Identifier
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Images
[1,0] => [(1,2)] => [2,1] => [2,1]
[1,0,1,0] => [(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3]
[1,1,0,0] => [(1,4),(2,3)] => [4,3,2,1] => [3,2,4,1]
[1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5]
[1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,5,4,6,3]
[1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [3,2,4,1,6,5]
[1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [3,2,5,4,6,1]
[1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [4,3,5,2,6,1]
[1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7]
[1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,8,5]
[1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,5,4,6,3,8,7]
[1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [2,1,5,4,7,6,8,3]
[1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [2,1,6,5,7,4,8,3]
[1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [3,2,4,1,6,5,8,7]
[1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [3,2,4,1,7,6,8,5]
[1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [3,2,5,4,6,1,8,7]
[1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [3,2,5,4,7,6,8,1]
[1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [3,2,6,5,7,4,8,1]
[1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [4,3,5,2,6,1,8,7]
[1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [4,3,5,2,7,6,8,1]
[1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [4,3,6,5,7,2,8,1]
[1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1]
[1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9]
[1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,9,8,10,7]
[1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,7,6,8,5,10,9]
[1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => [2,1,4,3,7,6,9,8,10,5]
[1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,8,7,9,6,10,5]
[1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [2,1,5,4,6,3,8,7,10,9]
[1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [2,1,5,4,6,3,9,8,10,7]
[1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => [2,1,5,4,7,6,8,3,10,9]
[1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,10,5,4,7,6,9,8,3] => [2,1,5,4,7,6,9,8,10,3]
[1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,10,5,4,9,8,7,6,3] => [2,1,5,4,8,7,9,6,10,3]
[1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [2,1,6,5,7,4,8,3,10,9]
[1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => [2,1,6,5,7,4,9,8,10,3]
[1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [2,1,6,5,8,7,9,4,10,3]
[1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [2,1,7,6,8,5,9,4,10,3]
[1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [3,2,4,1,6,5,8,7,10,9]
[1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [3,2,4,1,6,5,9,8,10,7]
[1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [3,2,4,1,7,6,8,5,10,9]
[1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => [4,3,2,1,10,7,6,9,8,5] => [3,2,4,1,7,6,9,8,10,5]
[1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [3,2,4,1,8,7,9,6,10,5]
[1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => [3,2,5,4,6,1,8,7,10,9]
[1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => [3,2,5,4,6,1,9,8,10,7]
[1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => [8,3,2,5,4,7,6,1,10,9] => [3,2,5,4,7,6,8,1,10,9]
[1,1,0,1,0,1,0,1,0,0] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => [10,3,2,5,4,7,6,9,8,1] => [3,2,5,4,7,6,9,8,10,1]
[1,1,0,1,0,1,1,0,0,0] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => [10,3,2,5,4,9,8,7,6,1] => [3,2,5,4,8,7,9,6,10,1]
[1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => [3,2,6,5,7,4,8,1,10,9]
[1,1,0,1,1,0,0,1,0,0] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => [10,3,2,7,6,5,4,9,8,1] => [3,2,6,5,7,4,9,8,10,1]
[1,1,0,1,1,0,1,0,0,0] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => [3,2,6,5,8,7,9,4,10,1]
[1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [3,2,7,6,8,5,9,4,10,1]
[1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [4,3,5,2,6,1,8,7,10,9]
[1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [4,3,5,2,6,1,9,8,10,7]
[1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => [4,3,5,2,7,6,8,1,10,9]
[1,1,1,0,0,1,0,1,0,0] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => [10,5,4,3,2,7,6,9,8,1] => [4,3,5,2,7,6,9,8,10,1]
[1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => [4,3,5,2,8,7,9,6,10,1]
[1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [4,3,6,5,7,2,8,1,10,9]
[1,1,1,0,1,0,0,1,0,0] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => [4,3,6,5,7,2,9,8,10,1]
[1,1,1,0,1,0,1,0,0,0] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => [10,9,4,3,6,5,8,7,2,1] => [4,3,6,5,8,7,9,2,10,1]
[1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [4,3,7,6,8,5,9,2,10,1]
[1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [5,4,6,3,7,2,8,1,10,9]
[1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [5,4,6,3,7,2,9,8,10,1]
[1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [5,4,6,3,8,7,9,2,10,1]
[1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [5,4,7,6,8,3,9,2,10,1]
[1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [6,5,7,4,8,3,9,2,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11]
[1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,11,10,12,9]
[1,0,1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,1,4,3,6,5,9,8,10,7,12,11]
[1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,12,9,8,11,10,7] => [2,1,4,3,6,5,9,8,11,10,12,7]
[1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,1,4,3,6,5,10,9,11,8,12,7]
[1,0,1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,1,4,3,7,6,8,5,10,9,12,11]
[1,0,1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,7,6,8,5,11,10,12,9]
[1,0,1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,10,7,6,9,8,5,12,11] => [2,1,4,3,7,6,9,8,10,5,12,11]
[1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,12,7,6,9,8,11,10,5] => [2,1,4,3,7,6,9,8,11,10,12,5]
[1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,12,7,6,11,10,9,8,5] => [2,1,4,3,7,6,10,9,11,8,12,5]
[1,0,1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,1,4,3,8,7,9,6,10,5,12,11]
[1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => [2,1,4,3,8,7,9,6,11,10,12,5]
[1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [2,1,4,3,8,7,10,9,11,6,12,5]
[1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,9,8,10,7,11,6,12,5]
[1,0,1,1,0,0,1,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,5,4,6,3,8,7,10,9,12,11]
[1,0,1,1,0,0,1,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,5,4,6,3,8,7,11,10,12,9]
[1,0,1,1,0,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,5,4,6,3,9,8,10,7,12,11]
[1,0,1,1,0,0,1,1,0,1,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,6,5,4,3,12,9,8,11,10,7] => [2,1,5,4,6,3,9,8,11,10,12,7]
[1,0,1,1,0,0,1,1,1,0,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,5,4,6,3,10,9,11,8,12,7]
[1,0,1,1,0,1,0,0,1,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,8,5,4,7,6,3,10,9,12,11] => [2,1,5,4,7,6,8,3,10,9,12,11]
[1,0,1,1,0,1,0,0,1,1,0,0] => [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,8,5,4,7,6,3,12,11,10,9] => [2,1,5,4,7,6,8,3,11,10,12,9]
[1,0,1,1,0,1,0,1,0,0,1,0] => [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,10,5,4,7,6,9,8,3,12,11] => [2,1,5,4,7,6,9,8,10,3,12,11]
[1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,12,5,4,7,6,9,8,11,10,3] => [2,1,5,4,7,6,9,8,11,10,12,3]
[1,0,1,1,0,1,0,1,1,0,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,12,5,4,7,6,11,10,9,8,3] => [2,1,5,4,7,6,10,9,11,8,12,3]
[1,0,1,1,0,1,1,0,0,0,1,0] => [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,10,5,4,9,8,7,6,3,12,11] => [2,1,5,4,8,7,9,6,10,3,12,11]
[1,0,1,1,0,1,1,0,0,1,0,0] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,12,5,4,9,8,7,6,11,10,3] => [2,1,5,4,8,7,9,6,11,10,12,3]
[1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,12,5,4,11,8,7,10,9,6,3] => [2,1,5,4,8,7,10,9,11,6,12,3]
[1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,12,5,4,11,10,9,8,7,6,3] => [2,1,5,4,9,8,10,7,11,6,12,3]
[1,0,1,1,1,0,0,0,1,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,6,5,7,4,8,3,10,9,12,11]
[1,0,1,1,1,0,0,0,1,1,0,0] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,6,5,7,4,8,3,11,10,12,9]
[1,0,1,1,1,0,0,1,0,0,1,0] => [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,10,7,6,5,4,9,8,3,12,11] => [2,1,6,5,7,4,9,8,10,3,12,11]
[1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,12,7,6,5,4,9,8,11,10,3] => [2,1,6,5,7,4,9,8,11,10,12,3]
[1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,12,7,6,5,4,11,10,9,8,3] => [2,1,6,5,7,4,10,9,11,8,12,3]
[1,0,1,1,1,0,1,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [2,1,6,5,8,7,9,4,10,3,12,11]
[1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,12,9,6,5,8,7,4,11,10,3] => [2,1,6,5,8,7,9,4,11,10,12,3]
[1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,12,11,6,5,8,7,10,9,4,3] => [2,1,6,5,8,7,10,9,11,4,12,3]
[1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [2,1,6,5,9,8,10,7,11,4,12,3]
>>> Load all 454 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,7,6,8,5,9,4,10,3,12,11]
[1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => [2,1,7,6,8,5,9,4,11,10,12,3]
[1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [2,1,7,6,8,5,10,9,11,4,12,3]
[1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [2,1,7,6,9,8,10,5,11,4,12,3]
[1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,8,7,9,6,10,5,11,4,12,3]
[1,1,0,0,1,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [3,2,4,1,6,5,8,7,10,9,12,11]
[1,1,0,0,1,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [3,2,4,1,6,5,8,7,11,10,12,9]
[1,1,0,0,1,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [3,2,4,1,6,5,9,8,10,7,12,11]
[1,1,0,0,1,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [4,3,2,1,6,5,12,9,8,11,10,7] => [3,2,4,1,6,5,9,8,11,10,12,7]
[1,1,0,0,1,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [3,2,4,1,6,5,10,9,11,8,12,7]
[1,1,0,0,1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [3,2,4,1,7,6,8,5,10,9,12,11]
[1,1,0,0,1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [3,2,4,1,7,6,8,5,11,10,12,9]
[1,1,0,0,1,1,0,1,0,0,1,0] => [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [4,3,2,1,10,7,6,9,8,5,12,11] => [3,2,4,1,7,6,9,8,10,5,12,11]
[1,1,0,0,1,1,0,1,0,1,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [4,3,2,1,12,7,6,9,8,11,10,5] => [3,2,4,1,7,6,9,8,11,10,12,5]
[1,1,0,0,1,1,0,1,1,0,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => [3,2,4,1,7,6,10,9,11,8,12,5]
[1,1,0,0,1,1,1,0,0,0,1,0] => [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [3,2,4,1,8,7,9,6,10,5,12,11]
[1,1,0,0,1,1,1,0,0,1,0,0] => [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [4,3,2,1,12,9,8,7,6,11,10,5] => [3,2,4,1,8,7,9,6,11,10,12,5]
[1,1,0,0,1,1,1,0,1,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [3,2,4,1,8,7,10,9,11,6,12,5]
[1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [3,2,4,1,9,8,10,7,11,6,12,5]
[1,1,0,1,0,0,1,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [6,3,2,5,4,1,8,7,10,9,12,11] => [3,2,5,4,6,1,8,7,10,9,12,11]
[1,1,0,1,0,0,1,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [6,3,2,5,4,1,8,7,12,11,10,9] => [3,2,5,4,6,1,8,7,11,10,12,9]
[1,1,0,1,0,0,1,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [6,3,2,5,4,1,10,9,8,7,12,11] => [3,2,5,4,6,1,9,8,10,7,12,11]
[1,1,0,1,0,0,1,1,0,1,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [6,3,2,5,4,1,12,9,8,11,10,7] => [3,2,5,4,6,1,9,8,11,10,12,7]
[1,1,0,1,0,0,1,1,1,0,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => [3,2,5,4,6,1,10,9,11,8,12,7]
[1,1,0,1,0,1,0,0,1,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [8,3,2,5,4,7,6,1,10,9,12,11] => [3,2,5,4,7,6,8,1,10,9,12,11]
[1,1,0,1,0,1,0,0,1,1,0,0] => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [8,3,2,5,4,7,6,1,12,11,10,9] => [3,2,5,4,7,6,8,1,11,10,12,9]
[1,1,0,1,0,1,0,1,0,0,1,0] => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [10,3,2,5,4,7,6,9,8,1,12,11] => [3,2,5,4,7,6,9,8,10,1,12,11]
[1,1,0,1,0,1,0,1,0,1,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [12,3,2,5,4,7,6,9,8,11,10,1] => [3,2,5,4,7,6,9,8,11,10,12,1]
[1,1,0,1,0,1,0,1,1,0,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [12,3,2,5,4,7,6,11,10,9,8,1] => [3,2,5,4,7,6,10,9,11,8,12,1]
[1,1,0,1,0,1,1,0,0,0,1,0] => [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [10,3,2,5,4,9,8,7,6,1,12,11] => [3,2,5,4,8,7,9,6,10,1,12,11]
[1,1,0,1,0,1,1,0,0,1,0,0] => [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [12,3,2,5,4,9,8,7,6,11,10,1] => [3,2,5,4,8,7,9,6,11,10,12,1]
[1,1,0,1,0,1,1,0,1,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [12,3,2,5,4,11,8,7,10,9,6,1] => [3,2,5,4,8,7,10,9,11,6,12,1]
[1,1,0,1,0,1,1,1,0,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [12,3,2,5,4,11,10,9,8,7,6,1] => [3,2,5,4,9,8,10,7,11,6,12,1]
[1,1,0,1,1,0,0,0,1,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => [3,2,6,5,7,4,8,1,10,9,12,11]
[1,1,0,1,1,0,0,0,1,1,0,0] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => [3,2,6,5,7,4,8,1,11,10,12,9]
[1,1,0,1,1,0,0,1,0,0,1,0] => [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [10,3,2,7,6,5,4,9,8,1,12,11] => [3,2,6,5,7,4,9,8,10,1,12,11]
[1,1,0,1,1,0,0,1,0,1,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [12,3,2,7,6,5,4,9,8,11,10,1] => [3,2,6,5,7,4,9,8,11,10,12,1]
[1,1,0,1,1,0,0,1,1,0,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [12,3,2,7,6,5,4,11,10,9,8,1] => [3,2,6,5,7,4,10,9,11,8,12,1]
[1,1,0,1,1,0,1,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [10,3,2,9,6,5,8,7,4,1,12,11] => [3,2,6,5,8,7,9,4,10,1,12,11]
[1,1,0,1,1,0,1,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [12,3,2,9,6,5,8,7,4,11,10,1] => [3,2,6,5,8,7,9,4,11,10,12,1]
[1,1,0,1,1,0,1,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [12,3,2,11,6,5,8,7,10,9,4,1] => [3,2,6,5,8,7,10,9,11,4,12,1]
[1,1,0,1,1,0,1,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [12,3,2,11,6,5,10,9,8,7,4,1] => [3,2,6,5,9,8,10,7,11,4,12,1]
[1,1,0,1,1,1,0,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => [3,2,7,6,8,5,9,4,10,1,12,11]
[1,1,0,1,1,1,0,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [12,3,2,9,8,7,6,5,4,11,10,1] => [3,2,7,6,8,5,9,4,11,10,12,1]
[1,1,0,1,1,1,0,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [12,3,2,11,8,7,6,5,10,9,4,1] => [3,2,7,6,8,5,10,9,11,4,12,1]
[1,1,0,1,1,1,0,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [12,3,2,11,10,7,6,9,8,5,4,1] => [3,2,7,6,9,8,10,5,11,4,12,1]
[1,1,0,1,1,1,1,0,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [12,3,2,11,10,9,8,7,6,5,4,1] => [3,2,8,7,9,6,10,5,11,4,12,1]
[1,1,1,0,0,0,1,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [4,3,5,2,6,1,8,7,10,9,12,11]
[1,1,1,0,0,0,1,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [4,3,5,2,6,1,8,7,11,10,12,9]
[1,1,1,0,0,0,1,1,0,0,1,0] => [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [4,3,5,2,6,1,9,8,10,7,12,11]
[1,1,1,0,0,0,1,1,0,1,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [6,5,4,3,2,1,12,9,8,11,10,7] => [4,3,5,2,6,1,9,8,11,10,12,7]
[1,1,1,0,0,0,1,1,1,0,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [4,3,5,2,6,1,10,9,11,8,12,7]
[1,1,1,0,0,1,0,0,1,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [8,5,4,3,2,7,6,1,10,9,12,11] => [4,3,5,2,7,6,8,1,10,9,12,11]
[1,1,1,0,0,1,0,0,1,1,0,0] => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [8,5,4,3,2,7,6,1,12,11,10,9] => [4,3,5,2,7,6,8,1,11,10,12,9]
[1,1,1,0,0,1,0,1,0,0,1,0] => [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [10,5,4,3,2,7,6,9,8,1,12,11] => [4,3,5,2,7,6,9,8,10,1,12,11]
[1,1,1,0,0,1,0,1,0,1,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [12,5,4,3,2,7,6,9,8,11,10,1] => [4,3,5,2,7,6,9,8,11,10,12,1]
[1,1,1,0,0,1,0,1,1,0,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [12,5,4,3,2,7,6,11,10,9,8,1] => [4,3,5,2,7,6,10,9,11,8,12,1]
[1,1,1,0,0,1,1,0,0,0,1,0] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => [4,3,5,2,8,7,9,6,10,1,12,11]
[1,1,1,0,0,1,1,0,0,1,0,0] => [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [12,5,4,3,2,9,8,7,6,11,10,1] => [4,3,5,2,8,7,9,6,11,10,12,1]
[1,1,1,0,0,1,1,0,1,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [12,5,4,3,2,11,8,7,10,9,6,1] => [4,3,5,2,8,7,10,9,11,6,12,1]
[1,1,1,0,0,1,1,1,0,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => [4,3,5,2,9,8,10,7,11,6,12,1]
[1,1,1,0,1,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [4,3,6,5,7,2,8,1,10,9,12,11]
[1,1,1,0,1,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [4,3,6,5,7,2,8,1,11,10,12,9]
[1,1,1,0,1,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [10,7,4,3,6,5,2,9,8,1,12,11] => [4,3,6,5,7,2,9,8,10,1,12,11]
[1,1,1,0,1,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [12,7,4,3,6,5,2,9,8,11,10,1] => [4,3,6,5,7,2,9,8,11,10,12,1]
[1,1,1,0,1,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [12,7,4,3,6,5,2,11,10,9,8,1] => [4,3,6,5,7,2,10,9,11,8,12,1]
[1,1,1,0,1,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [10,9,4,3,6,5,8,7,2,1,12,11] => [4,3,6,5,8,7,9,2,10,1,12,11]
[1,1,1,0,1,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [12,9,4,3,6,5,8,7,2,11,10,1] => [4,3,6,5,8,7,9,2,11,10,12,1]
[1,1,1,0,1,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [12,11,4,3,6,5,8,7,10,9,2,1] => [4,3,6,5,8,7,10,9,11,2,12,1]
[1,1,1,0,1,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [12,11,4,3,6,5,10,9,8,7,2,1] => [4,3,6,5,9,8,10,7,11,2,12,1]
[1,1,1,0,1,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [4,3,7,6,8,5,9,2,10,1,12,11]
[1,1,1,0,1,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [12,9,4,3,8,7,6,5,2,11,10,1] => [4,3,7,6,8,5,9,2,11,10,12,1]
[1,1,1,0,1,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [12,11,4,3,8,7,6,5,10,9,2,1] => [4,3,7,6,8,5,10,9,11,2,12,1]
[1,1,1,0,1,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [12,11,4,3,10,7,6,9,8,5,2,1] => [4,3,7,6,9,8,10,5,11,2,12,1]
[1,1,1,0,1,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [4,3,8,7,9,6,10,5,11,2,12,1]
[1,1,1,1,0,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [5,4,6,3,7,2,8,1,10,9,12,11]
[1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [5,4,6,3,7,2,8,1,11,10,12,9]
[1,1,1,1,0,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [10,7,6,5,4,3,2,9,8,1,12,11] => [5,4,6,3,7,2,9,8,10,1,12,11]
[1,1,1,1,0,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [12,7,6,5,4,3,2,9,8,11,10,1] => [5,4,6,3,7,2,9,8,11,10,12,1]
[1,1,1,1,0,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [12,7,6,5,4,3,2,11,10,9,8,1] => [5,4,6,3,7,2,10,9,11,8,12,1]
[1,1,1,1,0,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [5,4,6,3,8,7,9,2,10,1,12,11]
[1,1,1,1,0,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [12,9,6,5,4,3,8,7,2,11,10,1] => [5,4,6,3,8,7,9,2,11,10,12,1]
[1,1,1,1,0,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [12,11,6,5,4,3,8,7,10,9,2,1] => [5,4,6,3,8,7,10,9,11,2,12,1]
[1,1,1,1,0,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [5,4,6,3,9,8,10,7,11,2,12,1]
[1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [5,4,7,6,8,3,9,2,10,1,12,11]
[1,1,1,1,0,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [12,9,8,5,4,7,6,3,2,11,10,1] => [5,4,7,6,8,3,9,2,11,10,12,1]
[1,1,1,1,0,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [12,11,8,5,4,7,6,3,10,9,2,1] => [5,4,7,6,8,3,10,9,11,2,12,1]
[1,1,1,1,0,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [12,11,10,5,4,7,6,9,8,3,2,1] => [5,4,7,6,9,8,10,3,11,2,12,1]
[1,1,1,1,0,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [5,4,8,7,9,6,10,3,11,2,12,1]
[1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [6,5,7,4,8,3,9,2,10,1,12,11]
[1,1,1,1,1,0,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [12,9,8,7,6,5,4,3,2,11,10,1] => [6,5,7,4,8,3,9,2,11,10,12,1]
[1,1,1,1,1,0,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [6,5,7,4,8,3,10,9,11,2,12,1]
[1,1,1,1,1,0,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [6,5,7,4,9,8,10,3,11,2,12,1]
[1,1,1,1,1,0,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [6,5,8,7,9,4,10,3,11,2,12,1]
[1,1,1,1,1,1,0,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [7,6,8,5,9,4,10,3,11,2,12,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14)] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,14),(12,13)] => [2,1,4,3,6,5,8,7,10,9,14,13,12,11] => [2,1,4,3,6,5,8,7,10,9,13,12,14,11]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,14),(10,11),(12,13)] => [2,1,4,3,6,5,8,7,14,11,10,13,12,9] => [2,1,4,3,6,5,8,7,11,10,13,12,14,9]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,14),(10,13),(11,12)] => [2,1,4,3,6,5,8,7,14,13,12,11,10,9] => [2,1,4,3,6,5,8,7,12,11,13,10,14,9]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,14),(8,9),(10,11),(12,13)] => [2,1,4,3,6,5,14,9,8,11,10,13,12,7] => [2,1,4,3,6,5,9,8,11,10,13,12,14,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,6),(7,14),(8,11),(9,10),(12,13)] => [2,1,4,3,6,5,14,11,10,9,8,13,12,7] => [2,1,4,3,6,5,10,9,11,8,13,12,14,7]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,6),(7,14),(8,13),(9,10),(11,12)] => [2,1,4,3,6,5,14,13,10,9,12,11,8,7] => [2,1,4,3,6,5,10,9,12,11,13,8,14,7]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,6),(7,14),(8,13),(9,12),(10,11)] => [2,1,4,3,6,5,14,13,12,11,10,9,8,7] => [2,1,4,3,6,5,11,10,12,9,13,8,14,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,14),(6,7),(8,9),(10,11),(12,13)] => [2,1,4,3,14,7,6,9,8,11,10,13,12,5] => [2,1,4,3,7,6,9,8,11,10,13,12,14,5]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,4),(5,14),(6,9),(7,8),(10,11),(12,13)] => [2,1,4,3,14,9,8,7,6,11,10,13,12,5] => [2,1,4,3,8,7,9,6,11,10,13,12,14,5]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,4),(5,14),(6,11),(7,8),(9,10),(12,13)] => [2,1,4,3,14,11,8,7,10,9,6,13,12,5] => [2,1,4,3,8,7,10,9,11,6,13,12,14,5]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,4),(5,14),(6,13),(7,8),(9,10),(11,12)] => [2,1,4,3,14,13,8,7,10,9,12,11,6,5] => [2,1,4,3,8,7,10,9,12,11,13,6,14,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,4),(5,14),(6,13),(7,8),(9,12),(10,11)] => [2,1,4,3,14,13,8,7,12,11,10,9,6,5] => [2,1,4,3,8,7,11,10,12,9,13,6,14,5]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,4),(5,14),(6,11),(7,10),(8,9),(12,13)] => [2,1,4,3,14,11,10,9,8,7,6,13,12,5] => [2,1,4,3,9,8,10,7,11,6,13,12,14,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,4),(5,14),(6,13),(7,12),(8,9),(10,11)] => [2,1,4,3,14,13,12,9,8,11,10,7,6,5] => [2,1,4,3,9,8,11,10,12,7,13,6,14,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,14),(4,5),(6,7),(8,9),(10,11),(12,13)] => [2,1,14,5,4,7,6,9,8,11,10,13,12,3] => [2,1,5,4,7,6,9,8,11,10,13,12,14,3]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)] => [2,1,14,5,4,13,12,11,10,9,8,7,6,3] => [2,1,5,4,10,9,11,8,12,7,13,6,14,3]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [(1,2),(3,14),(4,7),(5,6),(8,9),(10,11),(12,13)] => [2,1,14,7,6,5,4,9,8,11,10,13,12,3] => [2,1,6,5,7,4,9,8,11,10,13,12,14,3]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [(1,2),(3,14),(4,9),(5,6),(7,8),(10,11),(12,13)] => [2,1,14,9,6,5,8,7,4,11,10,13,12,3] => [2,1,6,5,8,7,9,4,11,10,13,12,14,3]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,6),(7,8),(9,10),(12,13)] => [2,1,14,11,6,5,8,7,10,9,4,13,12,3] => [2,1,6,5,8,7,10,9,11,4,13,12,14,3]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,6),(7,10),(8,9),(12,13)] => [2,1,14,11,6,5,10,9,8,7,4,13,12,3] => [2,1,6,5,9,8,10,7,11,4,13,12,14,3]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)] => [2,1,14,13,6,5,12,9,8,11,10,7,4,3] => [2,1,6,5,9,8,11,10,12,7,13,4,14,3]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => [2,1,14,13,6,5,12,11,10,9,8,7,4,3] => [2,1,6,5,10,9,11,8,12,7,13,4,14,3]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [(1,2),(3,14),(4,9),(5,8),(6,7),(10,11),(12,13)] => [2,1,14,9,8,7,6,5,4,11,10,13,12,3] => [2,1,7,6,8,5,9,4,11,10,13,12,14,3]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)] => [2,1,14,13,8,7,6,5,12,11,10,9,4,3] => [2,1,7,6,8,5,11,10,12,9,13,4,14,3]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,10),(6,7),(8,9),(12,13)] => [2,1,14,11,10,7,6,9,8,5,4,13,12,3] => [2,1,7,6,9,8,10,5,11,4,13,12,14,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)] => [2,1,14,13,10,7,6,9,8,5,12,11,4,3] => [2,1,7,6,9,8,10,5,12,11,13,4,14,3]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)] => [2,1,14,13,12,7,6,9,8,11,10,5,4,3] => [2,1,7,6,9,8,11,10,12,5,13,4,14,3]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => [2,1,14,13,12,7,6,11,10,9,8,5,4,3] => [2,1,7,6,10,9,11,8,12,5,13,4,14,3]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,10),(6,9),(7,8),(12,13)] => [2,1,14,11,10,9,8,7,6,5,4,13,12,3] => [2,1,8,7,9,6,10,5,11,4,13,12,14,3]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)] => [2,1,14,13,10,9,8,7,6,5,12,11,4,3] => [2,1,8,7,9,6,10,5,12,11,13,4,14,3]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => [2,1,14,13,12,9,8,7,6,11,10,5,4,3] => [2,1,8,7,9,6,11,10,12,5,13,4,14,3]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => [2,1,14,13,12,11,8,7,10,9,6,5,4,3] => [2,1,8,7,10,9,11,6,12,5,13,4,14,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => [2,1,14,13,12,11,10,9,8,7,6,5,4,3] => [2,1,9,8,10,7,11,6,12,5,13,4,14,3]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)] => [4,3,2,1,14,13,12,11,10,9,8,7,6,5] => [3,2,4,1,10,9,11,8,12,7,13,6,14,5]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)] => [14,3,2,5,4,7,6,9,8,11,10,13,12,1] => [3,2,5,4,7,6,9,8,11,10,13,12,14,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,9),(10,13),(11,12)] => [14,3,2,5,4,7,6,9,8,13,12,11,10,1] => [3,2,5,4,7,6,9,8,12,11,13,10,14,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,11),(9,10),(12,13)] => [14,3,2,5,4,7,6,11,10,9,8,13,12,1] => [3,2,5,4,7,6,10,9,11,8,13,12,14,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,13),(9,10),(11,12)] => [14,3,2,5,4,7,6,13,10,9,12,11,8,1] => [3,2,5,4,7,6,10,9,12,11,13,8,14,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,13),(9,12),(10,11)] => [14,3,2,5,4,7,6,13,12,11,10,9,8,1] => [3,2,5,4,7,6,11,10,12,9,13,8,14,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [(1,14),(2,3),(4,5),(6,9),(7,8),(10,11),(12,13)] => [14,3,2,5,4,9,8,7,6,11,10,13,12,1] => [3,2,5,4,8,7,9,6,11,10,13,12,14,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [(1,14),(2,3),(4,5),(6,9),(7,8),(10,13),(11,12)] => [14,3,2,5,4,9,8,7,6,13,12,11,10,1] => [3,2,5,4,8,7,9,6,12,11,13,10,14,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [(1,14),(2,3),(4,5),(6,11),(7,8),(9,10),(12,13)] => [14,3,2,5,4,11,8,7,10,9,6,13,12,1] => [3,2,5,4,8,7,10,9,11,6,13,12,14,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,8),(9,10),(11,12)] => [14,3,2,5,4,13,8,7,10,9,12,11,6,1] => [3,2,5,4,8,7,10,9,12,11,13,6,14,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,8),(9,12),(10,11)] => [14,3,2,5,4,13,8,7,12,11,10,9,6,1] => [3,2,5,4,8,7,11,10,12,9,13,6,14,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [(1,14),(2,3),(4,5),(6,11),(7,10),(8,9),(12,13)] => [14,3,2,5,4,11,10,9,8,7,6,13,12,1] => [3,2,5,4,9,8,10,7,11,6,13,12,14,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,10),(8,9),(11,12)] => [14,3,2,5,4,13,10,9,8,7,12,11,6,1] => [3,2,5,4,9,8,10,7,12,11,13,6,14,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,12),(8,9),(10,11)] => [14,3,2,5,4,13,12,9,8,11,10,7,6,1] => [3,2,5,4,9,8,11,10,12,7,13,6,14,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,12),(8,11),(9,10)] => [14,3,2,5,4,13,12,11,10,9,8,7,6,1] => [3,2,5,4,10,9,11,8,12,7,13,6,14,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,9),(10,11),(12,13)] => [14,3,2,7,6,5,4,9,8,11,10,13,12,1] => [3,2,6,5,7,4,9,8,11,10,13,12,14,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,9),(10,13),(11,12)] => [14,3,2,7,6,5,4,9,8,13,12,11,10,1] => [3,2,6,5,7,4,9,8,12,11,13,10,14,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,11),(9,10),(12,13)] => [14,3,2,7,6,5,4,11,10,9,8,13,12,1] => [3,2,6,5,7,4,10,9,11,8,13,12,14,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,13),(9,10),(11,12)] => [14,3,2,7,6,5,4,13,10,9,12,11,8,1] => [3,2,6,5,7,4,10,9,12,11,13,8,14,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,13),(9,12),(10,11)] => [14,3,2,7,6,5,4,13,12,11,10,9,8,1] => [3,2,6,5,7,4,11,10,12,9,13,8,14,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [(1,14),(2,3),(4,9),(5,6),(7,8),(10,11),(12,13)] => [14,3,2,9,6,5,8,7,4,11,10,13,12,1] => [3,2,6,5,8,7,9,4,11,10,13,12,14,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [(1,14),(2,3),(4,9),(5,6),(7,8),(10,13),(11,12)] => [14,3,2,9,6,5,8,7,4,13,12,11,10,1] => [3,2,6,5,8,7,9,4,12,11,13,10,14,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,6),(7,8),(9,10),(12,13)] => [14,3,2,11,6,5,8,7,10,9,4,13,12,1] => [3,2,6,5,8,7,10,9,11,4,13,12,14,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,8),(9,10),(11,12)] => [14,3,2,13,6,5,8,7,10,9,12,11,4,1] => [3,2,6,5,8,7,10,9,12,11,13,4,14,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,8),(9,12),(10,11)] => [14,3,2,13,6,5,8,7,12,11,10,9,4,1] => [3,2,6,5,8,7,11,10,12,9,13,4,14,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,6),(7,10),(8,9),(12,13)] => [14,3,2,11,6,5,10,9,8,7,4,13,12,1] => [3,2,6,5,9,8,10,7,11,4,13,12,14,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,10),(8,9),(11,12)] => [14,3,2,13,6,5,10,9,8,7,12,11,4,1] => [3,2,6,5,9,8,10,7,12,11,13,4,14,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,12),(8,9),(10,11)] => [14,3,2,13,6,5,12,9,8,11,10,7,4,1] => [3,2,6,5,9,8,11,10,12,7,13,4,14,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,12),(8,11),(9,10)] => [14,3,2,13,6,5,12,11,10,9,8,7,4,1] => [3,2,6,5,10,9,11,8,12,7,13,4,14,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [(1,14),(2,3),(4,9),(5,8),(6,7),(10,11),(12,13)] => [14,3,2,9,8,7,6,5,4,11,10,13,12,1] => [3,2,7,6,8,5,9,4,11,10,13,12,14,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [(1,14),(2,3),(4,9),(5,8),(6,7),(10,13),(11,12)] => [14,3,2,9,8,7,6,5,4,13,12,11,10,1] => [3,2,7,6,8,5,9,4,12,11,13,10,14,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,8),(6,7),(9,10),(12,13)] => [14,3,2,11,8,7,6,5,10,9,4,13,12,1] => [3,2,7,6,8,5,10,9,11,4,13,12,14,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,8),(6,7),(9,10),(11,12)] => [14,3,2,13,8,7,6,5,10,9,12,11,4,1] => [3,2,7,6,8,5,10,9,12,11,13,4,14,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,8),(6,7),(9,12),(10,11)] => [14,3,2,13,8,7,6,5,12,11,10,9,4,1] => [3,2,7,6,8,5,11,10,12,9,13,4,14,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,10),(6,7),(8,9),(12,13)] => [14,3,2,11,10,7,6,9,8,5,4,13,12,1] => [3,2,7,6,9,8,10,5,11,4,13,12,14,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,10),(6,7),(8,9),(11,12)] => [14,3,2,13,10,7,6,9,8,5,12,11,4,1] => [3,2,7,6,9,8,10,5,12,11,13,4,14,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,7),(8,9),(10,11)] => [14,3,2,13,12,7,6,9,8,11,10,5,4,1] => [3,2,7,6,9,8,11,10,12,5,13,4,14,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,7),(8,11),(9,10)] => [14,3,2,13,12,7,6,11,10,9,8,5,4,1] => [3,2,7,6,10,9,11,8,12,5,13,4,14,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8),(13,14)] => [12,3,2,11,10,9,8,7,6,5,4,1,14,13] => [3,2,8,7,9,6,10,5,11,4,12,1,14,13]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,10),(6,9),(7,8),(12,13)] => [14,3,2,11,10,9,8,7,6,5,4,13,12,1] => [3,2,8,7,9,6,10,5,11,4,13,12,14,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,10),(6,9),(7,8),(11,12)] => [14,3,2,13,10,9,8,7,6,5,12,11,4,1] => [3,2,8,7,9,6,10,5,12,11,13,4,14,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,9),(7,8),(10,11)] => [14,3,2,13,12,9,8,7,6,11,10,5,4,1] => [3,2,8,7,9,6,11,10,12,5,13,4,14,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,11),(7,8),(9,10)] => [14,3,2,13,12,11,8,7,10,9,6,5,4,1] => [3,2,8,7,10,9,11,6,12,5,13,4,14,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,11),(7,10),(8,9)] => [14,3,2,13,12,11,10,9,8,7,6,5,4,1] => [3,2,9,8,10,7,11,6,12,5,13,4,14,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13)] => [14,5,4,3,2,7,6,9,8,11,10,13,12,1] => [4,3,5,2,7,6,9,8,11,10,13,12,14,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,9),(10,13),(11,12)] => [14,5,4,3,2,7,6,9,8,13,12,11,10,1] => [4,3,5,2,7,6,9,8,12,11,13,10,14,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,11),(9,10),(12,13)] => [14,5,4,3,2,7,6,11,10,9,8,13,12,1] => [4,3,5,2,7,6,10,9,11,8,13,12,14,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,13),(9,10),(11,12)] => [14,5,4,3,2,7,6,13,10,9,12,11,8,1] => [4,3,5,2,7,6,10,9,12,11,13,8,14,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,13),(9,12),(10,11)] => [14,5,4,3,2,7,6,13,12,11,10,9,8,1] => [4,3,5,2,7,6,11,10,12,9,13,8,14,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [(1,14),(2,5),(3,4),(6,9),(7,8),(10,11),(12,13)] => [14,5,4,3,2,9,8,7,6,11,10,13,12,1] => [4,3,5,2,8,7,9,6,11,10,13,12,14,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [(1,14),(2,5),(3,4),(6,9),(7,8),(10,13),(11,12)] => [14,5,4,3,2,9,8,7,6,13,12,11,10,1] => [4,3,5,2,8,7,9,6,12,11,13,10,14,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [(1,14),(2,5),(3,4),(6,11),(7,8),(9,10),(12,13)] => [14,5,4,3,2,11,8,7,10,9,6,13,12,1] => [4,3,5,2,8,7,10,9,11,6,13,12,14,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,8),(9,10),(11,12)] => [14,5,4,3,2,13,8,7,10,9,12,11,6,1] => [4,3,5,2,8,7,10,9,12,11,13,6,14,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,8),(9,12),(10,11)] => [14,5,4,3,2,13,8,7,12,11,10,9,6,1] => [4,3,5,2,8,7,11,10,12,9,13,6,14,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [(1,14),(2,5),(3,4),(6,11),(7,10),(8,9),(12,13)] => [14,5,4,3,2,11,10,9,8,7,6,13,12,1] => [4,3,5,2,9,8,10,7,11,6,13,12,14,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,10),(8,9),(11,12)] => [14,5,4,3,2,13,10,9,8,7,12,11,6,1] => [4,3,5,2,9,8,10,7,12,11,13,6,14,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,12),(8,9),(10,11)] => [14,5,4,3,2,13,12,9,8,11,10,7,6,1] => [4,3,5,2,9,8,11,10,12,7,13,6,14,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,12),(8,11),(9,10)] => [14,5,4,3,2,13,12,11,10,9,8,7,6,1] => [4,3,5,2,10,9,11,8,12,7,13,6,14,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,9),(10,11),(12,13)] => [14,7,4,3,6,5,2,9,8,11,10,13,12,1] => [4,3,6,5,7,2,9,8,11,10,13,12,14,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,9),(10,13),(11,12)] => [14,7,4,3,6,5,2,9,8,13,12,11,10,1] => [4,3,6,5,7,2,9,8,12,11,13,10,14,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,11),(9,10),(12,13)] => [14,7,4,3,6,5,2,11,10,9,8,13,12,1] => [4,3,6,5,7,2,10,9,11,8,13,12,14,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,13),(9,10),(11,12)] => [14,7,4,3,6,5,2,13,10,9,12,11,8,1] => [4,3,6,5,7,2,10,9,12,11,13,8,14,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,13),(9,12),(10,11)] => [14,7,4,3,6,5,2,13,12,11,10,9,8,1] => [4,3,6,5,7,2,11,10,12,9,13,8,14,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,4),(5,6),(7,8),(10,11),(12,13)] => [14,9,4,3,6,5,8,7,2,11,10,13,12,1] => [4,3,6,5,8,7,9,2,11,10,13,12,14,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,4),(5,6),(7,8),(10,13),(11,12)] => [14,9,4,3,6,5,8,7,2,13,12,11,10,1] => [4,3,6,5,8,7,9,2,12,11,13,10,14,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,6),(7,8),(9,10),(12,13)] => [14,11,4,3,6,5,8,7,10,9,2,13,12,1] => [4,3,6,5,8,7,10,9,11,2,13,12,14,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,8),(9,10),(11,12)] => [14,13,4,3,6,5,8,7,10,9,12,11,2,1] => [4,3,6,5,8,7,10,9,12,11,13,2,14,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,8),(9,12),(10,11)] => [14,13,4,3,6,5,8,7,12,11,10,9,2,1] => [4,3,6,5,8,7,11,10,12,9,13,2,14,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,6),(7,10),(8,9),(12,13)] => [14,11,4,3,6,5,10,9,8,7,2,13,12,1] => [4,3,6,5,9,8,10,7,11,2,13,12,14,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,10),(8,9),(11,12)] => [14,13,4,3,6,5,10,9,8,7,12,11,2,1] => [4,3,6,5,9,8,10,7,12,11,13,2,14,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,12),(8,9),(10,11)] => [14,13,4,3,6,5,12,9,8,11,10,7,2,1] => [4,3,6,5,9,8,11,10,12,7,13,2,14,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,12),(8,11),(9,10)] => [14,13,4,3,6,5,12,11,10,9,8,7,2,1] => [4,3,6,5,10,9,11,8,12,7,13,2,14,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,4),(5,8),(6,7),(10,11),(12,13)] => [14,9,4,3,8,7,6,5,2,11,10,13,12,1] => [4,3,7,6,8,5,9,2,11,10,13,12,14,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,4),(5,8),(6,7),(10,13),(11,12)] => [14,9,4,3,8,7,6,5,2,13,12,11,10,1] => [4,3,7,6,8,5,9,2,12,11,13,10,14,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,8),(6,7),(9,10),(12,13)] => [14,11,4,3,8,7,6,5,10,9,2,13,12,1] => [4,3,7,6,8,5,10,9,11,2,13,12,14,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,8),(6,7),(9,10),(11,12)] => [14,13,4,3,8,7,6,5,10,9,12,11,2,1] => [4,3,7,6,8,5,10,9,12,11,13,2,14,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,8),(6,7),(9,12),(10,11)] => [14,13,4,3,8,7,6,5,12,11,10,9,2,1] => [4,3,7,6,8,5,11,10,12,9,13,2,14,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9),(13,14)] => [12,11,4,3,10,7,6,9,8,5,2,1,14,13] => [4,3,7,6,9,8,10,5,11,2,12,1,14,13]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,10),(6,7),(8,9),(12,13)] => [14,11,4,3,10,7,6,9,8,5,2,13,12,1] => [4,3,7,6,9,8,10,5,11,2,13,12,14,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,10),(6,7),(8,9),(11,12)] => [14,13,4,3,10,7,6,9,8,5,12,11,2,1] => [4,3,7,6,9,8,10,5,12,11,13,2,14,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,7),(8,9),(10,11)] => [14,13,4,3,12,7,6,9,8,11,10,5,2,1] => [4,3,7,6,9,8,11,10,12,5,13,2,14,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,7),(8,11),(9,10)] => [14,13,4,3,12,7,6,11,10,9,8,5,2,1] => [4,3,7,6,10,9,11,8,12,5,13,2,14,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8),(13,14)] => [12,11,4,3,10,9,8,7,6,5,2,1,14,13] => [4,3,8,7,9,6,10,5,11,2,12,1,14,13]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,10),(6,9),(7,8),(12,13)] => [14,11,4,3,10,9,8,7,6,5,2,13,12,1] => [4,3,8,7,9,6,10,5,11,2,13,12,14,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,10),(6,9),(7,8),(11,12)] => [14,13,4,3,10,9,8,7,6,5,12,11,2,1] => [4,3,8,7,9,6,10,5,12,11,13,2,14,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,9),(7,8),(10,11)] => [14,13,4,3,12,9,8,7,6,11,10,5,2,1] => [4,3,8,7,9,6,11,10,12,5,13,2,14,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,11),(7,8),(9,10)] => [14,13,4,3,12,11,8,7,10,9,6,5,2,1] => [4,3,8,7,10,9,11,6,12,5,13,2,14,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,11),(7,10),(8,9)] => [14,13,4,3,12,11,10,9,8,7,6,5,2,1] => [4,3,9,8,10,7,11,6,12,5,13,2,14,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,9),(10,11),(12,13)] => [14,7,6,5,4,3,2,9,8,11,10,13,12,1] => [5,4,6,3,7,2,9,8,11,10,13,12,14,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,9),(10,13),(11,12)] => [14,7,6,5,4,3,2,9,8,13,12,11,10,1] => [5,4,6,3,7,2,9,8,12,11,13,10,14,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,11),(9,10),(12,13)] => [14,7,6,5,4,3,2,11,10,9,8,13,12,1] => [5,4,6,3,7,2,10,9,11,8,13,12,14,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,13),(9,10),(11,12)] => [14,7,6,5,4,3,2,13,10,9,12,11,8,1] => [5,4,6,3,7,2,10,9,12,11,13,8,14,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,13),(9,12),(10,11)] => [14,7,6,5,4,3,2,13,12,11,10,9,8,1] => [5,4,6,3,7,2,11,10,12,9,13,8,14,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,6),(4,5),(7,8),(10,11),(12,13)] => [14,9,6,5,4,3,8,7,2,11,10,13,12,1] => [5,4,6,3,8,7,9,2,11,10,13,12,14,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,6),(4,5),(7,8),(10,13),(11,12)] => [14,9,6,5,4,3,8,7,2,13,12,11,10,1] => [5,4,6,3,8,7,9,2,12,11,13,10,14,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,6),(4,5),(7,8),(9,10),(12,13)] => [14,11,6,5,4,3,8,7,10,9,2,13,12,1] => [5,4,6,3,8,7,10,9,11,2,13,12,14,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,8),(9,10),(11,12)] => [14,13,6,5,4,3,8,7,10,9,12,11,2,1] => [5,4,6,3,8,7,10,9,12,11,13,2,14,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,8),(9,12),(10,11)] => [14,13,6,5,4,3,8,7,12,11,10,9,2,1] => [5,4,6,3,8,7,11,10,12,9,13,2,14,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9),(13,14)] => [12,11,6,5,4,3,10,9,8,7,2,1,14,13] => [5,4,6,3,9,8,10,7,11,2,12,1,14,13]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,6),(4,5),(7,10),(8,9),(12,13)] => [14,11,6,5,4,3,10,9,8,7,2,13,12,1] => [5,4,6,3,9,8,10,7,11,2,13,12,14,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,10),(8,9),(11,12)] => [14,13,6,5,4,3,10,9,8,7,12,11,2,1] => [5,4,6,3,9,8,10,7,12,11,13,2,14,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,12),(8,9),(10,11)] => [14,13,6,5,4,3,12,9,8,11,10,7,2,1] => [5,4,6,3,9,8,11,10,12,7,13,2,14,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,12),(8,11),(9,10)] => [14,13,6,5,4,3,12,11,10,9,8,7,2,1] => [5,4,6,3,10,9,11,8,12,7,13,2,14,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,8),(4,5),(6,7),(10,11),(12,13)] => [14,9,8,5,4,7,6,3,2,11,10,13,12,1] => [5,4,7,6,8,3,9,2,11,10,13,12,14,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,8),(4,5),(6,7),(10,13),(11,12)] => [14,9,8,5,4,7,6,3,2,13,12,11,10,1] => [5,4,7,6,8,3,9,2,12,11,13,10,14,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10),(13,14)] => [12,11,8,5,4,7,6,3,10,9,2,1,14,13] => [5,4,7,6,8,3,10,9,11,2,12,1,14,13]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,8),(4,5),(6,7),(9,10),(12,13)] => [14,11,8,5,4,7,6,3,10,9,2,13,12,1] => [5,4,7,6,8,3,10,9,11,2,13,12,14,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,8),(4,5),(6,7),(9,10),(11,12)] => [14,13,8,5,4,7,6,3,10,9,12,11,2,1] => [5,4,7,6,8,3,10,9,12,11,13,2,14,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,8),(4,5),(6,7),(9,12),(10,11)] => [14,13,8,5,4,7,6,3,12,11,10,9,2,1] => [5,4,7,6,8,3,11,10,12,9,13,2,14,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9),(13,14)] => [12,11,10,5,4,7,6,9,8,3,2,1,14,13] => [5,4,7,6,9,8,10,3,11,2,12,1,14,13]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,5),(6,7),(8,9),(12,13)] => [14,11,10,5,4,7,6,9,8,3,2,13,12,1] => [5,4,7,6,9,8,10,3,11,2,13,12,14,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,5),(6,7),(8,9),(11,12)] => [14,13,10,5,4,7,6,9,8,3,12,11,2,1] => [5,4,7,6,9,8,10,3,12,11,13,2,14,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,7),(8,9),(10,11)] => [14,13,12,5,4,7,6,9,8,11,10,3,2,1] => [5,4,7,6,9,8,11,10,12,3,13,2,14,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,7),(8,11),(9,10)] => [14,13,12,5,4,7,6,11,10,9,8,3,2,1] => [5,4,7,6,10,9,11,8,12,3,13,2,14,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)] => [12,11,10,5,4,9,8,7,6,3,2,1,14,13] => [5,4,8,7,9,6,10,3,11,2,12,1,14,13]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,5),(6,9),(7,8),(12,13)] => [14,11,10,5,4,9,8,7,6,3,2,13,12,1] => [5,4,8,7,9,6,10,3,11,2,13,12,14,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,5),(6,9),(7,8),(11,12)] => [14,13,10,5,4,9,8,7,6,3,12,11,2,1] => [5,4,8,7,9,6,10,3,12,11,13,2,14,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,9),(7,8),(10,11)] => [14,13,12,5,4,9,8,7,6,11,10,3,2,1] => [5,4,8,7,9,6,11,10,12,3,13,2,14,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,11),(7,8),(9,10)] => [14,13,12,5,4,11,8,7,10,9,6,3,2,1] => [5,4,8,7,10,9,11,6,12,3,13,2,14,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9)] => [14,13,12,5,4,11,10,9,8,7,6,3,2,1] => [5,4,9,8,10,7,11,6,12,3,13,2,14,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)] => [10,9,8,7,6,5,4,3,2,1,14,13,12,11] => [6,5,7,4,8,3,9,2,10,1,13,12,14,11]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)] => [12,9,8,7,6,5,4,3,2,11,10,1,14,13] => [6,5,7,4,8,3,9,2,11,10,12,1,14,13]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,8),(4,7),(5,6),(10,11),(12,13)] => [14,9,8,7,6,5,4,3,2,11,10,13,12,1] => [6,5,7,4,8,3,9,2,11,10,13,12,14,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,8),(4,7),(5,6),(10,13),(11,12)] => [14,9,8,7,6,5,4,3,2,13,12,11,10,1] => [6,5,7,4,8,3,9,2,12,11,13,10,14,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)] => [12,11,8,7,6,5,4,3,10,9,2,1,14,13] => [6,5,7,4,8,3,10,9,11,2,12,1,14,13]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,8),(4,7),(5,6),(9,10),(12,13)] => [14,11,8,7,6,5,4,3,10,9,2,13,12,1] => [6,5,7,4,8,3,10,9,11,2,13,12,14,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,8),(4,7),(5,6),(9,10),(11,12)] => [14,13,8,7,6,5,4,3,10,9,12,11,2,1] => [6,5,7,4,8,3,10,9,12,11,13,2,14,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,8),(4,7),(5,6),(9,12),(10,11)] => [14,13,8,7,6,5,4,3,12,11,10,9,2,1] => [6,5,7,4,8,3,11,10,12,9,13,2,14,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)] => [12,11,10,7,6,5,4,9,8,3,2,1,14,13] => [6,5,7,4,9,8,10,3,11,2,12,1,14,13]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,7),(5,6),(8,9),(12,13)] => [14,11,10,7,6,5,4,9,8,3,2,13,12,1] => [6,5,7,4,9,8,10,3,11,2,13,12,14,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,7),(5,6),(8,9),(11,12)] => [14,13,10,7,6,5,4,9,8,3,12,11,2,1] => [6,5,7,4,9,8,10,3,12,11,13,2,14,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,7),(5,6),(8,9),(10,11)] => [14,13,12,7,6,5,4,9,8,11,10,3,2,1] => [6,5,7,4,9,8,11,10,12,3,13,2,14,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,7),(5,6),(8,11),(9,10)] => [14,13,12,7,6,5,4,11,10,9,8,3,2,1] => [6,5,7,4,10,9,11,8,12,3,13,2,14,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)] => [12,11,10,9,6,5,8,7,4,3,2,1,14,13] => [6,5,8,7,9,4,10,3,11,2,12,1,14,13]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,9),(5,6),(7,8),(12,13)] => [14,11,10,9,6,5,8,7,4,3,2,13,12,1] => [6,5,8,7,9,4,10,3,11,2,13,12,14,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,9),(5,6),(7,8),(11,12)] => [14,13,10,9,6,5,8,7,4,3,12,11,2,1] => [6,5,8,7,9,4,10,3,12,11,13,2,14,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,9),(5,6),(7,8),(10,11)] => [14,13,12,9,6,5,8,7,4,11,10,3,2,1] => [6,5,8,7,9,4,11,10,12,3,13,2,14,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10)] => [14,13,12,11,6,5,8,7,10,9,4,3,2,1] => [6,5,8,7,10,9,11,4,12,3,13,2,14,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9)] => [14,13,12,11,6,5,10,9,8,7,4,3,2,1] => [6,5,9,8,10,7,11,4,12,3,13,2,14,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)] => [12,11,10,9,8,7,6,5,4,3,2,1,14,13] => [7,6,8,5,9,4,10,3,11,2,12,1,14,13]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,9),(5,8),(6,7),(12,13)] => [14,11,10,9,8,7,6,5,4,3,2,13,12,1] => [7,6,8,5,9,4,10,3,11,2,13,12,14,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,9),(5,8),(6,7),(11,12)] => [14,13,10,9,8,7,6,5,4,3,12,11,2,1] => [7,6,8,5,9,4,10,3,12,11,13,2,14,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11)] => [14,13,12,9,8,7,6,5,4,11,10,3,2,1] => [7,6,8,5,9,4,11,10,12,3,13,2,14,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10)] => [14,13,12,11,8,7,6,5,10,9,4,3,2,1] => [7,6,8,5,10,9,11,4,12,3,13,2,14,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9)] => [14,13,12,11,10,7,6,9,8,5,4,3,2,1] => [7,6,9,8,10,5,11,4,12,3,13,2,14,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8)] => [14,13,12,11,10,9,8,7,6,5,4,3,2,1] => [8,7,9,6,10,5,11,4,12,3,13,2,14,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,16),(14,15)] => [2,1,4,3,6,5,8,7,10,9,12,11,16,15,14,13] => [2,1,4,3,6,5,8,7,10,9,12,11,15,14,16,13]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,16),(12,13),(14,15)] => [2,1,4,3,6,5,8,7,10,9,16,13,12,15,14,11] => [2,1,4,3,6,5,8,7,10,9,13,12,15,14,16,11]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,16),(12,15),(13,14)] => [2,1,4,3,6,5,8,7,10,9,16,15,14,13,12,11] => [2,1,4,3,6,5,8,7,10,9,14,13,15,12,16,11]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,16),(10,11),(12,13),(14,15)] => [2,1,4,3,6,5,8,7,16,11,10,13,12,15,14,9] => [2,1,4,3,6,5,8,7,11,10,13,12,15,14,16,9]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,16),(10,13),(11,12),(14,15)] => [2,1,4,3,6,5,8,7,16,13,12,11,10,15,14,9] => [2,1,4,3,6,5,8,7,12,11,13,10,15,14,16,9]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,16),(10,15),(11,12),(13,14)] => [2,1,4,3,6,5,8,7,16,15,12,11,14,13,10,9] => [2,1,4,3,6,5,8,7,12,11,14,13,15,10,16,9]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,16),(10,15),(11,14),(12,13)] => [2,1,4,3,6,5,8,7,16,15,14,13,12,11,10,9] => [2,1,4,3,6,5,8,7,13,12,14,11,15,10,16,9]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,16),(8,9),(10,11),(12,13),(14,15)] => [2,1,4,3,6,5,16,9,8,11,10,13,12,15,14,7] => [2,1,4,3,6,5,9,8,11,10,13,12,15,14,16,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,16),(8,11),(9,10),(12,13),(14,15)] => [2,1,4,3,6,5,16,11,10,9,8,13,12,15,14,7] => [2,1,4,3,6,5,10,9,11,8,13,12,15,14,16,7]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,4),(5,6),(7,16),(8,13),(9,10),(11,12),(14,15)] => [2,1,4,3,6,5,16,13,10,9,12,11,8,15,14,7] => [2,1,4,3,6,5,10,9,12,11,13,8,15,14,16,7]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,4),(5,6),(7,16),(8,13),(9,12),(10,11),(14,15)] => [2,1,4,3,6,5,16,13,12,11,10,9,8,15,14,7] => [2,1,4,3,6,5,11,10,12,9,13,8,15,14,16,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,16),(6,7),(8,9),(10,11),(12,13),(14,15)] => [2,1,4,3,16,7,6,9,8,11,10,13,12,15,14,5] => [2,1,4,3,7,6,9,8,11,10,13,12,15,14,16,5]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,16),(6,9),(7,8),(10,11),(12,13),(14,15)] => [2,1,4,3,16,9,8,7,6,11,10,13,12,15,14,5] => [2,1,4,3,8,7,9,6,11,10,13,12,15,14,16,5]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [(1,2),(3,4),(5,16),(6,11),(7,8),(9,10),(12,13),(14,15)] => [2,1,4,3,16,11,8,7,10,9,6,13,12,15,14,5] => [2,1,4,3,8,7,10,9,11,6,13,12,15,14,16,5]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [(1,2),(3,4),(5,16),(6,11),(7,10),(8,9),(12,13),(14,15)] => [2,1,4,3,16,11,10,9,8,7,6,13,12,15,14,5] => [2,1,4,3,9,8,10,7,11,6,13,12,15,14,16,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,16),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15)] => [2,1,16,5,4,7,6,9,8,11,10,13,12,15,14,3] => [2,1,5,4,7,6,9,8,11,10,13,12,15,14,16,3]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,16),(4,7),(5,6),(8,9),(10,11),(12,13),(14,15)] => [2,1,16,7,6,5,4,9,8,11,10,13,12,15,14,3] => [2,1,6,5,7,4,9,8,11,10,13,12,15,14,16,3]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [(1,2),(3,16),(4,9),(5,6),(7,8),(10,11),(12,13),(14,15)] => [2,1,16,9,6,5,8,7,4,11,10,13,12,15,14,3] => [2,1,6,5,8,7,9,4,11,10,13,12,15,14,16,3]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [(1,2),(3,16),(4,9),(5,8),(6,7),(10,11),(12,13),(14,15)] => [2,1,16,9,8,7,6,5,4,11,10,13,12,15,14,3] => [2,1,7,6,8,5,9,4,11,10,13,12,15,14,16,3]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)] => [2,1,16,15,14,7,6,13,12,11,10,9,8,5,4,3] => [2,1,7,6,11,10,12,9,13,8,14,5,15,4,16,3]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)] => [2,1,16,15,14,13,8,7,10,9,12,11,6,5,4,3] => [2,1,8,7,10,9,12,11,13,6,14,5,15,4,16,3]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => [2,1,16,15,14,13,8,7,12,11,10,9,6,5,4,3] => [2,1,8,7,11,10,12,9,13,6,14,5,15,4,16,3]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)] => [2,1,16,15,14,11,10,9,8,7,6,13,12,5,4,3] => [2,1,9,8,10,7,11,6,13,12,14,5,15,4,16,3]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)] => [2,1,16,15,14,13,10,9,8,7,12,11,6,5,4,3] => [2,1,9,8,10,7,12,11,13,6,14,5,15,4,16,3]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => [2,1,16,15,14,13,12,9,8,11,10,7,6,5,4,3] => [2,1,9,8,11,10,12,7,13,6,14,5,15,4,16,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => [2,1,16,15,14,13,12,11,10,9,8,7,6,5,4,3] => [2,1,10,9,11,8,12,7,13,6,14,5,15,4,16,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15)] => [16,3,2,5,4,7,6,9,8,11,10,13,12,15,14,1] => [3,2,5,4,7,6,9,8,11,10,13,12,15,14,16,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13),(14,15)] => [16,5,4,3,2,7,6,9,8,11,10,13,12,15,14,1] => [4,3,5,2,7,6,9,8,11,10,13,12,15,14,16,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,7),(3,4),(5,6),(8,9),(10,11),(12,13),(14,15)] => [16,7,4,3,6,5,2,9,8,11,10,13,12,15,14,1] => [4,3,6,5,7,2,9,8,11,10,13,12,15,14,16,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,7),(3,6),(4,5),(8,9),(10,11),(12,13),(14,15)] => [16,7,6,5,4,3,2,9,8,11,10,13,12,15,14,1] => [5,4,6,3,7,2,9,8,11,10,13,12,15,14,16,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9),(15,16)] => [14,13,12,5,4,11,10,9,8,7,6,3,2,1,16,15] => [5,4,9,8,10,7,11,6,12,3,13,2,14,1,16,15]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10),(15,16)] => [14,13,12,11,6,5,8,7,10,9,4,3,2,1,16,15] => [6,5,8,7,10,9,11,4,12,3,13,2,14,1,16,15]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9),(15,16)] => [14,13,12,11,6,5,10,9,8,7,4,3,2,1,16,15] => [6,5,9,8,10,7,11,4,12,3,13,2,14,1,16,15]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11),(15,16)] => [14,13,12,9,8,7,6,5,4,11,10,3,2,1,16,15] => [7,6,8,5,9,4,11,10,12,3,13,2,14,1,16,15]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10),(15,16)] => [14,13,12,11,8,7,6,5,10,9,4,3,2,1,16,15] => [7,6,8,5,10,9,11,4,12,3,13,2,14,1,16,15]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9),(15,16)] => [14,13,12,11,10,7,6,9,8,5,4,3,2,1,16,15] => [7,6,9,8,10,5,11,4,12,3,13,2,14,1,16,15]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)] => [14,13,12,11,10,9,8,7,6,5,4,3,2,1,16,15] => [8,7,9,6,10,5,11,4,12,3,13,2,14,1,16,15]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9),(17,18)] => [16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,18,17] => [9,8,10,7,11,6,12,5,13,4,14,3,15,2,16,1,18,17]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => [2,1,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3] => [2,1,11,10,12,9,13,8,14,7,15,6,16,5,17,4,18,3]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10),(19,20)] => [18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,20,19] => [10,9,11,8,12,7,13,6,14,5,15,4,16,3,17,2,18,1,20,19]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10),(17,18)] => [16,15,14,13,12,11,8,7,10,9,6,5,4,3,2,1,18,17] => [8,7,10,9,11,6,12,5,13,4,14,3,15,2,16,1,18,17]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)] => [2,1,18,17,16,15,14,13,10,9,12,11,8,7,6,5,4,3] => [2,1,10,9,12,11,13,8,14,7,15,6,16,5,17,4,18,3]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => [2,1,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3] => [2,1,12,11,13,10,14,9,15,8,16,7,17,6,18,5,19,4,20,3]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [(1,20),(2,19),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11),(21,22)] => [20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,22,21] => [11,10,12,9,13,8,14,7,15,6,16,5,17,4,18,3,19,2,20,1,22,21]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11),(19,20)] => [18,17,16,15,14,13,12,9,8,11,10,7,6,5,4,3,2,1,20,19] => [9,8,11,10,12,7,13,6,14,5,15,4,16,3,17,2,18,1,20,19]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [(1,16),(2,15),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11),(17,18)] => [16,15,14,13,12,9,8,7,6,11,10,5,4,3,2,1,18,17] => [8,7,9,6,11,10,12,5,13,4,14,3,15,2,16,1,18,17]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [(1,16),(2,15),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10),(17,18)] => [16,15,14,13,12,7,6,11,10,9,8,5,4,3,2,1,18,17] => [7,6,10,9,11,8,12,5,13,4,14,3,15,2,16,1,18,17]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,11),(9,10),(12,13)] => [2,1,18,17,16,15,14,11,10,9,8,13,12,7,6,5,4,3] => [2,1,10,9,11,8,13,12,14,7,15,6,16,5,17,4,18,3]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)] => [2,1,18,17,16,15,14,9,8,13,12,11,10,7,6,5,4,3] => [2,1,9,8,12,11,13,10,14,7,15,6,16,5,17,4,18,3]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)] => [2,1,20,19,18,17,16,15,14,11,10,13,12,9,8,7,6,5,4,3] => [2,1,11,10,13,12,14,9,15,8,16,7,17,6,18,5,19,4,20,3]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)] => [2,1,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3] => [2,1,13,12,14,11,15,10,16,9,17,8,18,7,19,6,20,5,21,4,22,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,18),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)] => [18,3,2,5,4,7,6,9,8,11,10,13,12,15,14,17,16,1] => [3,2,5,4,7,6,9,8,11,10,13,12,15,14,17,16,18,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,18),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)] => [18,5,4,3,2,7,6,9,8,11,10,13,12,15,14,17,16,1] => [4,3,5,2,7,6,9,8,11,10,13,12,15,14,17,16,18,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,18),(16,17)] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,18,17,16,15] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,17,16,18,15]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,18),(14,15),(16,17)] => [2,1,4,3,6,5,8,7,10,9,12,11,18,15,14,17,16,13] => [2,1,4,3,6,5,8,7,10,9,12,11,15,14,17,16,18,13]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,18),(12,13),(14,15),(16,17)] => [2,1,4,3,6,5,8,7,10,9,18,13,12,15,14,17,16,11] => [2,1,4,3,6,5,8,7,10,9,13,12,15,14,17,16,18,11]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,18),(10,11),(12,13),(14,15),(16,17)] => [2,1,4,3,6,5,8,7,18,11,10,13,12,15,14,17,16,9] => [2,1,4,3,6,5,8,7,11,10,13,12,15,14,17,16,18,9]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,18),(8,9),(10,11),(12,13),(14,15),(16,17)] => [2,1,4,3,6,5,18,9,8,11,10,13,12,15,14,17,16,7] => [2,1,4,3,6,5,9,8,11,10,13,12,15,14,17,16,18,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,18),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)] => [2,1,4,3,18,7,6,9,8,11,10,13,12,15,14,17,16,5] => [2,1,4,3,7,6,9,8,11,10,13,12,15,14,17,16,18,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,18),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)] => [2,1,18,5,4,7,6,9,8,11,10,13,12,15,14,17,16,3] => [2,1,5,4,7,6,9,8,11,10,13,12,15,14,17,16,18,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17,20,19] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17,20,19]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,20),(18,19)] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,20,19,18,17] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,19,18,20,17]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,18),(14,17),(15,16)] => [2,1,4,3,6,5,8,7,10,9,12,11,18,17,16,15,14,13] => [2,1,4,3,6,5,8,7,10,9,12,11,16,15,17,14,18,13]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,20),(16,17),(18,19)] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,20,17,16,19,18,15] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,17,16,19,18,20,15]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,18),(12,15),(13,14),(16,17)] => [2,1,4,3,6,5,8,7,10,9,18,15,14,13,12,17,16,11] => [2,1,4,3,6,5,8,7,10,9,14,13,15,12,17,16,18,11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,20),(14,15),(16,17),(18,19)] => [2,1,4,3,6,5,8,7,10,9,12,11,20,15,14,17,16,19,18,13] => [2,1,4,3,6,5,8,7,10,9,12,11,15,14,17,16,19,18,20,13]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,18),(10,13),(11,12),(14,15),(16,17)] => [2,1,4,3,6,5,8,7,18,13,12,11,10,15,14,17,16,9] => [2,1,4,3,6,5,8,7,12,11,13,10,15,14,17,16,18,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,20),(12,13),(14,15),(16,17),(18,19)] => [2,1,4,3,6,5,8,7,10,9,20,13,12,15,14,17,16,19,18,11] => [2,1,4,3,6,5,8,7,10,9,13,12,15,14,17,16,19,18,20,11]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,18),(8,11),(9,10),(12,13),(14,15),(16,17)] => [2,1,4,3,6,5,18,11,10,9,8,13,12,15,14,17,16,7] => [2,1,4,3,6,5,10,9,11,8,13,12,15,14,17,16,18,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,20),(10,11),(12,13),(14,15),(16,17),(18,19)] => [2,1,4,3,6,5,8,7,20,11,10,13,12,15,14,17,16,19,18,9] => [2,1,4,3,6,5,8,7,11,10,13,12,15,14,17,16,19,18,20,9]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,18),(6,9),(7,8),(10,11),(12,13),(14,15),(16,17)] => [2,1,4,3,18,9,8,7,6,11,10,13,12,15,14,17,16,5] => [2,1,4,3,8,7,9,6,11,10,13,12,15,14,17,16,18,5]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,20),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)] => [2,1,4,3,6,5,20,9,8,11,10,13,12,15,14,17,16,19,18,7] => [2,1,4,3,6,5,9,8,11,10,13,12,15,14,17,16,19,18,20,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,18),(4,7),(5,6),(8,9),(10,11),(12,13),(14,15),(16,17)] => [2,1,18,7,6,5,4,9,8,11,10,13,12,15,14,17,16,3] => [2,1,6,5,7,4,9,8,11,10,13,12,15,14,17,16,18,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,20),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)] => [2,1,4,3,20,7,6,9,8,11,10,13,12,15,14,17,16,19,18,5] => [2,1,4,3,7,6,9,8,11,10,13,12,15,14,17,16,19,18,20,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,2),(3,20),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)] => [2,1,20,5,4,7,6,9,8,11,10,13,12,15,14,17,16,19,18,3] => [2,1,5,4,7,6,9,8,11,10,13,12,15,14,17,16,19,18,20,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,20),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)] => [20,3,2,5,4,7,6,9,8,11,10,13,12,15,14,17,16,19,18,1] => [3,2,5,4,7,6,9,8,11,10,13,12,15,14,17,16,19,18,20,1]
Map
to tunnel matching
Description
Sends a Dyck path of semilength n to the noncrossing perfect matching given by matching an up-step with the corresponding down-step.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.