],.]=>15
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>21
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>21
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>18
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>21
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>21
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>17
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>17
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>17
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>17
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>21
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>21
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>18
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>21
[.,[.,[.,[[[[.,.],.],.],.]]]]=>21
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>16
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>16
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>13
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>16
[.,[.,[[.,.],[[[.,.],.],.]]]]=>16
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>13
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>13
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>13
[.,[.,[[[.,.],.],[[.,.],.]]]]=>13
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>16
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>16
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>13
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>16
[.,[.,[[[[.,.],.],.],[.,.]]]]=>16
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>21
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>21
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>18
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>21
[.,[.,[[.,[[[.,.],.],.]],.]]]=>21
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>17
[.,[.,[[[.,.],[[.,.],.]],.]]]=>17
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>17
[.,[.,[[[[.,.],.],[.,.]],.]]]=>17
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>21
[.,[.,[[[.,[[.,.],.]],.],.]]]=>21
[.,[.,[[[[.,.],[.,.]],.],.]]]=>18
[.,[.,[[[[.,[.,.]],.],.],.]]]=>21
[.,[.,[[[[[.,.],.],.],.],.]]]=>21
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>15
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>15
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>12
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>15
[.,[[.,.],[.,[[[.,.],.],.]]]]=>15
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>11
[.,[[.,.],[[.,.],[[.,.],.]]]]=>11
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>11
[.,[[.,.],[[[.,.],.],[.,.]]]]=>11
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>15
[.,[[.,.],[[.,[[.,.],.]],.]]]=>15
[.,[[.,.],[[[.,.],[.,.]],.]]]=>12
[.,[[.,.],[[[.,[.,.]],.],.]]]=>15
[.,[[.,.],[[[[.,.],.],.],.]]]=>15
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>11
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>11
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>8
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>11
[.,[[.,[.,.]],[[[.,.],.],.]]]=>11
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>11
[.,[[[.,.],.],[.,[[.,.],.]]]]=>11
[.,[[[.,.],.],[[.,.],[.,.]]]]=>8
[.,[[[.,.],.],[[.,[.,.]],.]]]=>11
[.,[[[.,.],.],[[[.,.],.],.]]]=>11
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>11
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>11
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>11
[.,[[.,[[.,.],.]],[[.,.],.]]]=>11
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>8
[.,[[[.,.],[.,.]],[[.,.],.]]]=>8
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>11
[.,[[[.,[.,.]],.],[[.,.],.]]]=>11
[.,[[[[.,.],.],.],[.,[.,.]]]]=>11
[.,[[[[.,.],.],.],[[.,.],.]]]=>11
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>15
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>15
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>12
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>15
[.,[[.,[[[.,.],.],.]],[.,.]]]=>15
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>11
[.,[[[.,.],[[.,.],.]],[.,.]]]=>11
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>11
[.,[[[[.,.],.],[.,.]],[.,.]]]=>11
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>15
[.,[[[.,[[.,.],.]],.],[.,.]]]=>15
[.,[[[[.,.],[.,.]],.],[.,.]]]=>12
[.,[[[[.,[.,.]],.],.],[.,.]]]=>15
[.,[[[[[.,.],.],.],.],[.,.]]]=>15
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>21
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>21
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>18
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>21
[.,[[.,[.,[[[.,.],.],.]]],.]]=>21
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>17
[.,[[.,[[.,.],[[.,.],.]]],.]]=>17
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>17
[.,[[.,[[[.,.],.],[.,.]]],.]]=>17
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>21
[.,[[.,[[.,[[.,.],.]],.]],.]]=>21
[.,[[.,[[[.,.],[.,.]],.]],.]]=>18
[.,[[.,[[[.,[.,.]],.],.]],.]]=>21
[.,[[.,[[[[.,.],.],.],.]],.]]=>21
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>16
[.,[[[.,.],[.,[[.,.],.]]],.]]=>16
[.,[[[.,.],[[.,.],[.,.]]],.]]=>13
[.,[[[.,.],[[.,[.,.]],.]],.]]=>16
[.,[[[.,.],[[[.,.],.],.]],.]]=>16
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>13
[.,[[[.,[.,.]],[[.,.],.]],.]]=>13
[.,[[[[.,.],.],[.,[.,.]]],.]]=>13
[.,[[[[.,.],.],[[.,.],.]],.]]=>13
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>16
[.,[[[.,[[.,.],.]],[.,.]],.]]=>16
[.,[[[[.,.],[.,.]],[.,.]],.]]=>13
[.,[[[[.,[.,.]],.],[.,.]],.]]=>16
[.,[[[[[.,.],.],.],[.,.]],.]]=>16
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>21
[.,[[[.,[.,[[.,.],.]]],.],.]]=>21
[.,[[[.,[[.,.],[.,.]]],.],.]]=>18
[.,[[[.,[[.,[.,.]],.]],.],.]]=>21
[.,[[[.,[[[.,.],.],.]],.],.]]=>21
[.,[[[[.,.],[.,[.,.]]],.],.]]=>17
[.,[[[[.,.],[[.,.],.]],.],.]]=>17
[.,[[[[.,[.,.]],[.,.]],.],.]]=>17
[.,[[[[[.,.],.],[.,.]],.],.]]=>17
[.,[[[[.,[.,[.,.]]],.],.],.]]=>21
[.,[[[[.,[[.,.],.]],.],.],.]]=>21
[.,[[[[[.,.],[.,.]],.],.],.]]=>18
[.,[[[[[.,[.,.]],.],.],.],.]]=>21
[.,[[[[[[.,.],.],.],.],.],.]]=>21
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>14
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>14
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>11
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>14
[[.,.],[.,[.,[[[.,.],.],.]]]]=>14
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>10
[[.,.],[.,[[.,.],[[.,.],.]]]]=>10
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>10
[[.,.],[.,[[[.,.],.],[.,.]]]]=>10
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>14
[[.,.],[.,[[.,[[.,.],.]],.]]]=>14
[[.,.],[.,[[[.,.],[.,.]],.]]]=>11
[[.,.],[.,[[[.,[.,.]],.],.]]]=>14
[[.,.],[.,[[[[.,.],.],.],.]]]=>14
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>9
[[.,.],[[.,.],[.,[[.,.],.]]]]=>9
[[.,.],[[.,.],[[.,.],[.,.]]]]=>6
[[.,.],[[.,.],[[.,[.,.]],.]]]=>9
[[.,.],[[.,.],[[[.,.],.],.]]]=>9
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>6
[[.,.],[[.,[.,.]],[[.,.],.]]]=>6
[[.,.],[[[.,.],.],[.,[.,.]]]]=>6
[[.,.],[[[.,.],.],[[.,.],.]]]=>6
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>9
[[.,.],[[.,[[.,.],.]],[.,.]]]=>9
[[.,.],[[[.,.],[.,.]],[.,.]]]=>6
[[.,.],[[[.,[.,.]],.],[.,.]]]=>9
[[.,.],[[[[.,.],.],.],[.,.]]]=>9
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>14
[[.,.],[[.,[.,[[.,.],.]]],.]]=>14
[[.,.],[[.,[[.,.],[.,.]]],.]]=>11
[[.,.],[[.,[[.,[.,.]],.]],.]]=>14
[[.,.],[[.,[[[.,.],.],.]],.]]=>14
[[.,.],[[[.,.],[.,[.,.]]],.]]=>10
[[.,.],[[[.,.],[[.,.],.]],.]]=>10
[[.,.],[[[.,[.,.]],[.,.]],.]]=>10
[[.,.],[[[[.,.],.],[.,.]],.]]=>10
[[.,.],[[[.,[.,[.,.]]],.],.]]=>14
[[.,.],[[[.,[[.,.],.]],.],.]]=>14
[[.,.],[[[[.,.],[.,.]],.],.]]=>11
[[.,.],[[[[.,[.,.]],.],.],.]]=>14
[[.,.],[[[[[.,.],.],.],.],.]]=>14
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>9
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>9
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>6
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>9
[[.,[.,.]],[.,[[[.,.],.],.]]]=>9
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>5
[[.,[.,.]],[[.,.],[[.,.],.]]]=>5
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>5
[[.,[.,.]],[[[.,.],.],[.,.]]]=>5
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>9
[[.,[.,.]],[[.,[[.,.],.]],.]]=>9
[[.,[.,.]],[[[.,.],[.,.]],.]]=>6
[[.,[.,.]],[[[.,[.,.]],.],.]]=>9
[[.,[.,.]],[[[[.,.],.],.],.]]=>9
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>9
[[[.,.],.],[.,[.,[[.,.],.]]]]=>9
[[[.,.],.],[.,[[.,.],[.,.]]]]=>6
[[[.,.],.],[.,[[.,[.,.]],.]]]=>9
[[[.,.],.],[.,[[[.,.],.],.]]]=>9
[[[.,.],.],[[.,.],[.,[.,.]]]]=>5
[[[.,.],.],[[.,.],[[.,.],.]]]=>5
[[[.,.],.],[[.,[.,.]],[.,.]]]=>5
[[[.,.],.],[[[.,.],.],[.,.]]]=>5
[[[.,.],.],[[.,[.,[.,.]]],.]]=>9
[[[.,.],.],[[.,[[.,.],.]],.]]=>9
[[[.,.],.],[[[.,.],[.,.]],.]]=>6
[[[.,.],.],[[[.,[.,.]],.],.]]=>9
[[[.,.],.],[[[[.,.],.],.],.]]=>9
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>6
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>6
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>3
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>6
[[.,[.,[.,.]]],[[[.,.],.],.]]=>6
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>6
[[.,[[.,.],.]],[.,[[.,.],.]]]=>6
[[.,[[.,.],.]],[[.,.],[.,.]]]=>3
[[.,[[.,.],.]],[[.,[.,.]],.]]=>6
[[.,[[.,.],.]],[[[.,.],.],.]]=>6
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>3
[[[.,.],[.,.]],[.,[[.,.],.]]]=>3
[[[.,.],[.,.]],[[.,.],[.,.]]]=>0
[[[.,.],[.,.]],[[.,[.,.]],.]]=>3
[[[.,.],[.,.]],[[[.,.],.],.]]=>3
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>6
[[[.,[.,.]],.],[.,[[.,.],.]]]=>6
[[[.,[.,.]],.],[[.,.],[.,.]]]=>3
[[[.,[.,.]],.],[[.,[.,.]],.]]=>6
[[[.,[.,.]],.],[[[.,.],.],.]]=>6
[[[[.,.],.],.],[.,[.,[.,.]]]]=>6
[[[[.,.],.],.],[.,[[.,.],.]]]=>6
[[[[.,.],.],.],[[.,.],[.,.]]]=>3
[[[[.,.],.],.],[[.,[.,.]],.]]=>6
[[[[.,.],.],.],[[[.,.],.],.]]=>6
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>9
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>9
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>9
[[.,[.,[[.,.],.]]],[[.,.],.]]=>9
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>6
[[.,[[.,.],[.,.]]],[[.,.],.]]=>6
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>9
[[.,[[.,[.,.]],.]],[[.,.],.]]=>9
[[.,[[[.,.],.],.]],[.,[.,.]]]=>9
[[.,[[[.,.],.],.]],[[.,.],.]]=>9
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>5
[[[.,.],[.,[.,.]]],[[.,.],.]]=>5
[[[.,.],[[.,.],.]],[.,[.,.]]]=>5
[[[.,.],[[.,.],.]],[[.,.],.]]=>5
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>5
[[[.,[.,.]],[.,.]],[[.,.],.]]=>5
[[[[.,.],.],[.,.]],[.,[.,.]]]=>5
[[[[.,.],.],[.,.]],[[.,.],.]]=>5
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>9
[[[.,[.,[.,.]]],.],[[.,.],.]]=>9
[[[.,[[.,.],.]],.],[.,[.,.]]]=>9
[[[.,[[.,.],.]],.],[[.,.],.]]=>9
[[[[.,.],[.,.]],.],[.,[.,.]]]=>6
[[[[.,.],[.,.]],.],[[.,.],.]]=>6
[[[[.,[.,.]],.],.],[.,[.,.]]]=>9
[[[[.,[.,.]],.],.],[[.,.],.]]=>9
[[[[[.,.],.],.],.],[.,[.,.]]]=>9
[[[[[.,.],.],.],.],[[.,.],.]]=>9
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>14
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>14
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>11
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>14
[[.,[.,[[[.,.],.],.]]],[.,.]]=>14
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>10
[[.,[[.,.],[[.,.],.]]],[.,.]]=>10
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>10
[[.,[[[.,.],.],[.,.]]],[.,.]]=>10
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>14
[[.,[[.,[[.,.],.]],.]],[.,.]]=>14
[[.,[[[.,.],[.,.]],.]],[.,.]]=>11
[[.,[[[.,[.,.]],.],.]],[.,.]]=>14
[[.,[[[[.,.],.],.],.]],[.,.]]=>14
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>9
[[[.,.],[.,[[.,.],.]]],[.,.]]=>9
[[[.,.],[[.,.],[.,.]]],[.,.]]=>6
[[[.,.],[[.,[.,.]],.]],[.,.]]=>9
[[[.,.],[[[.,.],.],.]],[.,.]]=>9
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>6
[[[.,[.,.]],[[.,.],.]],[.,.]]=>6
[[[[.,.],.],[.,[.,.]]],[.,.]]=>6
[[[[.,.],.],[[.,.],.]],[.,.]]=>6
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>9
[[[.,[[.,.],.]],[.,.]],[.,.]]=>9
[[[[.,.],[.,.]],[.,.]],[.,.]]=>6
[[[[.,[.,.]],.],[.,.]],[.,.]]=>9
[[[[[.,.],.],.],[.,.]],[.,.]]=>9
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>14
[[[.,[.,[[.,.],.]]],.],[.,.]]=>14
[[[.,[[.,.],[.,.]]],.],[.,.]]=>11
[[[.,[[.,[.,.]],.]],.],[.,.]]=>14
[[[.,[[[.,.],.],.]],.],[.,.]]=>14
[[[[.,.],[.,[.,.]]],.],[.,.]]=>10
[[[[.,.],[[.,.],.]],.],[.,.]]=>10
[[[[.,[.,.]],[.,.]],.],[.,.]]=>10
[[[[[.,.],.],[.,.]],.],[.,.]]=>10
[[[[.,[.,[.,.]]],.],.],[.,.]]=>14
[[[[.,[[.,.],.]],.],.],[.,.]]=>14
[[[[[.,.],[.,.]],.],.],[.,.]]=>11
[[[[[.,[.,.]],.],.],.],[.,.]]=>14
[[[[[[.,.],.],.],.],.],[.,.]]=>14
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>21
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>21
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>18
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>21
[[.,[.,[.,[[[.,.],.],.]]]],.]=>21
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>17
[[.,[.,[[.,.],[[.,.],.]]]],.]=>17
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>17
[[.,[.,[[[.,.],.],[.,.]]]],.]=>17
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>21
[[.,[.,[[.,[[.,.],.]],.]]],.]=>21
[[.,[.,[[[.,.],[.,.]],.]]],.]=>18
[[.,[.,[[[.,[.,.]],.],.]]],.]=>21
[[.,[.,[[[[.,.],.],.],.]]],.]=>21
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>16
[[.,[[.,.],[.,[[.,.],.]]]],.]=>16
[[.,[[.,.],[[.,.],[.,.]]]],.]=>13
[[.,[[.,.],[[.,[.,.]],.]]],.]=>16
[[.,[[.,.],[[[.,.],.],.]]],.]=>16
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>13
[[.,[[.,[.,.]],[[.,.],.]]],.]=>13
[[.,[[[.,.],.],[.,[.,.]]]],.]=>13
[[.,[[[.,.],.],[[.,.],.]]],.]=>13
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>16
[[.,[[.,[[.,.],.]],[.,.]]],.]=>16
[[.,[[[.,.],[.,.]],[.,.]]],.]=>13
[[.,[[[.,[.,.]],.],[.,.]]],.]=>16
[[.,[[[[.,.],.],.],[.,.]]],.]=>16
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>21
[[.,[[.,[.,[[.,.],.]]],.]],.]=>21
[[.,[[.,[[.,.],[.,.]]],.]],.]=>18
[[.,[[.,[[.,[.,.]],.]],.]],.]=>21
[[.,[[.,[[[.,.],.],.]],.]],.]=>21
[[.,[[[.,.],[.,[.,.]]],.]],.]=>17
[[.,[[[.,.],[[.,.],.]],.]],.]=>17
[[.,[[[.,[.,.]],[.,.]],.]],.]=>17
[[.,[[[[.,.],.],[.,.]],.]],.]=>17
[[.,[[[.,[.,[.,.]]],.],.]],.]=>21
[[.,[[[.,[[.,.],.]],.],.]],.]=>21
[[.,[[[[.,.],[.,.]],.],.]],.]=>18
[[.,[[[[.,[.,.]],.],.],.]],.]=>21
[[.,[[[[[.,.],.],.],.],.]],.]=>21
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>15
[[[.,.],[.,[.,[[.,.],.]]]],.]=>15
[[[.,.],[.,[[.,.],[.,.]]]],.]=>12
[[[.,.],[.,[[.,[.,.]],.]]],.]=>15
[[[.,.],[.,[[[.,.],.],.]]],.]=>15
[[[.,.],[[.,.],[.,[.,.]]]],.]=>11
[[[.,.],[[.,.],[[.,.],.]]],.]=>11
[[[.,.],[[.,[.,.]],[.,.]]],.]=>11
[[[.,.],[[[.,.],.],[.,.]]],.]=>11
[[[.,.],[[.,[.,[.,.]]],.]],.]=>15
[[[.,.],[[.,[[.,.],.]],.]],.]=>15
[[[.,.],[[[.,.],[.,.]],.]],.]=>12
[[[.,.],[[[.,[.,.]],.],.]],.]=>15
[[[.,.],[[[[.,.],.],.],.]],.]=>15
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>11
[[[.,[.,.]],[.,[[.,.],.]]],.]=>11
[[[.,[.,.]],[[.,.],[.,.]]],.]=>8
[[[.,[.,.]],[[.,[.,.]],.]],.]=>11
[[[.,[.,.]],[[[.,.],.],.]],.]=>11
[[[[.,.],.],[.,[.,[.,.]]]],.]=>11
[[[[.,.],.],[.,[[.,.],.]]],.]=>11
[[[[.,.],.],[[.,.],[.,.]]],.]=>8
[[[[.,.],.],[[.,[.,.]],.]],.]=>11
[[[[.,.],.],[[[.,.],.],.]],.]=>11
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>11
[[[.,[.,[.,.]]],[[.,.],.]],.]=>11
[[[.,[[.,.],.]],[.,[.,.]]],.]=>11
[[[.,[[.,.],.]],[[.,.],.]],.]=>11
[[[[.,.],[.,.]],[.,[.,.]]],.]=>8
[[[[.,.],[.,.]],[[.,.],.]],.]=>8
[[[[.,[.,.]],.],[.,[.,.]]],.]=>11
[[[[.,[.,.]],.],[[.,.],.]],.]=>11
[[[[[.,.],.],.],[.,[.,.]]],.]=>11
[[[[[.,.],.],.],[[.,.],.]],.]=>11
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>15
[[[.,[.,[[.,.],.]]],[.,.]],.]=>15
[[[.,[[.,.],[.,.]]],[.,.]],.]=>12
[[[.,[[.,[.,.]],.]],[.,.]],.]=>15
[[[.,[[[.,.],.],.]],[.,.]],.]=>15
[[[[.,.],[.,[.,.]]],[.,.]],.]=>11
[[[[.,.],[[.,.],.]],[.,.]],.]=>11
[[[[.,[.,.]],[.,.]],[.,.]],.]=>11
[[[[[.,.],.],[.,.]],[.,.]],.]=>11
[[[[.,[.,[.,.]]],.],[.,.]],.]=>15
[[[[.,[[.,.],.]],.],[.,.]],.]=>15
[[[[[.,.],[.,.]],.],[.,.]],.]=>12
[[[[[.,[.,.]],.],.],[.,.]],.]=>15
[[[[[[.,.],.],.],.],[.,.]],.]=>15
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>21
[[[.,[.,[.,[[.,.],.]]]],.],.]=>21
[[[.,[.,[[.,.],[.,.]]]],.],.]=>18
[[[.,[.,[[.,[.,.]],.]]],.],.]=>21
[[[.,[.,[[[.,.],.],.]]],.],.]=>21
[[[.,[[.,.],[.,[.,.]]]],.],.]=>17
[[[.,[[.,.],[[.,.],.]]],.],.]=>17
[[[.,[[.,[.,.]],[.,.]]],.],.]=>17
[[[.,[[[.,.],.],[.,.]]],.],.]=>17
[[[.,[[.,[.,[.,.]]],.]],.],.]=>21
[[[.,[[.,[[.,.],.]],.]],.],.]=>21
[[[.,[[[.,.],[.,.]],.]],.],.]=>18
[[[.,[[[.,[.,.]],.],.]],.],.]=>21
[[[.,[[[[.,.],.],.],.]],.],.]=>21
[[[[.,.],[.,[.,[.,.]]]],.],.]=>16
[[[[.,.],[.,[[.,.],.]]],.],.]=>16
[[[[.,.],[[.,.],[.,.]]],.],.]=>13
[[[[.,.],[[.,[.,.]],.]],.],.]=>16
[[[[.,.],[[[.,.],.],.]],.],.]=>16
[[[[.,[.,.]],[.,[.,.]]],.],.]=>13
[[[[.,[.,.]],[[.,.],.]],.],.]=>13
[[[[[.,.],.],[.,[.,.]]],.],.]=>13
[[[[[.,.],.],[[.,.],.]],.],.]=>13
[[[[.,[.,[.,.]]],[.,.]],.],.]=>16
[[[[.,[[.,.],.]],[.,.]],.],.]=>16
[[[[[.,.],[.,.]],[.,.]],.],.]=>13
[[[[[.,[.,.]],.],[.,.]],.],.]=>16
[[[[[[.,.],.],.],[.,.]],.],.]=>16
[[[[.,[.,[.,[.,.]]]],.],.],.]=>21
[[[[.,[.,[[.,.],.]]],.],.],.]=>21
[[[[.,[[.,.],[.,.]]],.],.],.]=>18
[[[[.,[[.,[.,.]],.]],.],.],.]=>21
[[[[.,[[[.,.],.],.]],.],.],.]=>21
[[[[[.,.],[.,[.,.]]],.],.],.]=>17
[[[[[.,.],[[.,.],.]],.],.],.]=>17
[[[[[.,[.,.]],[.,.]],.],.],.]=>17
[[[[[[.,.],.],[.,.]],.],.],.]=>17
[[[[[.,[.,[.,.]]],.],.],.],.]=>21
[[[[[.,[[.,.],.]],.],.],.],.]=>21
[[[[[[.,.],[.,.]],.],.],.],.]=>18
[[[[[[.,[.,.]],.],.],.],.],.]=>21
[[[[[[[.,.],.],.],.],.],.],.]=>21
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>28
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>28
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>25
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>28
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>28
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>24
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>24
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>24
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>24
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>28
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>28
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>25
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>28
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>28
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>23
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>23
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>20
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>23
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>23
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>20
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>20
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>20
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>20
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>23
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>23
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>20
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>23
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>23
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>28
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>28
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>25
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>28
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>28
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>24
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>24
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>24
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>24
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>28
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>28
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>25
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>28
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>28
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>22
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>22
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>19
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>22
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>22
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>18
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>18
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>18
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>18
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>22
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>22
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>19
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>22
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>22
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>18
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>18
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>15
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>18
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>18
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>18
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>18
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[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>18
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>18
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[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>18
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[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>15
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>15
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[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>18
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>18
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>18
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[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>22
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[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>22
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>22
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[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>28
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[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>25
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>28
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>28
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>24
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>24
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>24
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>24
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>28
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[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>28
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[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>20
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[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>28
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>28
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>24
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>24
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>24
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>24
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>28
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>28
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>25
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>28
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>28
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[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>21
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[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>17
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>17
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[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>21
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[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>21
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[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>21
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[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>21
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>21
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>17
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>17
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>17
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[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>10
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>10
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>10
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>7
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[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>10
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[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>10
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>10
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[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>20
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>20
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>17
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>20
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>20
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>16
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>16
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>16
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>16
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>20
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>20
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>17
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>20
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>20
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>15
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>15
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>12
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>15
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>15
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>12
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>12
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>12
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>12
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>15
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>15
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>12
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>15
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>15
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>20
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>20
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>17
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>20
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>20
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>16
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>16
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>16
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>16
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>20
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>20
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>17
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>20
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>20
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>14
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>14
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>11
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>14
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>14
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>10
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>10
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>10
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>10
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>14
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>14
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>11
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>14
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>14
                    

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Description

The Colless index of a binary tree.
The Colless index is the sum of the absolute values of the differences of the number of leaves in the left and the right subtree over all internal nodes.

References

[1] Coronado, T. M., Rosselló, F. The minimum value of the Colless index arXiv:1903.11670

Code

def statistic(B):
    return sum(abs(t[0].node_number()-t[1].node_number()) for t in B.subtrees())

Created

Mar 29, 2019 at 10:03 by Martin Rubey

Updated

Mar 29, 2019 at 10:03 by Martin Rubey