Identifier
Values
[1,0,1,0] => [[.,.],.] => [1,2] => ([(0,1)],2) => 3
[1,1,0,0] => [.,[.,.]] => [2,1] => ([],2) => 2
[1,0,1,0,1,0] => [[[.,.],.],.] => [1,2,3] => ([(0,2),(2,1)],3) => 5
[1,0,1,1,0,0] => [[.,.],[.,.]] => [3,1,2] => ([(1,2)],3) => 4
[1,1,0,0,1,0] => [[.,[.,.]],.] => [2,1,3] => ([(0,2),(1,2)],3) => 5
[1,1,0,1,0,0] => [.,[[.,.],.]] => [2,3,1] => ([(1,2)],3) => 4
[1,1,1,0,0,0] => [.,[.,[.,.]]] => [3,2,1] => ([],3) => 3
[1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 7
[1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 6
[1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 7
[1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 6
[1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => [4,3,1,2] => ([(2,3)],4) => 5
[1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 7
[1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 6
[1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4) => 7
[1,1,0,1,0,1,0,0] => [.,[[[.,.],.],.]] => [2,3,4,1] => ([(1,2),(2,3)],4) => 6
[1,1,0,1,1,0,0,0] => [.,[[.,.],[.,.]]] => [4,2,3,1] => ([(2,3)],4) => 5
[1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 7
[1,1,1,0,0,1,0,0] => [.,[[.,[.,.]],.]] => [3,2,4,1] => ([(1,3),(2,3)],4) => 6
[1,1,1,0,1,0,0,0] => [.,[.,[[.,.],.]]] => [3,4,2,1] => ([(2,3)],4) => 5
[1,1,1,1,0,0,0,0] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => ([],4) => 4
[1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 9
[1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 8
[1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 9
[1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 8
[1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 7
[1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 9
[1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 8
[1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 9
[1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5) => 8
[1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 7
[1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 9
[1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 8
[1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 7
[1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => ([(3,4)],5) => 6
[1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 9
[1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 8
[1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 9
[1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => 8
[1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 7
[1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 9
[1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5) => 8
[1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 9
[1,1,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => 8
[1,1,0,1,0,1,1,0,0,0] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 7
[1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 9
[1,1,0,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5) => 8
[1,1,0,1,1,0,1,0,0,0] => [.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 7
[1,1,0,1,1,1,0,0,0,0] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => ([(3,4)],5) => 6
[1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 9
[1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 8
[1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 9
[1,1,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5) => 8
[1,1,1,0,0,1,1,0,0,0] => [.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 7
[1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 9
[1,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5) => 8
[1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 7
[1,1,1,0,1,1,0,0,0,0] => [.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => ([(3,4)],5) => 6
[1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 9
[1,1,1,1,0,0,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 8
[1,1,1,1,0,0,1,0,0,0] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 7
[1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => ([(3,4)],5) => 6
[1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => ([],5) => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 11
[1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 10
[1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 11
[1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 10
[1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6) => 9
[1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 11
[1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 10
[1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 11
[1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 10
[1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 9
[1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 11
[1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 10
[1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 9
[1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 8
[1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 11
[1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 10
[1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 11
[1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 10
[1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => ([(2,5),(3,4),(4,5)],6) => 9
[1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 11
[1,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => 10
[1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 11
[1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6) => 10
[1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6) => 9
[1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 11
[1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 10
[1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6) => 9
[1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => 8
[1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 11
[1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 10
[1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 11
[1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => ([(0,5),(1,5),(2,3),(5,4)],6) => 10
[1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6) => 9
[1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 11
[1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 10
[1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => ([(1,3),(2,4),(4,5)],6) => 9
[1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 8
[1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 11
>>> Load all 473 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => ([(0,5),(1,5),(2,5),(3,4)],6) => 10
[1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => ([(1,5),(2,5),(3,4)],6) => 9
[1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 8
[1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => ([(4,5)],6) => 7
[1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 11
[1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6) => 10
[1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 11
[1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => ([(0,5),(1,5),(2,3),(5,4)],6) => 10
[1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => ([(2,5),(3,5),(5,4)],6) => 9
[1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 11
[1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 10
[1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 11
[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 10
[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 9
[1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 11
[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6) => 10
[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 9
[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 8
[1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 11
[1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 10
[1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 11
[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 10
[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => ([(2,5),(3,4),(4,5)],6) => 9
[1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 11
[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 10
[1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 11
[1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => 10
[1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => 9
[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 11
[1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 10
[1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => ([(1,3),(2,4),(4,5)],6) => 9
[1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => ([(3,4),(4,5)],6) => 8
[1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 11
[1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 10
[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 11
[1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 10
[1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => ([(2,5),(3,4),(4,5)],6) => 9
[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 11
[1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6) => 10
[1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6) => 9
[1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 8
[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 11
[1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 10
[1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => ([(1,5),(2,5),(3,4)],6) => 9
[1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 8
[1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => ([(4,5)],6) => 7
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 11
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6) => 10
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 11
[1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6) => 10
[1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => ([(2,5),(3,5),(4,5)],6) => 9
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 11
[1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 10
[1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 11
[1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6) => 10
[1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6) => 9
[1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 11
[1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 10
[1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6) => 9
[1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => 8
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 11
[1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 10
[1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 11
[1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 10
[1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6) => 9
[1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 11
[1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 10
[1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6) => 9
[1,1,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 8
[1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 11
[1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 10
[1,1,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 9
[1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 8
[1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => ([(4,5)],6) => 7
[1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 11
[1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 10
[1,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 11
[1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => 10
[1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => 9
[1,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 11
[1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 10
[1,1,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => ([(2,5),(3,5),(5,4)],6) => 9
[1,1,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 8
[1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 11
[1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 10
[1,1,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 9
[1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 8
[1,1,1,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => ([(4,5)],6) => 7
[1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 11
[1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6) => 10
[1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6) => 9
[1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 8
[1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => ([(4,5)],6) => 7
[1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => ([],6) => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 13
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 12
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 13
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 12
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 10
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 13
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 12
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 13
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 12
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 11
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 13
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 12
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 11
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7) => 9
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 13
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 13
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 12
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 12
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => ([(0,6),(1,6),(2,5),(3,4)],7) => 11
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7) => 9
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 13
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 12
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 13
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 12
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 11
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 13
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 12
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 13
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 12
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => 11
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 12
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => ([(0,6),(1,6),(2,5),(3,4)],7) => 11
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => ([(2,6),(3,6),(4,5)],7) => 10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 12
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => ([(3,6),(4,5)],7) => 9
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 13
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 12
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 13
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 12
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 12
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => 11
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 10
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => ([(3,6),(4,5)],7) => 9
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 12
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 10
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => ([(3,6),(4,5)],7) => 9
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => ([(5,6)],7) => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 13
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 12
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 13
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 12
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => ([(2,6),(3,6),(4,5),(6,4)],7) => 11
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 13
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 12
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 13
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 12
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => 11
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 13
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => ([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 12
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => 11
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => ([(3,6),(4,6),(6,5)],7) => 10
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 13
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 12
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 13
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 12
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => 11
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 13
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 12
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 13
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 12
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 11
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 12
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => ([(0,6),(1,6),(2,5),(3,4)],7) => 11
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 10
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 12
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 13
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => ([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 12
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 11
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 12
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 11
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 10
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 13
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 12
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 11
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 10
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => ([(4,6),(5,6)],7) => 9
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 13
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 13
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 12
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 13
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 12
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 13
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 12
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => ([(3,4),(4,6),(6,5)],7) => 10
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 13
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 12
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 13
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 12
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 11
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => ([(4,5),(5,6)],7) => 9
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 13
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 12
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 13
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 12
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 11
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 13
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 13
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => ([(3,6),(4,5)],7) => 9
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 13
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 12
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 13
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 12
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 11
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 12
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => ([(1,6),(2,6),(3,4),(6,5)],7) => 11
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => ([(2,6),(3,6),(4,5)],7) => 10
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => ([(3,6),(4,5)],7) => 9
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 12
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => ([(2,6),(3,6),(4,5)],7) => 10
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => ([(3,6),(4,5)],7) => 9
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => ([(5,6)],7) => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 13
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 12
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 13
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 12
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => ([(2,6),(3,6),(4,6),(6,5)],7) => 11
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 13
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 12
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 13
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 12
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 13
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 12
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => ([(3,6),(4,6),(5,6)],7) => 10
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 13
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 12
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 13
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 12
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => 11
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 13
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 12
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 13
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 12
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => 11
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 13
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 12
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => ([(1,6),(2,6),(3,4),(6,5)],7) => 11
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => ([(3,6),(4,6),(6,5)],7) => 10
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 13
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 12
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 13
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 12
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 11
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 12
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 11
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => ([(2,6),(3,6),(4,5)],7) => 10
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 13
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 12
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => ([(1,6),(2,6),(3,5),(4,5)],7) => 11
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => ([(2,6),(3,6),(4,5)],7) => 10
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => ([(4,6),(5,6)],7) => 9
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 13
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 12
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 13
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 12
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 11
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 13
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 13
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 13
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 12
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 13
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 12
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => ([(3,4),(4,6),(6,5)],7) => 10
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 13
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 12
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => ([(4,5),(5,6)],7) => 9
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 13
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 12
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 13
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 12
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 11
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 13
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 13
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => ([(3,6),(4,5)],7) => 9
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 12
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 11
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => ([(2,6),(3,6),(4,5)],7) => 10
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => ([(3,6),(4,5)],7) => 9
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => ([(5,6)],7) => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 13
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 12
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 13
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 12
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => ([(2,6),(3,6),(4,6),(5,6)],7) => 11
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 13
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 12
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 13
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 12
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => ([(2,6),(3,6),(4,6),(6,5)],7) => 11
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 13
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 12
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => ([(3,6),(4,6),(5,6)],7) => 10
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 13
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 12
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 13
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 12
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 11
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 13
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 12
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => 11
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => ([(3,6),(4,6),(6,5)],7) => 10
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 13
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 12
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 11
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => ([(2,6),(3,6),(4,5)],7) => 10
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => ([(4,6),(5,6)],7) => 9
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 13
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 12
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 13
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 12
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 11
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 13
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 13
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 12
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => ([(3,4),(4,6),(6,5)],7) => 10
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => ([(4,5),(5,6)],7) => 9
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 12
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 11
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => ([(3,6),(4,5)],7) => 9
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 13
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 12
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 13
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 12
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => 11
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 13
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 12
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => ([(2,6),(3,6),(4,6),(6,5)],7) => 11
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7) => 10
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 13
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 12
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 11
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => ([(3,6),(4,6),(6,5)],7) => 10
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => ([(4,6),(5,6)],7) => 9
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 12
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 11
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => ([(4,5),(5,6)],7) => 9
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => ([(5,6)],7) => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 13
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 12
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => 11
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => ([(3,6),(4,6),(5,6)],7) => 10
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => 9
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => ([(5,6)],7) => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => ([],7) => 7
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Description
The number of non-empty boolean intervals in a poset.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
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.