Identifier
Values
[[1,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1],[2]] => ([],1) => ([],1) => 1
[[1,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1],[2]] => ([],1) => ([],1) => 1
[[1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[3,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[4,4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[2],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[2,2,3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[2,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[3,3,3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,3],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,3],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,3],[3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1],[2],[3]] => ([],1) => ([],1) => 1
[[1,1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1],[2]] => ([],1) => ([],1) => 1
[[1,1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,2,2],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1],[2,2]] => ([],1) => ([],1) => 1
[[1,5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[3,5]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[4,5]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[5,5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[2],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[3],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[4],[5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,3,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,4,4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,2,4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[2,3,4]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[2,4,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[3,3,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,4],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,4],[3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([],1) => 1
[[1,4],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([],1) => 1
[[2,2],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[2,3],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,4],[3]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[2,4],[4]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => ([(0,2),(2,1)],3) => 0
[[3,3],[4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1],[2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1],[3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,2,2,3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,3,3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,2,2,3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[2,2,3,3]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[2,3,3,3]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[3,3,3,3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,1,1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,3],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,3],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,3],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,2,3],[3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,3,3],[2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,3,3],[3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[2,2,2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1],[2,3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1],[3,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2],[2,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2],[3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[2,2],[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1],[2],[3]] => ([],1) => ([],1) => 1
[[1,2],[2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,3],[2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
>>> Load all 1322 entries. <<<[[1,1,1,2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,2,2,2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1,1,1],[2]] => ([],1) => ([],1) => 1
[[1,1,1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,2,2],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2,2,2],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1],[2,2]] => ([],1) => ([],1) => 1
[[1,1,2],[2,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[3,6]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[4,6]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[5,6]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[6,6]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1],[6]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2],[6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[3],[6]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[4],[6]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[5],[6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,1,5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,3,5]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,4,5]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,5,5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[2,2,5]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,3,5]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[3,3,5]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[3,4,5]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[3,5,5]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[4,4,5]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[4,5,5]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[5,5,5]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,1],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,5],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,5],[3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[1,4],[5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,5],[4]] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,5],[5]] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,2],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[2,3],[5]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[2,4],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[3,3],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[3,5],[4]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[3,5],[5]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,23),(5,24),(6,17),(7,22),(8,13),(8,24),(9,10),(9,27),(10,26),(11,16),(11,20),(12,19),(12,27),(13,18),(13,19),(15,28),(16,4),(16,28),(17,7),(18,17),(19,25),(20,22),(20,28),(21,14),(22,21),(23,14),(24,6),(24,18),(25,15),(25,20),(26,15),(26,16),(27,11),(27,25),(27,26),(28,21),(28,23)],29) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1],[2],[5]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1],[3],[5]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1],[4],[5]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[2],[3],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[2],[4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[3],[4],[5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,3,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,4,4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,2,3,4]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,4,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,3,3,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[2,2,2,4]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,2,3,4]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,2,4,4]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[2,3,4,4]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[2,4,4,4]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[3,3,4,4]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[3,4,4,4]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[4,4,4,4]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,1,1],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,4],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,4],[3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([],1) => 1
[[1,1,4],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([],1) => 1
[[1,2,2],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2,4],[2]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2,3],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,4],[3]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,3,4],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,4],[4]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => ([(0,2),(2,1)],3) => 0
[[1,4,4],[2]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,3],[4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,4],[3]] => ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11) => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 2
[[2,2,2],[4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[2,2,3],[4]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[2,2,4],[3]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,5),(5,1),(5,10),(6,4),(7,8),(8,2),(8,3),(9,12),(10,11),(10,12),(11,13),(12,13)],14) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[2,3,3],[4]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[2,3,4],[3]] => ([(0,9),(0,11),(1,14),(2,12),(2,13),(3,12),(3,17),(4,18),(5,15),(5,16),(6,7),(7,4),(7,13),(8,5),(8,19),(9,6),(10,2),(10,3),(10,14),(11,1),(11,10),(12,20),(13,18),(13,20),(14,8),(14,17),(15,22),(16,22),(17,19),(18,15),(18,21),(19,16),(20,21),(21,22)],23) => ([(0,2),(2,1)],3) => 0
[[2,4,4],[3]] => ([(0,10),(0,12),(1,15),(2,13),(2,14),(3,16),(3,18),(4,20),(5,13),(5,17),(6,21),(7,8),(8,6),(8,14),(9,3),(9,24),(10,7),(11,2),(11,5),(11,15),(12,1),(12,11),(13,22),(14,21),(14,22),(15,9),(15,17),(16,20),(16,25),(17,24),(18,25),(20,19),(21,18),(21,23),(22,23),(23,25),(24,4),(24,16),(25,19)],26) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,4,4],[4]] => ([(0,11),(0,13),(1,19),(2,20),(3,26),(4,17),(4,22),(5,16),(6,14),(6,21),(7,14),(7,15),(8,9),(9,1),(9,15),(10,4),(10,25),(11,8),(12,6),(12,7),(12,16),(13,5),(13,12),(14,23),(15,19),(15,23),(16,10),(16,21),(17,26),(17,27),(18,20),(19,22),(19,24),(21,25),(22,27),(23,24),(24,27),(25,3),(25,17),(26,2),(26,18),(27,18)],28) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[3,3,3],[4]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,1],[2,4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1],[3,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1],[4,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,2],[2,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,2],[3,4]] => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8) => ([],1) => 1
[[1,3],[2,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,2],[4,4]] => ([(0,5),(1,6),(2,9),(3,6),(3,9),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7),(9,4),(9,8)],10) => ([],1) => 1
[[1,3],[3,4]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[2,2],[3,4]] => ([(0,5),(1,6),(2,9),(3,6),(3,9),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7),(9,4),(9,8)],10) => ([],1) => 1
[[2,2],[4,4]] => ([(0,6),(1,12),(2,11),(3,11),(3,12),(4,8),(5,9),(6,1),(6,2),(6,3),(7,8),(7,9),(8,10),(9,10),(11,4),(11,7),(12,5),(12,7)],13) => ([(0,1)],2) => 0
[[2,3],[4,4]] => ([(0,2),(1,8),(2,5),(2,6),(2,7),(3,17),(4,16),(5,12),(5,13),(6,12),(6,14),(7,13),(7,14),(8,10),(8,11),(9,18),(10,18),(11,18),(12,1),(13,4),(13,15),(14,3),(14,15),(15,16),(15,17),(16,9),(16,10),(17,9),(17,11)],19) => ([(0,2),(2,1)],3) => 0
[[3,3],[4,4]] => ([(0,9),(1,10),(1,18),(2,10),(2,17),(3,17),(3,18),(5,14),(6,15),(7,12),(7,13),(8,7),(9,1),(9,2),(9,3),(10,8),(11,14),(11,15),(12,19),(13,19),(14,12),(14,16),(15,13),(15,16),(16,19),(17,5),(17,11),(18,6),(18,11),(19,4)],20) => ([(0,2),(2,1)],3) => 0
[[1,1],[2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1],[3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2],[2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,3],[2],[4]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([],1) => 1
[[1,4],[2],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,4],[2],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3],[3],[4]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([],1) => 1
[[2,2],[3],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1],[2],[3],[4]] => ([],1) => ([],1) => 1
[[1,1,1,1,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,2,2,3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,2,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,3,3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,2,3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,2,3,3]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,2,3,3,3]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,3,3,3,3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[2,2,2,3,3]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,2,3,3,3]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[2,3,3,3,3]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[3,3,3,3,3]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,1,1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,3],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,2,3],[3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,3,3],[2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,3,3],[3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,2,2,2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,3],[2]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2,3,3],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,3,3],[2]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,3,3],[3]] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,2,2,2],[3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1,1],[2,3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1],[3,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2],[2,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,3],[2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2],[3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,3],[2,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,3],[3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2],[2,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2],[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,2,3],[2,3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[2,2,2],[3,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,1,1],[2],[3]] => ([],1) => ([],1) => 1
[[1,1,2],[2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,3],[2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2,2],[2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2,3],[2],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,3,3],[2],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1],[2,2],[3]] => ([],1) => ([],1) => 1
[[1,1],[2,3],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,2],[2,3],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,2,2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[2,2,2,2,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,1,1,1],[2]] => ([],1) => ([],1) => 1
[[1,1,1,1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,2,2],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2,2,2],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,2,2],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1],[2,2]] => ([],1) => ([],1) => 1
[[1,1,1,2],[2,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,2,2],[2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[2,2,2]] => ([],1) => ([],1) => 1
[[1,7]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1],[7]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[3],[7]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[4],[7]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[5],[7]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[6],[7]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,3,6]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,4,6]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,5,6]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,6,6]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1],[6]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2],[6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,6],[2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,3],[6]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,4],[6]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,5],[6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[2,2],[6]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,3],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[3,3],[6]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[3,4],[6]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[3,5],[6]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[4,4],[6]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[4,5],[6]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[5,5],[6]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1],[2],[6]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1],[3],[6]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1],[4],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1],[5],[6]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2],[3],[6]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[2],[4],[6]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[2],[5],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[3],[4],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,1,5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,3,5]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,1,4,5]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,1,5,5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,2,2,5]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,3,5]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,3,3,5]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[1,3,4,5]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[1,3,5,5]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[1,4,4,5]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[1,4,5,5]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[1,5,5,5]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,1,1],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,5],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,5],[3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[1,1,4],[5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,5],[4]] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,5],[5]] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,2,5],[2]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,3],[5]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,3,5],[2]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,2,4],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,4,5],[2]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,5,5],[2]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,3,3],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,3,5],[4]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,3,5],[5]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,23),(5,24),(6,17),(7,22),(8,13),(8,24),(9,10),(9,27),(10,26),(11,16),(11,20),(12,19),(12,27),(13,18),(13,19),(15,28),(16,4),(16,28),(17,7),(18,17),(19,25),(20,22),(20,28),(21,14),(22,21),(23,14),(24,6),(24,18),(25,15),(25,20),(26,15),(26,16),(27,11),(27,25),(27,26),(28,21),(28,23)],29) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[2,2,2],[5]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,2,3],[5]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,2,4],[5]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[2,3,4],[5]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[2,4,4],[5]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[3,3,4],[5]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[3,4,4],[5]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[4,4,4],[5]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,1],[2,5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1],[3,5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1],[4,5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1],[5,5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2],[2,5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,3],[2,5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,4],[2,5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3],[3,5]] => ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11) => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 2
[[1,1],[2],[5]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1],[3],[5]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1],[4],[5]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,2],[2],[5]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,2],[3],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,3],[2],[5]] => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,5],[2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2],[4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,4],[2],[5]] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,5],[2],[4]] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => ([],1) => 1
[[1,3],[3],[5]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 2
[[1,3],[4],[5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,2],[3],[5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[2,2],[4],[5]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[2,3],[4],[5]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[3,3],[4],[5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1],[2],[3],[5]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1],[2],[4],[5]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1],[3],[4],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[2],[3],[4],[5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,4,4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2,4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,1,2,3,4]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,2,4,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,3,3,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,2,2,2,4]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,3,4]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,4,4]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[1,2,3,4,4]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[1,2,4,4,4]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[1,3,3,4,4]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[1,3,4,4,4]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[1,4,4,4,4]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,1,1,1],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,4],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1,4],[3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([],1) => 1
[[1,1,1,4],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([],1) => 1
[[1,1,2,2],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,2,4],[2]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,2,3],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,4],[3]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,1,3,4],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,4],[4]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => ([(0,2),(2,1)],3) => 0
[[1,1,4,4],[2]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,3],[4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,4],[3]] => ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11) => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 2
[[1,2,2,2],[4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,2,4],[2]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,2,2,3],[4]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,2,2,4],[3]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,5),(5,1),(5,10),(6,4),(7,8),(8,2),(8,3),(9,12),(10,11),(10,12),(11,13),(12,13)],14) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,2,3,4],[2]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,4,4],[2]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,2,3,3],[4]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,2,3,4],[3]] => ([(0,9),(0,11),(1,14),(2,12),(2,13),(3,12),(3,17),(4,18),(5,15),(5,16),(6,7),(7,4),(7,13),(8,5),(8,19),(9,6),(10,2),(10,3),(10,14),(11,1),(11,10),(12,20),(13,18),(13,20),(14,8),(14,17),(15,22),(16,22),(17,19),(18,15),(18,21),(19,16),(20,21),(21,22)],23) => ([(0,2),(2,1)],3) => 0
[[1,3,3,4],[2]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,2,4,4],[3]] => ([(0,10),(0,12),(1,15),(2,13),(2,14),(3,16),(3,18),(4,20),(5,13),(5,17),(6,21),(7,8),(8,6),(8,14),(9,3),(9,24),(10,7),(11,2),(11,5),(11,15),(12,1),(12,11),(13,22),(14,21),(14,22),(15,9),(15,17),(16,20),(16,25),(17,24),(18,25),(20,19),(21,18),(21,23),(22,23),(23,25),(24,4),(24,16),(25,19)],26) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,4,4],[4]] => ([(0,11),(0,13),(1,19),(2,20),(3,26),(4,17),(4,22),(5,16),(6,14),(6,21),(7,14),(7,15),(8,9),(9,1),(9,15),(10,4),(10,25),(11,8),(12,6),(12,7),(12,16),(13,5),(13,12),(14,23),(15,19),(15,23),(16,10),(16,21),(17,26),(17,27),(18,20),(19,22),(19,24),(21,25),(22,27),(23,24),(24,27),(25,3),(25,17),(26,2),(26,18),(27,18)],28) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,3,3],[4]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[2,2,2,3],[4]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,2,3,3],[4]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[2,3,3,3],[4]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[3,3,3,3],[4]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,1],[2,4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[3,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1],[4,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,2],[2,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,4],[2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2],[3,4]] => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8) => ([],1) => 1
[[1,1,3],[2,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,4],[2,3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([],1) => 1
[[1,1,2],[4,4]] => ([(0,5),(1,6),(2,9),(3,6),(3,9),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7),(9,4),(9,8)],10) => ([],1) => 1
[[1,1,4],[2,4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([],1) => 1
[[1,1,3],[3,4]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,1,4],[3,3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[1,1,4],[3,4]] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,4],[4,4]] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2],[2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2,2],[3,4]] => ([(0,5),(1,6),(2,9),(3,6),(3,9),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7),(9,4),(9,8)],10) => ([],1) => 1
[[1,2,3],[2,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,4],[2,3]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,2,2],[4,4]] => ([(0,6),(1,12),(2,11),(3,11),(3,12),(4,8),(5,9),(6,1),(6,2),(6,3),(7,8),(7,9),(8,10),(9,10),(11,4),(11,7),(12,5),(12,7)],13) => ([(0,1)],2) => 0
[[1,2,4],[2,4]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => ([(0,2),(2,1)],3) => 0
[[1,3,3],[2,4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,3],[4,4]] => ([(0,2),(1,8),(2,5),(2,6),(2,7),(3,17),(4,16),(5,12),(5,13),(6,12),(6,14),(7,13),(7,14),(8,10),(8,11),(9,18),(10,18),(11,18),(12,1),(13,4),(13,15),(14,3),(14,15),(15,16),(15,17),(16,9),(16,10),(17,9),(17,11)],19) => ([(0,2),(2,1)],3) => 0
[[1,3,3],[3,4]] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,3],[4,4]] => ([(0,9),(1,10),(1,18),(2,10),(2,17),(3,17),(3,18),(5,14),(6,15),(7,12),(7,13),(8,7),(9,1),(9,2),(9,3),(10,8),(11,14),(11,15),(12,19),(13,19),(14,12),(14,16),(15,13),(15,16),(16,19),(17,5),(17,11),(18,6),(18,11),(19,4)],20) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1],[3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2],[2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,3],[2],[4]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([],1) => 1
[[1,1,4],[2],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,4],[2],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3],[3],[4]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([],1) => 1
[[1,2,2],[2],[4]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,2,2],[3],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,3],[2],[4]] => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,4],[2],[3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2,4],[2],[4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,3,3],[2],[4]] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,4],[2],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,4,4],[2],[3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,4,4],[2],[4]] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,3],[3],[4]] => ([(0,4),(0,6),(1,8),(3,7),(4,9),(5,2),(6,3),(6,9),(7,8),(8,5),(9,1),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,2,2],[3],[4]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1],[2,2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1],[2,3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1],[2,4],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1],[2,4],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1],[3,3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1],[3,4],[4]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,2],[2,3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2],[2,4],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,2],[2,4],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2],[3,3],[4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([],1) => 1
[[1,3],[2,4],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,2],[3,4],[4]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,3],[2,4],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3],[3,4],[4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,2],[3,3],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([],1) => 1
[[2,2],[3,4],[4]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => ([(0,2),(2,1)],3) => 0
[[1,1],[2],[3],[4]] => ([],1) => ([],1) => 1
[[1,2],[2],[3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,3],[2],[3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,4],[2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,1,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1,2,2,3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,3,3,3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2,2,3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,2,2,3,3]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,1,2,3,3,3]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,1,3,3,3,3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,2,2,2,3,3]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,3,3,3]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,2,3,3,3,3]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,3,3,3,3,3]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,1,1,1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,3],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,3],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2,3],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,2,3],[3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,3,3],[2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1,3,3],[3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,1,2,2,2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2,3],[2]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,2,3,3],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,3,3],[2]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,3,3],[3]] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,2,2],[3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,2,2,2,3],[2]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,2,3,3],[2]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,2,3,3,3],[2]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,3,3,3,3],[2]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[2,2,2,2,2],[3]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,1,1],[2,3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1],[3,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2],[2,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3],[2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2],[3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,3],[2,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,3],[3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2],[2,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,3],[2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,2,2],[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,2,3],[2,3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,3,3],[2,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,3,3],[2,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,2,2,2],[2,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,2],[3,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,1,1,1],[2],[3]] => ([],1) => ([],1) => 1
[[1,1,1,2],[2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,3],[2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2,2],[2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2,3],[2],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,3,3],[2],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,2,2,2],[2],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,3],[2],[3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2,3,3],[2],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,3,3],[2],[3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1],[2,2,3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1],[2,3,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[3,3,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2],[2,2,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2],[2,3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,2],[3,3,3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2,2],[2,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,2,2],[3,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,2,2],[3,3,3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1],[2,2],[3]] => ([],1) => ([],1) => 1
[[1,1,1],[2,3],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,2],[2,2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,2],[2,3],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,3],[2,2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,3],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,3],[2,3],[3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1],[2,2],[3,3]] => ([],1) => ([],1) => 1
[[1,1,1,1,1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,1,2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2,2,2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,2,2,2,2,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[2,2,2,2,2,2,2]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 0
[[1,1,1,1,1,1],[2]] => ([],1) => ([],1) => 1
[[1,1,1,1,1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,2,2],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2,2,2],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,2,2,2],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,2,2,2],[2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1,1,1,1],[2,2]] => ([],1) => ([],1) => 1
[[1,1,1,1,2],[2,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,2,2],[2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2,2,2],[2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1],[2,2,2]] => ([],1) => ([],1) => 1
[[1,1,1,2],[2,2,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,8]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 0
[[1],[8]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,7]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1],[7]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,7],[2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,3],[7]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,4],[7]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,5],[7]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,6],[7]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1],[2],[7]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1],[3],[7]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1],[4],[7]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1],[5],[7]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1],[6],[7]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[2],[3],[7]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[2],[4],[7]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[3],[4],[7]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[3],[5],[7]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[3],[6],[7]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[4],[5],[7]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[4],[6],[7]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[5],[6],[7]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,1,1,6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1,3,6]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,4,6]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,5,6]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,6,6]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,1],[6]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2],[6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,6],[2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1,3],[6]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,1,4],[6]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,1,5],[6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,2,2],[6]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,3],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,3,6],[2]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,4,6],[2]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,5,6],[2]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,6,6],[2]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,3,3],[6]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[1,3,4],[6]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[1,3,5],[6]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[1,4,4],[6]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[1,4,5],[6]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[1,5,5],[6]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,1],[2,6]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1],[3,6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1],[4,6]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,1],[5,6]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,1],[6,6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,2],[2,6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,3],[2,6]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,4],[2,6]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,5],[2,6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,1],[2],[6]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1],[3],[6]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1],[4],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1],[5],[6]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2],[2],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2],[3],[6]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,3],[2],[6]] => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11) => ([],1) => 1
[[1,6],[2],[3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,2],[4],[6]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2],[5],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,5],[2],[6]] => ([(0,5),(0,7),(1,13),(3,12),(4,10),(5,11),(6,4),(6,8),(7,6),(7,11),(8,10),(8,12),(9,13),(10,9),(11,3),(11,8),(12,1),(12,9),(13,2)],14) => ([],1) => 1
[[1,3],[4],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[2,2],[3],[6]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,2],[4],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,2],[5],[6]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[2,3],[5],[6]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[2,4],[5],[6]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[3,3],[5],[6]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[3,4],[5],[6]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[4,4],[5],[6]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1],[2],[3],[6]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1],[2],[4],[6]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1],[2],[5],[6]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1],[3],[4],[6]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1],[3],[5],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1],[4],[5],[6]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2],[3],[4],[6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[2],[3],[5],[6]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[2],[4],[5],[6]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[3],[4],[5],[6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,1,1,1,5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,2,5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,3,5]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,1,1,4,5]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,1,1,5,5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,1,2,2,5]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,3,5]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,3,3,5]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[1,1,3,4,5]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[1,1,3,5,5]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[1,1,4,4,5]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[1,1,4,5,5]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[1,1,5,5,5]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,1,1,1],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,5],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,3],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,5],[3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[1,1,1,4],[5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,5],[4]] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,5],[5]] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,1,2,5],[2]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,2,3],[5]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,3,5],[2]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,1,2,4],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,4,5],[2]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,1,5,5],[2]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,1,3,3],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,3,5],[4]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,3,5],[5]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,23),(5,24),(6,17),(7,22),(8,13),(8,24),(9,10),(9,27),(10,26),(11,16),(11,20),(12,19),(12,27),(13,18),(13,19),(15,28),(16,4),(16,28),(17,7),(18,17),(19,25),(20,22),(20,28),(21,14),(22,21),(23,14),(24,6),(24,18),(25,15),(25,20),(26,15),(26,16),(27,11),(27,25),(27,26),(28,21),(28,23)],29) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,2,2,2],[5]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,5],[2]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,3],[5]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,3,5],[2]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,4],[5]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[1,3,3,5],[2]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[1,2,3,4],[5]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[1,3,4,5],[2]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[1,3,5,5],[2]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[1,2,4,4],[5]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[1,4,4,5],[2]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[1,4,5,5],[2]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[1,5,5,5],[2]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,3,3,4],[5]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[1,3,4,4],[5]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[1,4,4,4],[5]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,1,1],[2,5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1],[3,5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[4,5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1],[5,5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2],[2,5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,5],[2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3],[2,5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,5],[2,3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[1,1,4],[2,5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,5],[2,4]] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,5],[2,5]] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3],[3,5]] => ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11) => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 2
[[1,2,2],[2,5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,2,3],[2,5]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,4],[2,5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,3,3],[2,5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,3,5],[2,4]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,3,5],[2,5]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,23),(5,24),(6,17),(7,22),(8,13),(8,24),(9,10),(9,27),(10,26),(11,16),(11,20),(12,19),(12,27),(13,18),(13,19),(15,28),(16,4),(16,28),(17,7),(18,17),(19,25),(20,22),(20,28),(21,14),(22,21),(23,14),(24,6),(24,18),(25,15),(25,20),(26,15),(26,16),(27,11),(27,25),(27,26),(28,21),(28,23)],29) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,1],[2],[5]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[3],[5]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1],[4],[5]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,2],[2],[5]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,1,2],[3],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,3],[2],[5]] => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,5],[2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2],[4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,4],[2],[5]] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,5],[2],[4]] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => ([],1) => 1
[[1,1,3],[3],[5]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 2
[[1,1,3],[4],[5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2],[2],[5]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => ([],1) => 1
[[1,2,2],[3],[5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,3],[2],[5]] => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,9),(4,1),(4,9),(5,7),(5,8),(6,12),(7,12),(8,12),(9,5),(9,10),(9,11),(10,6),(10,7),(11,6),(11,8)],13) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,5],[2],[3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,2],[4],[5]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,3,5],[2],[3]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,2,3],[4],[5]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,4,5],[2],[3]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,5,5],[2],[3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,3,3],[4],[5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[2,2,2],[4],[5]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[2,2,3],[4],[5]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[2,3,3],[4],[5]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[3,3,3],[4],[5]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1],[2,2],[5]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1],[2,3],[5]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1],[2,5],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1],[2,4],[5]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1],[2,5],[4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([],1) => 1
[[1,1],[2,5],[5]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([],1) => 1
[[1,1],[3,3],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1],[3,4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1],[3,5],[4]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,1],[3,5],[5]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => ([(0,2),(2,1)],3) => 0
[[1,1],[4,4],[5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2],[2,3],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2],[2,5],[3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2],[2,4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2],[2,5],[4]] => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,2],[3,3],[5]] => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,3],[2,5],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3],[2,4],[5]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,4],[2,5],[3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,4],[2,5],[4]] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3],[3,4],[5]] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1],[2],[3],[5]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1],[2],[4],[5]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1],[3],[4],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2],[2],[3],[5]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,2],[2],[4],[5]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,3],[2],[3],[5]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,2],[3],[4],[5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3],[2],[4],[5]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,2),(2,1)],3) => 0
[[1,4],[2],[3],[5]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,2),(2,1)],3) => 0
[[1,5],[2],[3],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,5],[2],[3],[5]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,4],[2],[4],[5]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,2),(2,1)],3) => 0
[[1,3],[3],[4],[5]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,2),(2,1)],3) => 0
[[2,2],[3],[4],[5]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1],[2],[3],[4],[5]] => ([],1) => ([],1) => 1
[[1,1,1,1,1,4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,3,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,4,4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,2,2,4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,1,1,2,3,4]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,2,4,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,1,3,3,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,2,2,2,4]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,2,3,4]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,2,4,4]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[1,1,2,3,4,4]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[1,1,2,4,4,4]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[1,1,3,3,4,4]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[1,1,3,4,4,4]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[1,1,4,4,4,4]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,1,1,1,1],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,1,4],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1,1,4],[3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([],1) => 1
[[1,1,1,1,4],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([],1) => 1
[[1,1,1,2,2],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2,4],[2]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2,3],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,2,4],[3]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3,4],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,2,4],[4]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => ([(0,2),(2,1)],3) => 0
[[1,1,1,4,4],[2]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,3,3],[4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,3,4],[3]] => ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11) => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 2
[[1,1,2,2,2],[4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,2,2,4],[2]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,1,2,2,3],[4]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,1,2,2,4],[3]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,5),(5,1),(5,10),(6,4),(7,8),(8,2),(8,3),(9,12),(10,11),(10,12),(11,13),(12,13)],14) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1,2,3,4],[2]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,2,4,4],[2]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,2,3,3],[4]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,1,2,3,4],[3]] => ([(0,9),(0,11),(1,14),(2,12),(2,13),(3,12),(3,17),(4,18),(5,15),(5,16),(6,7),(7,4),(7,13),(8,5),(8,19),(9,6),(10,2),(10,3),(10,14),(11,1),(11,10),(12,20),(13,18),(13,20),(14,8),(14,17),(15,22),(16,22),(17,19),(18,15),(18,21),(19,16),(20,21),(21,22)],23) => ([(0,2),(2,1)],3) => 0
[[1,1,3,3,4],[2]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,2,4,4],[3]] => ([(0,10),(0,12),(1,15),(2,13),(2,14),(3,16),(3,18),(4,20),(5,13),(5,17),(6,21),(7,8),(8,6),(8,14),(9,3),(9,24),(10,7),(11,2),(11,5),(11,15),(12,1),(12,11),(13,22),(14,21),(14,22),(15,9),(15,17),(16,20),(16,25),(17,24),(18,25),(20,19),(21,18),(21,23),(22,23),(23,25),(24,4),(24,16),(25,19)],26) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,4,4],[4]] => ([(0,11),(0,13),(1,19),(2,20),(3,26),(4,17),(4,22),(5,16),(6,14),(6,21),(7,14),(7,15),(8,9),(9,1),(9,15),(10,4),(10,25),(11,8),(12,6),(12,7),(12,16),(13,5),(13,12),(14,23),(15,19),(15,23),(16,10),(16,21),(17,26),(17,27),(18,20),(19,22),(19,24),(21,25),(22,27),(23,24),(24,27),(25,3),(25,17),(26,2),(26,18),(27,18)],28) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,3,3],[4]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,2,2,2,4],[2]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,2,3],[4]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,3,4],[2]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,4,4],[2]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2
[[1,2,2,3,3],[4]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,2,3,4,4],[2]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => ([],1) => 1
[[1,2,4,4,4],[2]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => ([],1) => 1
[[1,2,3,3,3],[4]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,3,3,4,4],[2]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => ([],1) => 1
[[1,3,4,4,4],[2]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[1,4,4,4,4],[2]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => ([],1) => 1
[[1,3,3,3,3],[4]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,1,1],[2,4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1],[3,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,1],[4,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1,2],[2,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,4],[2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2],[3,4]] => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8) => ([],1) => 1
[[1,1,1,3],[2,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1,4],[2,3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([],1) => 1
[[1,1,1,2],[4,4]] => ([(0,5),(1,6),(2,9),(3,6),(3,9),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7),(9,4),(9,8)],10) => ([],1) => 1
[[1,1,1,4],[2,4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([],1) => 1
[[1,1,1,3],[3,4]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,1,1,4],[3,3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[1,1,1,4],[3,4]] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,4],[4,4]] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2],[2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,2,4],[2,2]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,2,2],[3,4]] => ([(0,5),(1,6),(2,9),(3,6),(3,9),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7),(9,4),(9,8)],10) => ([],1) => 1
[[1,1,2,3],[2,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,4],[2,3]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,1,3,4],[2,2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2],[4,4]] => ([(0,6),(1,12),(2,11),(3,11),(3,12),(4,8),(5,9),(6,1),(6,2),(6,3),(7,8),(7,9),(8,10),(9,10),(11,4),(11,7),(12,5),(12,7)],13) => ([(0,1)],2) => 0
[[1,1,2,4],[2,4]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => ([(0,2),(2,1)],3) => 0
[[1,1,4,4],[2,2]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,3],[2,4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,4],[2,3]] => ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11) => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 2
[[1,1,2,3],[4,4]] => ([(0,2),(1,8),(2,5),(2,6),(2,7),(3,17),(4,16),(5,12),(5,13),(6,12),(6,14),(7,13),(7,14),(8,10),(8,11),(9,18),(10,18),(11,18),(12,1),(13,4),(13,15),(14,3),(14,15),(15,16),(15,17),(16,9),(16,10),(17,9),(17,11)],19) => ([(0,2),(2,1)],3) => 0
[[1,1,3,3],[3,4]] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,3],[4,4]] => ([(0,9),(1,10),(1,18),(2,10),(2,17),(3,17),(3,18),(5,14),(6,15),(7,12),(7,13),(8,7),(9,1),(9,2),(9,3),(10,8),(11,14),(11,15),(12,19),(13,19),(14,12),(14,16),(15,13),(15,16),(16,19),(17,5),(17,11),(18,6),(18,11),(19,4)],20) => ([(0,2),(2,1)],3) => 0
[[1,2,2,2],[2,4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,2,3],[2,4]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,2,2,4],[2,3]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,5),(5,1),(5,10),(6,4),(7,8),(8,2),(8,3),(9,12),(10,11),(10,12),(11,13),(12,13)],14) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,2,3,3],[2,4]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,2,3,4],[2,3]] => ([(0,9),(0,11),(1,14),(2,12),(2,13),(3,12),(3,17),(4,18),(5,15),(5,16),(6,7),(7,4),(7,13),(8,5),(8,19),(9,6),(10,2),(10,3),(10,14),(11,1),(11,10),(12,20),(13,18),(13,20),(14,8),(14,17),(15,22),(16,22),(17,19),(18,15),(18,21),(19,16),(20,21),(21,22)],23) => ([(0,2),(2,1)],3) => 0
[[1,2,4,4],[2,3]] => ([(0,10),(0,12),(1,15),(2,13),(2,14),(3,16),(3,18),(4,20),(5,13),(5,17),(6,21),(7,8),(8,6),(8,14),(9,3),(9,24),(10,7),(11,2),(11,5),(11,15),(12,1),(12,11),(13,22),(14,21),(14,22),(15,9),(15,17),(16,20),(16,25),(17,24),(18,25),(20,19),(21,18),(21,23),(22,23),(23,25),(24,4),(24,16),(25,19)],26) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,4,4],[2,4]] => ([(0,11),(0,13),(1,19),(2,20),(3,26),(4,17),(4,22),(5,16),(6,14),(6,21),(7,14),(7,15),(8,9),(9,1),(9,15),(10,4),(10,25),(11,8),(12,6),(12,7),(12,16),(13,5),(13,12),(14,23),(15,19),(15,23),(16,10),(16,21),(17,26),(17,27),(18,20),(19,22),(19,24),(21,25),(22,27),(23,24),(24,27),(25,3),(25,17),(26,2),(26,18),(27,18)],28) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,3,3],[2,4]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,1,1,1],[2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1],[3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2],[2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,1,2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,3],[2],[4]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([],1) => 1
[[1,1,1,4],[2],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,4],[2],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,3],[3],[4]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([],1) => 1
[[1,1,2,2],[2],[4]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,1,2,2],[3],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,3],[2],[4]] => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,4],[2],[3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,2,4],[2],[4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,3,3],[2],[4]] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,4],[2],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,4,4],[2],[3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,4,4],[2],[4]] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,3],[3],[4]] => ([(0,4),(0,6),(1,8),(3,7),(4,9),(5,2),(6,3),(6,9),(7,8),(8,5),(9,1),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,2],[2],[4]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,2,2],[3],[4]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,2,2,3],[2],[4]] => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11) => ([],1) => 1
[[1,2,2,4],[2],[3]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,2,2,4],[2],[4]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,3,4],[2],[3]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,4,4],[2],[3]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,3,3,3],[2],[4]] => ([(0,5),(0,7),(1,13),(3,12),(4,10),(5,11),(6,4),(6,8),(7,6),(7,11),(8,10),(8,12),(9,13),(10,9),(11,3),(11,8),(12,1),(12,9),(13,2)],14) => ([],1) => 1
[[1,3,3,4],[2],[3]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[2,2,2,2],[3],[4]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,1],[2,2,4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[2,3,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1],[2,4,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1],[3,3,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[3,4,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1],[4,4,4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2],[2,2,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,2],[2,3,4]] => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8) => ([],1) => 1
[[1,1,3],[2,2,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,2],[2,4,4]] => ([(0,5),(1,6),(2,9),(3,6),(3,9),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7),(9,4),(9,8)],10) => ([],1) => 1
[[1,1,3],[2,3,4]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,2,2],[2,3,4]] => ([(0,5),(1,6),(2,9),(3,6),(3,9),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7),(9,4),(9,8)],10) => ([],1) => 1
[[1,2,2],[2,4,4]] => ([(0,6),(1,12),(2,11),(3,11),(3,12),(4,8),(5,9),(6,1),(6,2),(6,3),(7,8),(7,9),(8,10),(9,10),(11,4),(11,7),(12,5),(12,7)],13) => ([(0,1)],2) => 0
[[1,2,3],[2,4,4]] => ([(0,2),(1,8),(2,5),(2,6),(2,7),(3,17),(4,16),(5,12),(5,13),(6,12),(6,14),(7,13),(7,14),(8,10),(8,11),(9,18),(10,18),(11,18),(12,1),(13,4),(13,15),(14,3),(14,15),(15,16),(15,17),(16,9),(16,10),(17,9),(17,11)],19) => ([(0,2),(2,1)],3) => 0
[[1,3,3],[2,4,4]] => ([(0,9),(1,10),(1,18),(2,10),(2,17),(3,17),(3,18),(5,14),(6,15),(7,12),(7,13),(8,7),(9,1),(9,2),(9,3),(10,8),(11,14),(11,15),(12,19),(13,19),(14,12),(14,16),(15,13),(15,16),(16,19),(17,5),(17,11),(18,6),(18,11),(19,4)],20) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[2,2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1],[2,3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[2,4],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[2,4],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1],[3,3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1],[3,4],[4]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,2],[2,2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,2],[2,3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2],[2,4],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,3],[2,2],[4]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([],1) => 1
[[1,1,4],[2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2],[2,4],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,4],[2,2],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2],[3,3],[4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([],1) => 1
[[1,1,3],[2,3],[4]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([],1) => 1
[[1,1,3],[2,4],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,4],[2,3],[3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([],1) => 1
[[1,1,2],[3,4],[4]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,1,3],[2,4],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,4],[2,4],[3]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([],1) => 1
[[1,1,4],[2,4],[4]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[1,1,3],[3,3],[4]] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => ([],1) => 1
[[1,1,3],[3,4],[4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2],[2,3],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2],[2,4],[3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2,2],[2,4],[4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,2,2],[3,3],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([],1) => 1
[[1,2,3],[2,4],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,4],[2,3],[3]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,2,2],[3,4],[4]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => ([(0,2),(2,1)],3) => 0
[[1,2,3],[2,4],[4]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,4],[2,4],[3]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => ([(0,2),(2,1)],3) => 0
[[1,2,4],[2,4],[4]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => ([(0,2),(2,1)],3) => 0
[[1,3,3],[2,4],[3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,3,3],[3,4],[4]] => ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[2,2,2],[3,3],[4]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[2,2,2],[3,4],[4]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => ([(0,2),(2,1)],3) => 0
[[1,1,1],[2],[3],[4]] => ([],1) => ([],1) => 1
[[1,1,2],[2],[3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,3],[2],[3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,4],[2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2],[2],[3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2,3],[2],[3],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,2,4],[2],[3],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,3,3],[2],[3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,3,4],[2],[3],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,4,4],[2],[3],[4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1],[2,2],[3,4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1],[2,2],[4,4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1],[2,3],[3,4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1],[2,3],[4,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1],[3,3],[4,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,2],[2,3],[3,4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2],[2,3],[4,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,2],[3,3],[4,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,2],[3,3],[4,4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1],[2,2],[3],[4]] => ([],1) => ([],1) => 1
[[1,1],[2,3],[3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1],[2,4],[3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2],[2,3],[3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,2],[2,4],[3],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,3],[2,4],[3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1,1,1,1,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,1,1,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1,1,2,2,3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,3,3,3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,2,2,2,3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,2,2,3,3]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,1,1,2,3,3,3]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,1,1,3,3,3,3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,1,2,2,2,3,3]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,2,3,3,3]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,2,3,3,3,3]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,3,3,3,3,3]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,1,1,1,1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,1,2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,3],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,3],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,2,3],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,1,2,3],[3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,1,3,3],[2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1,1,3,3],[3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,1,1,2,2,2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,2,2,3],[2]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2,3,3],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,3,3,3],[2]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,3,3,3],[3]] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2,2,2],[3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1,2,2,2,3],[2]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,2,2,3,3],[2]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,1,2,3,3,3],[2]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,1,3,3,3,3],[2]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,2,2,2,2,2],[3]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,2,2,2,3,3],[2]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,2,3,3,3],[2]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,2,3,3,3,3],[2]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,3,3,3,3,3],[2]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[2,2,2,2,2,2],[3]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 0
[[1,1,1,1,1],[2,3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,1],[3,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2],[2,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,3],[2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2],[3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,1,3],[2,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,3],[3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,2,2],[2,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2,3],[2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,2,2],[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1,2,3],[2,3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,3,3],[2,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1,3,3],[2,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,1,2,2,2],[2,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2,3],[2,2]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,2,2,2],[3,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,1,2,3,3],[2,2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,3,3],[2,2]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,3,3],[2,3]] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,2,2],[2,3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1,1,1,1],[2],[3]] => ([],1) => ([],1) => 1
[[1,1,1,1,2],[2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,3],[2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2,2],[2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2,3],[2],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,3,3],[2],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,2,2,2],[2],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,2,3],[2],[3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,2,3,3],[2],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,3,3,3],[2],[3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,2,2],[2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,2,3],[2],[3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,2,3,3],[2],[3]] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => ([],1) => 1
[[1,2,3,3,3],[2],[3]] => ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => ([],1) => 1
[[1,3,3,3,3],[2],[3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,1,1,1],[2,2,3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1],[2,3,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1],[3,3,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2],[2,2,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3],[2,2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2],[2,3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,1,3],[2,2,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2],[3,3,3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3],[2,3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,3],[3,3,3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1,2,2],[2,2,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,2],[2,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,2,3],[2,2,3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,2,2],[3,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,2,2,2],[2,3,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,2,2,2],[3,3,3]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[2,2,2,2],[3,3,3]] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1],[2,2],[3]] => ([],1) => ([],1) => 1
[[1,1,1,1],[2,3],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,2],[2,2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,2],[2,3],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3],[2,2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,2],[2,2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2,2],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,3],[2,2],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,1,2,3],[2,3],[3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,3,3],[2,2],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,3,3],[2,3],[3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([],1) => 1
[[1,2,2,2],[2,3],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1],[2,2,2],[3]] => ([],1) => ([],1) => 1
[[1,1,1],[2,2,3],[3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1],[2,3,3],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2],[2,2,3],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,2],[2,3,3],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([],1) => 1
[[1,2,2],[2,3,3],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([],1) => 1
[[1,1,1],[2,2],[3,3]] => ([],1) => ([],1) => 1
[[1,1,2],[2,2],[3,3]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,3],[2,2],[3,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,1,1,2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,2,2,2,2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1,2,2,2,2,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,2,2,2,2,2,2,2]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 0
[[1,1,1,1,1,1,1],[2]] => ([],1) => ([],1) => 1
[[1,1,1,1,1,1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,1,2,2],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2,2,2],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2,2,2,2],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2,2,2,2],[2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,2,2,2,2,2,2],[2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,1,1,1,1,1],[2,2]] => ([],1) => ([],1) => 1
[[1,1,1,1,1,2],[2,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,2,2],[2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2,2,2],[2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,2,2,2],[2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,1],[2,2,2]] => ([],1) => ([],1) => 1
[[1,1,1,1,2],[2,2,2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,2,2],[2,2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1],[2,2,2,2]] => ([],1) => ([],1) => 1
[[1]] => ([],1) => ([],1) => 1
[[1,1,1,1],[2,2,2],[3,3],[4]] => ([],1) => ([],1) => 1
[[1,1,1,2],[2,2,2],[3,3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1],[2,2,3],[3,3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,2],[2,2,3],[3,3],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3],[2,2,3],[3,3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,2],[2,2,3],[3,3],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,2,3],[2,2,3],[3,3],[4]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,1],[2,2,2],[3,4],[4]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,2],[2,2,2],[3,4],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,1,1],[2,2,3],[3,4],[4]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,2],[2,2,3],[3,4],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,3],[2,2,3],[3,4],[4]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([],1) => 1
[[1,1,2,2],[2,2,3],[3,4],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1],[2,2,4],[3,4],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2],[2,2,4],[3,4],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3],[2,2,4],[3,4],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,4],[2,2,4],[3,4],[4]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[1,1,2,2],[2,2,4],[3,4],[4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,1,2,3],[2,2,4],[3,4],[4]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,2,4],[2,2,4],[3,4],[4]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1],[2,3,3],[3,4],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2],[2,3,3],[3,4],[4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([],1) => 1
[[1,1,1,3],[2,3,3],[3,4],[4]] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => ([],1) => 1
[[1,1,2,2],[2,3,3],[3,4],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([],1) => 1
[[1,1,1,1],[2,3,4],[3,4],[4]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,2],[2,3,4],[3,4],[4]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3],[2,3,4],[3,4],[4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,2,2],[2,3,4],[3,4],[4]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => ([(0,2),(2,1)],3) => 0
[[1,1,3,3],[2,3,4],[3,4],[4]] => ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,2,2],[2,3,3],[3,4],[4]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[1,2,2,2],[2,3,4],[3,4],[4]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]] => ([],1) => ([],1) => 1
[[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,4],[5]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([],1) => 1
[[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => ([],1) => 1
[[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,1,1,3,3],[2,2,3,4],[3,3,4],[4,4],[5]] => ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,2,2,2],[2,2,3,3],[3,3,4],[4,4],[5]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,5],[5]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,5],[5]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,5],[5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,5],[5]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,5],[5]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([],1) => 1
[[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,5],[5]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 2
[[1,1,1,1,1],[2,2,2,2],[3,3,5],[4,5],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1],[2,2,2,3],[3,3,5],[4,5],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2],[2,2,2,3],[3,3,5],[4,5],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,1,1,1,1],[2,2,2,4],[3,3,5],[4,5],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,2],[2,2,2,4],[3,3,5],[4,5],[5]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,3],[2,2,2,4],[3,3,5],[4,5],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,2],[2,2,2,2],[3,4,4],[4,5],[5]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => ([],1) => 1
[[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,1,1],[2,2,2,3],[3,4,5],[4,5],[5]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,2],[2,2,3,4],[3,4,5],[4,5],[5]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]] => ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1],[2,3,3,3],[3,4,4],[4,5],[5]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[1,1,1,1,1],[2,3,3,3],[3,4,5],[4,5],[5]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => ([],1) => ([],1) => 1
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([],1) => 1
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([],1) => 1
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([],1) => 1
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => ([(0,1)],2) => 0
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14) => ([],1) => 1
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => ([],1) => 1
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,6],[6]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([],1) => 1
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,6],[6]] => ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,6],[5,6],[6]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,6],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]] => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16) => ([],1) => 1
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,6],[5,6],[6]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,6],[5,6],[6]] => ([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14) => ([],1) => 1
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => ([],1) => 1
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,6],[5,6],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,6],[4,4,6],[5,6],[6]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => ([(0,2),(2,1)],3) => 0
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[2]] => ([(0,1)],2) => ([(0,1)],2) => 0
[[1,1]] => ([],1) => ([],1) => 1
[[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[1,1,1]] => ([],1) => ([],1) => 1
[[4]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[1,1,1,1]] => ([],1) => ([],1) => 1
[[5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[1,1,1,1,1]] => ([],1) => ([],1) => 1
[[6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,2,3],[4],[5],[6]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,2],[3],[4],[5],[6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1,3,4],[2,5],[6]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[1,3],[2,4],[5],[6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,3],[2],[4],[5],[6]] => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,4,5],[2,6],[3]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => ([],1) => 1
[[1,4],[2],[3],[5],[6]] => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => ([],1) => 1
[[1,5,6],[2],[3],[4]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[1,5],[2,6],[3],[4]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => ([],1) => 1
[[1,5],[2],[3],[4],[6]] => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,6],[2],[3],[4],[5]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[1],[2],[3],[4],[5],[6]] => ([],1) => ([],1) => 1
[[1,1,1,1,2,2,2],[3,3],[4]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([],1) => 1
[[1,1,1,1,2,2,2],[3,4],[4]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => ([(0,2),(2,1)],3) => 0
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Generating function
$F_{(2, 2)} = 2 + q$
$F_{(2, 3)} = 3 + 2\ q$
$F_{(3, 2)} = 4 + q$
$F_{(2, 4)} = 5 + 2\ q$
$F_{(3, 3)} = 9 + 3\ q + q^{2}$
$F_{(4, 2)} = 6 + 2\ q$
$F_{(2, 5)} = 5 + 3\ q + q^{2}$
$F_{(5, 2)} = 9 + 2\ q$
$F_{(6, 2)} = 12 + 3\ q$
$F_{(7, 2)} = 16 + 3\ q$
Description
The cardinality of the Frattini sublattice of a lattice.
The Frattini sublattice is the intersection of all proper maximal sublattices of the lattice.
The Frattini sublattice is the intersection of all proper maximal sublattices of the lattice.
Map
antichains of maximal size
Description
The lattice of antichains of maximal size in a poset.
The set of antichains of maximal size can be ordered by setting $A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$, where $\mathop{\downarrow} A$ is the order ideal generated by $A$.
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.
The set of antichains of maximal size can be ordered by setting $A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$, where $\mathop{\downarrow} A$ is the order ideal generated by $A$.
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.
Map
subcrystal
Description
The underlying poset of the subcrystal obtained by applying the raising operators to a semistandard tableau.
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