Identifier
Values
[1] => [1,0,1,0] => [[.,.],.] => ([(0,1)],2) => 1
[2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => ([(0,2),(2,1)],3) => 1
[1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => ([(0,2),(1,2)],3) => 2
[3] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => ([(0,3),(2,1),(3,2)],4) => 1
[2,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => ([(0,2),(2,1)],3) => 1
[1,1,1] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4) => 2
[4] => [1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,1] => [1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => ([(0,3),(2,1),(3,2)],4) => 1
[2,2] => [1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4) => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,2] => [1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => ([(0,3),(2,1),(3,2)],4) => 1
[3,1,1] => [1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => ([(0,3),(1,3),(3,2)],4) => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4) => 2
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => 2
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4) => 1
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 2
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 2
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 3
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 2
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => 2
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 2
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9) => 2
[7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
>>> Load all 563 entries. <<<
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 3
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 3
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 3
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[8,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,1,1,1] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9) => 2
[7,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,2,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,2,1,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,.]],.]]],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 2
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 3
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[.,.],[.,[[[.,.],[.,.]],.]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 3
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 3
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[9,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,3,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,2,2] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9) => 2
[7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,4,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,3,1,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[7,2,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 2
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 2
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 3
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[8,3,2] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,2,2,1] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9) => 2
[7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,4,1,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[.,.]]]],.],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 3
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 3
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 2
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 3
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 2
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[9,3,2] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,1,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[7,4,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,4,2,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[[.,.],.],.]],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,4,1,1,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[.,.]]],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],.],.]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[.,.],[.,[.,.]]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 2
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],.]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 2
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],[.,.]]]]],.],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[7,5,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[[.,.],.],.]]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,4,3,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[[.,.],.]],.],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,4,2,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,4,2,1,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,.],.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],[.,.]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],.]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],.],.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,.]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,5,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,2,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,5,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,4,3,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[.,.]],.],.],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,4,3,1,1] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],[.,.]],.],.]]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[7,4,2,2,1] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],.],[.,.]],.]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],[.,.]],.]],.],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[.,.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[[.,.],.]]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 3
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],.],.],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],[.,.]],.]],.] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 3
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 3
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,.],.],[.,.]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 4
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[9,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,5,4] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[[.,.],.]],.]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,5,4,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[[.,.],.]]],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,3,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[7,5,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[.,.]]],.],.],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],.],.],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,[.,.]],.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[.,.]]],.],.] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[.,.],.],.],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 3
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],[.,.]]],.] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 3
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[.,.],.],.],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[.,.],.],[[.,.],.]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[[.,.],.],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[.,.],.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,[.,.]]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,.]],.],.],.],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,.]],.],[.,.]],.] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 3
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[.,.]],[.,.]],.],.] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],[.,.]],[[.,.],.]],.] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 3
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[[.,.],.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[.,.],.],.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,.]]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,.]],.],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[.,.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],[[.,.],.]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,.],.]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,.],.]],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],.],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[.,.],.],.]],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[[.,.],.],.],.],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],.],[.,.]]],.],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2
[7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,.],[.,.]]],.],.],.],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2
[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,[.,.]],.]],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,[.,.]],.],.]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,[.,.]],.],.],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[[.,.],.]]],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[[.,.],.],.]]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[[.,.],.],.]],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[[.,.],.],.]],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[[.,.],.],.],.]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,5,4,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
[8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[9,8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[9,7,5,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[[.,.],.],.],.]],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9) => 2
[9,7,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,5,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[[[.,.],.],.],.],.],.]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[[[.,.],.],.],.],.]]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,6,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[[[.,.],.],.],.]]],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[[[.,.],.],.]]],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9) => 2
[8,7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9) => 2
[9,8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[8,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[9,8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[9,8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
[9,8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
[8,7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,[.,.]],.]],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
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Description
The number of maximal chains in a poset.
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 poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.