- FindStat

Identifier

Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00197: Lattices —lattice of congruences⟶ Lattices

Images

[[1],[]] => ([],1) => ([],1)

[[2],[]] => ([],1) => ([],1)

[[1,1],[]] => ([],1) => ([],1)

[[2,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3],[]] => ([],1) => ([],1)

[[2,1],[]] => ([],1) => ([],1)

[[3,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2],[1]] => ([],1) => ([],1)

[[3,2],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[1,1,1],[]] => ([],1) => ([],1)

[[2,2,1],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,2,1],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4],[]] => ([],1) => ([],1)

[[3,1],[]] => ([],1) => ([],1)

[[4,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2],[]] => ([],1) => ([],1)

[[3,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,2],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[2,1,1],[]] => ([],1) => ([],1)

[[3,2,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3],[2]] => ([],1) => ([],1)

[[4,3],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,1],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,2,1],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,1],[3,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[2,2,2],[1,1]] => ([],1) => ([],1)

[[3,3,2],[2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,2,2],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,2],[3,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,2,1],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,1,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,2,1],[2,2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[2,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,2,2,1],[2,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,2,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,2,1],[3,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5],[]] => ([],1) => ([],1)

[[4,1],[]] => ([],1) => ([],1)

[[5,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,2],[]] => ([],1) => ([],1)

[[4,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,2],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,1,1],[]] => ([],1) => ([],1)

[[4,2,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3],[1]] => ([],1) => ([],1)

[[4,3],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[5,3],[3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[2,2,1],[]] => ([],1) => ([],1)

[[3,3,1],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,2,1],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,2,1],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,1],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,2,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,3,2],[2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,2,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,2],[3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[2,1,1,1],[]] => ([],1) => ([],1)

[[3,2,2,1],[1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,2,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,2,1],[2,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,2,2,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,2,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,3,2,1],[3,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4],[3]] => ([],1) => ([],1)

[[5,4],[4]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,1],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,1],[3,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,1],[3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,1],[4,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[2,2,2],[1]] => ([],1) => ([],1)

[[3,3,2],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,2],[3,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,2,2],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,3,2],[3,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,4,2],[4,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[2,2,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,1],[2,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,2,1],[3,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,2,1,1],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,2,1],[3,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,1,1],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,2,1],[4,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,3],[2,2]] => ([],1) => ([],1)

[[4,4,3],[3,3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,3,3],[3,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,3],[4,3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[2,2,2,1],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,1],[2,2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,2,1],[2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,3,1],[3,3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,2,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

>>> Load all 1349 entries. <<<

[[4,3,3,1],[3,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,2,1],[3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,3,1],[4,3,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[2,2,2,2],[1,1,1]] => ([],1) => ([],1)

[[3,3,3,2],[2,2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,2],[2,2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,3,2],[3,3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,2,2,2],[2,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,2],[3,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,2,2],[3,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,3,2],[4,3,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,2,2,1],[1,1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,2,1,1],[1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,2,1],[2,2,2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[2,2,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,2,2,1],[2,2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,2,1,1],[2,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,2,1],[3,3,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[2,1,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,2,2,2,1],[2,1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,2,2,1,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,2,1],[3,2,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,2,1,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,2,2,1],[3,2,1,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,2,1,1],[3,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,3,2,1],[4,3,2,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[6],[]] => ([],1) => ([],1)

[[5,1],[]] => ([],1) => ([],1)

[[6,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,2],[]] => ([],1) => ([],1)

[[5,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[6,2],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,1,1],[]] => ([],1) => ([],1)

[[5,2,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[6,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3],[]] => ([],1) => ([],1)

[[4,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,3],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,3],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,2,1],[]] => ([],1) => ([],1)

[[4,3,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,2,1],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,3,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[5,2,1],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[6,3,1],[3,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,2,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,3,2],[2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[5,2,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[6,3,2],[3,2]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,1,1,1],[]] => ([],1) => ([],1)

[[4,2,2,1],[1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,2,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,2,1],[2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,2,2,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,2,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,3,2,1],[3,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4],[2]] => ([],1) => ([],1)

[[5,4],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[6,4],[4]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,1],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,1],[3,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[5,3,1],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[6,4,1],[4,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[2,2,2],[]] => ([],1) => ([],1)

[[3,3,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2],[2,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,3,2],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[5,4,2],[3,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,2,2],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,3,2],[3,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,4,2],[4,2]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[2,2,1,1],[]] => ([],1) => ([],1)

[[3,3,2,1],[1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,1,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,2,1],[2,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,2,1,1],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,2,1],[2,1,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,1,1],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,2,1],[3,2,1]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,2,1,1],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,2,1],[3,1,1]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,3,1,1],[3,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[6,4,2,1],[4,2,1]] => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,3,3],[2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[5,4,3],[3,3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,3],[3,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[6,4,3],[4,3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,1],[2,2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[4,3,2,1],[2,2]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,3,1],[3,3,1]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,2,2,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,3,3,1],[3,2,1]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,3,2,1],[3,2]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[6,4,3,1],[4,3,1]] => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,2,2,2],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,3,3,2],[2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,2,2],[2,2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,3,2],[3,3,2]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,2,2,2],[2,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,3,2],[3,2,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,3,2,2],[3,2,1]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[6,4,3,2],[4,3,2]] => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[2,1,1,1,1],[]] => ([],1) => ([],1)

[[3,2,2,2,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,3,3,2,1],[2,2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,2,1,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,2,2,1],[2,2,1,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,2,1,1],[2,2,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,3,2,1],[3,3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,1,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,2,2,2,1],[2,1,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,2,2,1,1],[2,1,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,3,3,2,1],[3,2,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,2,1,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,3,2,2,1],[3,2,1,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[5,3,2,1,1],[3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[6,4,3,2,1],[4,3,2,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,23),(1,24),(1,25),(1,26),(1,27),(1,28),(2,18),(2,19),(2,20),(2,21),(2,22),(2,28),(3,14),(3,15),(3,16),(3,17),(3,22),(3,27),(4,11),(4,12),(4,13),(4,17),(4,21),(4,26),(5,9),(5,10),(5,13),(5,16),(5,20),(5,25),(6,8),(6,10),(6,12),(6,15),(6,19),(6,24),(7,8),(7,9),(7,11),(7,14),(7,18),(7,23),(8,29),(8,32),(8,35),(8,41),(8,51),(9,29),(9,30),(9,33),(9,39),(9,49),(10,29),(10,31),(10,34),(10,40),(10,50),(11,30),(11,32),(11,36),(11,42),(11,52),(12,31),(12,32),(12,37),(12,43),(12,53),(13,30),(13,31),(13,38),(13,44),(13,54),(14,33),(14,35),(14,36),(14,45),(14,55),(15,34),(15,35),(15,37),(15,46),(15,56),(16,33),(16,34),(16,38),(16,47),(16,57),(17,36),(17,37),(17,38),(17,48),(17,58),(18,39),(18,41),(18,42),(18,45),(18,59),(19,40),(19,41),(19,43),(19,46),(19,60),(20,39),(20,40),(20,44),(20,47),(20,61),(21,42),(21,43),(21,44),(21,48),(21,62),(22,45),(22,46),(22,47),(22,48),(22,63),(23,49),(23,51),(23,52),(23,55),(23,59),(24,50),(24,51),(24,53),(24,56),(24,60),(25,49),(25,50),(25,54),(25,57),(25,61),(26,52),(26,53),(26,54),(26,58),(26,62),(27,55),(27,56),(27,57),(27,58),(27,63),(28,59),(28,60),(28,61),(28,62),(28,63),(29,67),(29,68),(29,78),(29,88),(30,64),(30,68),(30,75),(30,85),(31,65),(31,68),(31,76),(31,86),(32,66),(32,68),(32,77),(32,87),(33,64),(33,67),(33,69),(33,79),(34,65),(34,67),(34,70),(34,80),(35,66),(35,67),(35,71),(35,81),(36,64),(36,66),(36,72),(36,82),(37,65),(37,66),(37,73),(37,83),(38,64),(38,65),(38,74),(38,84),(39,69),(39,75),(39,78),(39,89),(40,70),(40,76),(40,78),(40,90),(41,71),(41,77),(41,78),(41,91),(42,72),(42,75),(42,77),(42,92),(43,73),(43,76),(43,77),(43,93),(44,74),(44,75),(44,76),(44,94),(45,69),(45,71),(45,72),(45,95),(46,70),(46,71),(46,73),(46,96),(47,69),(47,70),(47,74),(47,97),(48,72),(48,73),(48,74),(48,98),(49,79),(49,85),(49,88),(49,89),(50,80),(50,86),(50,88),(50,90),(51,81),(51,87),(51,88),(51,91),(52,82),(52,85),(52,87),(52,92),(53,83),(53,86),(53,87),(53,93),(54,84),(54,85),(54,86),(54,94),(55,79),(55,81),(55,82),(55,95),(56,80),(56,81),(56,83),(56,96),(57,79),(57,80),(57,84),(57,97),(58,82),(58,83),(58,84),(58,98),(59,89),(59,91),(59,92),(59,95),(60,90),(60,91),(60,93),(60,96),(61,89),(61,90),(61,94),(61,97),(62,92),(62,93),(62,94),(62,98),(63,95),(63,96),(63,97),(63,98),(64,109),(64,114),(64,119),(65,110),(65,115),(65,119),(66,111),(66,116),(66,119),(67,112),(67,117),(67,119),(68,113),(68,118),(68,119),(69,99),(69,114),(69,117),(70,100),(70,115),(70,117),(71,101),(71,116),(71,117),(72,102),(72,114),(72,116),(73,103),(73,115),(73,116),(74,104),(74,114),(74,115),(75,105),(75,114),(75,118),(76,106),(76,115),(76,118),(77,107),(77,116),(77,118),(78,108),(78,117),(78,118),(79,99),(79,109),(79,112),(80,100),(80,110),(80,112),(81,101),(81,111),(81,112),(82,102),(82,109),(82,111),(83,103),(83,110),(83,111),(84,104),(84,109),(84,110),(85,105),(85,109),(85,113),(86,106),(86,110),(86,113),(87,107),(87,111),(87,113),(88,108),(88,112),(88,113),(89,99),(89,105),(89,108),(90,100),(90,106),(90,108),(91,101),(91,107),(91,108),(92,102),(92,105),(92,107),(93,103),(93,106),(93,107),(94,104),(94,105),(94,106),(95,99),(95,101),(95,102),(96,100),(96,101),(96,103),(97,99),(97,100),(97,104),(98,102),(98,103),(98,104),(99,120),(99,123),(100,121),(100,123),(101,122),(101,123),(102,120),(102,122),(103,121),(103,122),(104,120),(104,121),(105,120),(105,124),(106,121),(106,124),(107,122),(107,124),(108,123),(108,124),(109,120),(109,125),(110,121),(110,125),(111,122),(111,125),(112,123),(112,125),(113,124),(113,125),(114,120),(114,126),(115,121),(115,126),(116,122),(116,126),(117,123),(117,126),(118,124),(118,126),(119,125),(119,126),(120,127),(121,127),(122,127),(123,127),(124,127),(125,127),(126,127)],128)

[[5,5],[4]] => ([],1) => ([],1)

[[6,5],[5]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,1],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,1],[4,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,1],[4]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5,1],[5,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,2],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2],[3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,2],[4,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[4,3,2],[3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,2],[4,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[6,5,2],[5,2]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,1,1],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2,1],[3,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,4,1,1],[3,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,5,2,1],[4,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,1,1],[3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,2,1],[4,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,1,1],[4,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,5,2,1],[5,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,3],[2,1]] => ([],1) => ([],1)

[[4,4,3],[3,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,3],[4,3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,3],[3,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,3],[4,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[6,5,3],[5,3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[2,2,2,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,1],[2,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,2,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[4,4,3,1],[3,2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,2,1],[3,2]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,5,3,1],[4,3,1]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,2,2,1],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,1],[3,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,2,1],[3,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,3,1],[4,2,1]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,2,1],[4,2]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[6,5,3,1],[5,3,1]] => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,3,2,2],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,3,2],[3,2,2]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,2,2],[3,2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,5,3,2],[4,3,2]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,2,2],[3,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[5,4,3,2],[4,2,2]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,2,2],[4,2,1]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[6,5,3,2],[5,3,2]] => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[2,2,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,2,1],[2,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[3,3,2,1,1],[2,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,2,1],[3,2,2,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,1,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,2,2,1],[3,2,1,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,2,1,1],[3,2,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,5,3,2,1],[4,3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,2,1,1,1],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,2,2,1],[3,1,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,2,1,1],[3,1,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,3,2,1],[4,2,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,3,1,1,1],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,2,2,1],[4,2,1,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[5,4,2,1,1],[4,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[6,5,3,2,1],[5,3,2,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,23),(1,24),(1,25),(1,26),(1,27),(1,28),(2,18),(2,19),(2,20),(2,21),(2,22),(2,28),(3,14),(3,15),(3,16),(3,17),(3,22),(3,27),(4,11),(4,12),(4,13),(4,17),(4,21),(4,26),(5,9),(5,10),(5,13),(5,16),(5,20),(5,25),(6,8),(6,10),(6,12),(6,15),(6,19),(6,24),(7,8),(7,9),(7,11),(7,14),(7,18),(7,23),(8,29),(8,32),(8,35),(8,41),(8,51),(9,29),(9,30),(9,33),(9,39),(9,49),(10,29),(10,31),(10,34),(10,40),(10,50),(11,30),(11,32),(11,36),(11,42),(11,52),(12,31),(12,32),(12,37),(12,43),(12,53),(13,30),(13,31),(13,38),(13,44),(13,54),(14,33),(14,35),(14,36),(14,45),(14,55),(15,34),(15,35),(15,37),(15,46),(15,56),(16,33),(16,34),(16,38),(16,47),(16,57),(17,36),(17,37),(17,38),(17,48),(17,58),(18,39),(18,41),(18,42),(18,45),(18,59),(19,40),(19,41),(19,43),(19,46),(19,60),(20,39),(20,40),(20,44),(20,47),(20,61),(21,42),(21,43),(21,44),(21,48),(21,62),(22,45),(22,46),(22,47),(22,48),(22,63),(23,49),(23,51),(23,52),(23,55),(23,59),(24,50),(24,51),(24,53),(24,56),(24,60),(25,49),(25,50),(25,54),(25,57),(25,61),(26,52),(26,53),(26,54),(26,58),(26,62),(27,55),(27,56),(27,57),(27,58),(27,63),(28,59),(28,60),(28,61),(28,62),(28,63),(29,67),(29,68),(29,78),(29,88),(30,64),(30,68),(30,75),(30,85),(31,65),(31,68),(31,76),(31,86),(32,66),(32,68),(32,77),(32,87),(33,64),(33,67),(33,69),(33,79),(34,65),(34,67),(34,70),(34,80),(35,66),(35,67),(35,71),(35,81),(36,64),(36,66),(36,72),(36,82),(37,65),(37,66),(37,73),(37,83),(38,64),(38,65),(38,74),(38,84),(39,69),(39,75),(39,78),(39,89),(40,70),(40,76),(40,78),(40,90),(41,71),(41,77),(41,78),(41,91),(42,72),(42,75),(42,77),(42,92),(43,73),(43,76),(43,77),(43,93),(44,74),(44,75),(44,76),(44,94),(45,69),(45,71),(45,72),(45,95),(46,70),(46,71),(46,73),(46,96),(47,69),(47,70),(47,74),(47,97),(48,72),(48,73),(48,74),(48,98),(49,79),(49,85),(49,88),(49,89),(50,80),(50,86),(50,88),(50,90),(51,81),(51,87),(51,88),(51,91),(52,82),(52,85),(52,87),(52,92),(53,83),(53,86),(53,87),(53,93),(54,84),(54,85),(54,86),(54,94),(55,79),(55,81),(55,82),(55,95),(56,80),(56,81),(56,83),(56,96),(57,79),(57,80),(57,84),(57,97),(58,82),(58,83),(58,84),(58,98),(59,89),(59,91),(59,92),(59,95),(60,90),(60,91),(60,93),(60,96),(61,89),(61,90),(61,94),(61,97),(62,92),(62,93),(62,94),(62,98),(63,95),(63,96),(63,97),(63,98),(64,109),(64,114),(64,119),(65,110),(65,115),(65,119),(66,111),(66,116),(66,119),(67,112),(67,117),(67,119),(68,113),(68,118),(68,119),(69,99),(69,114),(69,117),(70,100),(70,115),(70,117),(71,101),(71,116),(71,117),(72,102),(72,114),(72,116),(73,103),(73,115),(73,116),(74,104),(74,114),(74,115),(75,105),(75,114),(75,118),(76,106),(76,115),(76,118),(77,107),(77,116),(77,118),(78,108),(78,117),(78,118),(79,99),(79,109),(79,112),(80,100),(80,110),(80,112),(81,101),(81,111),(81,112),(82,102),(82,109),(82,111),(83,103),(83,110),(83,111),(84,104),(84,109),(84,110),(85,105),(85,109),(85,113),(86,106),(86,110),(86,113),(87,107),(87,111),(87,113),(88,108),(88,112),(88,113),(89,99),(89,105),(89,108),(90,100),(90,106),(90,108),(91,101),(91,107),(91,108),(92,102),(92,105),(92,107),(93,103),(93,106),(93,107),(94,104),(94,105),(94,106),(95,99),(95,101),(95,102),(96,100),(96,101),(96,103),(97,99),(97,100),(97,104),(98,102),(98,103),(98,104),(99,120),(99,123),(100,121),(100,123),(101,122),(101,123),(102,120),(102,122),(103,121),(103,122),(104,120),(104,121),(105,120),(105,124),(106,121),(106,124),(107,122),(107,124),(108,123),(108,124),(109,120),(109,125),(110,121),(110,125),(111,122),(111,125),(112,123),(112,125),(113,124),(113,125),(114,120),(114,126),(115,121),(115,126),(116,122),(116,126),(117,123),(117,126),(118,124),(118,126),(119,125),(119,126),(120,127),(121,127),(122,127),(123,127),(124,127),(125,127),(126,127)],128)

[[4,4,4],[3,3]] => ([],1) => ([],1)

[[5,5,4],[4,4]] => ([(0,1)],2) => ([(0,1)],2)

[[5,4,4],[4,3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5,4],[5,4]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,3,1],[2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,1],[3,3,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,3,1],[3,3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,5,4,1],[4,4,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,1],[3,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[5,4,4,1],[4,3,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,3,1],[4,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,5,4,1],[5,4,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[2,2,2,2],[1,1]] => ([],1) => ([],1)

[[3,3,3,2],[2,2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,2],[3,3,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,2,2],[2,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,3,2],[3,3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,5,4,2],[4,4,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,2,2,2],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,2],[3,2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,4,2],[4,3,2]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,2,2],[3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,3,2],[4,3,1]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[6,5,4,2],[5,4,2]] => ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[2,2,2,1,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,2,1],[2,2,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[3,3,3,1,1],[2,2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,4,4,2,1],[3,3,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,2,1,1],[2,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,4,3,2,1],[3,3,1,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,3,1,1],[3,3,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,5,4,2,1],[4,4,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,2,2,1,1],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,3,3,2,1],[3,2,1,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,3,1,1],[3,2,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,4,2,1],[4,3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,3,2,1,1],[3,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,3,2,1],[4,3,1,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[5,4,3,1,1],[4,3,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[6,5,4,2,1],[5,4,2,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,23),(1,24),(1,25),(1,26),(1,27),(1,28),(2,18),(2,19),(2,20),(2,21),(2,22),(2,28),(3,14),(3,15),(3,16),(3,17),(3,22),(3,27),(4,11),(4,12),(4,13),(4,17),(4,21),(4,26),(5,9),(5,10),(5,13),(5,16),(5,20),(5,25),(6,8),(6,10),(6,12),(6,15),(6,19),(6,24),(7,8),(7,9),(7,11),(7,14),(7,18),(7,23),(8,29),(8,32),(8,35),(8,41),(8,51),(9,29),(9,30),(9,33),(9,39),(9,49),(10,29),(10,31),(10,34),(10,40),(10,50),(11,30),(11,32),(11,36),(11,42),(11,52),(12,31),(12,32),(12,37),(12,43),(12,53),(13,30),(13,31),(13,38),(13,44),(13,54),(14,33),(14,35),(14,36),(14,45),(14,55),(15,34),(15,35),(15,37),(15,46),(15,56),(16,33),(16,34),(16,38),(16,47),(16,57),(17,36),(17,37),(17,38),(17,48),(17,58),(18,39),(18,41),(18,42),(18,45),(18,59),(19,40),(19,41),(19,43),(19,46),(19,60),(20,39),(20,40),(20,44),(20,47),(20,61),(21,42),(21,43),(21,44),(21,48),(21,62),(22,45),(22,46),(22,47),(22,48),(22,63),(23,49),(23,51),(23,52),(23,55),(23,59),(24,50),(24,51),(24,53),(24,56),(24,60),(25,49),(25,50),(25,54),(25,57),(25,61),(26,52),(26,53),(26,54),(26,58),(26,62),(27,55),(27,56),(27,57),(27,58),(27,63),(28,59),(28,60),(28,61),(28,62),(28,63),(29,67),(29,68),(29,78),(29,88),(30,64),(30,68),(30,75),(30,85),(31,65),(31,68),(31,76),(31,86),(32,66),(32,68),(32,77),(32,87),(33,64),(33,67),(33,69),(33,79),(34,65),(34,67),(34,70),(34,80),(35,66),(35,67),(35,71),(35,81),(36,64),(36,66),(36,72),(36,82),(37,65),(37,66),(37,73),(37,83),(38,64),(38,65),(38,74),(38,84),(39,69),(39,75),(39,78),(39,89),(40,70),(40,76),(40,78),(40,90),(41,71),(41,77),(41,78),(41,91),(42,72),(42,75),(42,77),(42,92),(43,73),(43,76),(43,77),(43,93),(44,74),(44,75),(44,76),(44,94),(45,69),(45,71),(45,72),(45,95),(46,70),(46,71),(46,73),(46,96),(47,69),(47,70),(47,74),(47,97),(48,72),(48,73),(48,74),(48,98),(49,79),(49,85),(49,88),(49,89),(50,80),(50,86),(50,88),(50,90),(51,81),(51,87),(51,88),(51,91),(52,82),(52,85),(52,87),(52,92),(53,83),(53,86),(53,87),(53,93),(54,84),(54,85),(54,86),(54,94),(55,79),(55,81),(55,82),(55,95),(56,80),(56,81),(56,83),(56,96),(57,79),(57,80),(57,84),(57,97),(58,82),(58,83),(58,84),(58,98),(59,89),(59,91),(59,92),(59,95),(60,90),(60,91),(60,93),(60,96),(61,89),(61,90),(61,94),(61,97),(62,92),(62,93),(62,94),(62,98),(63,95),(63,96),(63,97),(63,98),(64,109),(64,114),(64,119),(65,110),(65,115),(65,119),(66,111),(66,116),(66,119),(67,112),(67,117),(67,119),(68,113),(68,118),(68,119),(69,99),(69,114),(69,117),(70,100),(70,115),(70,117),(71,101),(71,116),(71,117),(72,102),(72,114),(72,116),(73,103),(73,115),(73,116),(74,104),(74,114),(74,115),(75,105),(75,114),(75,118),(76,106),(76,115),(76,118),(77,107),(77,116),(77,118),(78,108),(78,117),(78,118),(79,99),(79,109),(79,112),(80,100),(80,110),(80,112),(81,101),(81,111),(81,112),(82,102),(82,109),(82,111),(83,103),(83,110),(83,111),(84,104),(84,109),(84,110),(85,105),(85,109),(85,113),(86,106),(86,110),(86,113),(87,107),(87,111),(87,113),(88,108),(88,112),(88,113),(89,99),(89,105),(89,108),(90,100),(90,106),(90,108),(91,101),(91,107),(91,108),(92,102),(92,105),(92,107),(93,103),(93,106),(93,107),(94,104),(94,105),(94,106),(95,99),(95,101),(95,102),(96,100),(96,101),(96,103),(97,99),(97,100),(97,104),(98,102),(98,103),(98,104),(99,120),(99,123),(100,121),(100,123),(101,122),(101,123),(102,120),(102,122),(103,121),(103,122),(104,120),(104,121),(105,120),(105,124),(106,121),(106,124),(107,122),(107,124),(108,123),(108,124),(109,120),(109,125),(110,121),(110,125),(111,122),(111,125),(112,123),(112,125),(113,124),(113,125),(114,120),(114,126),(115,121),(115,126),(116,122),(116,126),(117,123),(117,126),(118,124),(118,126),(119,125),(119,126),(120,127),(121,127),(122,127),(123,127),(124,127),(125,127),(126,127)],128)

[[3,3,3,3],[2,2,2]] => ([],1) => ([],1)

[[4,4,4,3],[3,3,3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,3],[3,3,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,5,4,3],[4,4,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,3],[3,2,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,4,3],[4,3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,3,3],[4,3,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,5,4,3],[5,4,3]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[2,2,2,2,1],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,1],[2,2,2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,2,1],[2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,4,3,1],[3,3,3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,2,2,1],[2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,3,1],[3,3,2,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,3,2,1],[3,3,2]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,5,4,3,1],[4,4,3,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,2,2,2,1],[2,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,3,3,3,1],[3,2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,2,1],[3,2,2]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,4,3,1],[4,3,3,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,3,2,2,1],[3,2,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,3,3,1],[4,3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[5,4,3,2,1],[4,3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[6,5,4,3,1],[5,4,3,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,23),(1,24),(1,25),(1,26),(1,27),(1,28),(2,18),(2,19),(2,20),(2,21),(2,22),(2,28),(3,14),(3,15),(3,16),(3,17),(3,22),(3,27),(4,11),(4,12),(4,13),(4,17),(4,21),(4,26),(5,9),(5,10),(5,13),(5,16),(5,20),(5,25),(6,8),(6,10),(6,12),(6,15),(6,19),(6,24),(7,8),(7,9),(7,11),(7,14),(7,18),(7,23),(8,29),(8,32),(8,35),(8,41),(8,51),(9,29),(9,30),(9,33),(9,39),(9,49),(10,29),(10,31),(10,34),(10,40),(10,50),(11,30),(11,32),(11,36),(11,42),(11,52),(12,31),(12,32),(12,37),(12,43),(12,53),(13,30),(13,31),(13,38),(13,44),(13,54),(14,33),(14,35),(14,36),(14,45),(14,55),(15,34),(15,35),(15,37),(15,46),(15,56),(16,33),(16,34),(16,38),(16,47),(16,57),(17,36),(17,37),(17,38),(17,48),(17,58),(18,39),(18,41),(18,42),(18,45),(18,59),(19,40),(19,41),(19,43),(19,46),(19,60),(20,39),(20,40),(20,44),(20,47),(20,61),(21,42),(21,43),(21,44),(21,48),(21,62),(22,45),(22,46),(22,47),(22,48),(22,63),(23,49),(23,51),(23,52),(23,55),(23,59),(24,50),(24,51),(24,53),(24,56),(24,60),(25,49),(25,50),(25,54),(25,57),(25,61),(26,52),(26,53),(26,54),(26,58),(26,62),(27,55),(27,56),(27,57),(27,58),(27,63),(28,59),(28,60),(28,61),(28,62),(28,63),(29,67),(29,68),(29,78),(29,88),(30,64),(30,68),(30,75),(30,85),(31,65),(31,68),(31,76),(31,86),(32,66),(32,68),(32,77),(32,87),(33,64),(33,67),(33,69),(33,79),(34,65),(34,67),(34,70),(34,80),(35,66),(35,67),(35,71),(35,81),(36,64),(36,66),(36,72),(36,82),(37,65),(37,66),(37,73),(37,83),(38,64),(38,65),(38,74),(38,84),(39,69),(39,75),(39,78),(39,89),(40,70),(40,76),(40,78),(40,90),(41,71),(41,77),(41,78),(41,91),(42,72),(42,75),(42,77),(42,92),(43,73),(43,76),(43,77),(43,93),(44,74),(44,75),(44,76),(44,94),(45,69),(45,71),(45,72),(45,95),(46,70),(46,71),(46,73),(46,96),(47,69),(47,70),(47,74),(47,97),(48,72),(48,73),(48,74),(48,98),(49,79),(49,85),(49,88),(49,89),(50,80),(50,86),(50,88),(50,90),(51,81),(51,87),(51,88),(51,91),(52,82),(52,85),(52,87),(52,92),(53,83),(53,86),(53,87),(53,93),(54,84),(54,85),(54,86),(54,94),(55,79),(55,81),(55,82),(55,95),(56,80),(56,81),(56,83),(56,96),(57,79),(57,80),(57,84),(57,97),(58,82),(58,83),(58,84),(58,98),(59,89),(59,91),(59,92),(59,95),(60,90),(60,91),(60,93),(60,96),(61,89),(61,90),(61,94),(61,97),(62,92),(62,93),(62,94),(62,98),(63,95),(63,96),(63,97),(63,98),(64,109),(64,114),(64,119),(65,110),(65,115),(65,119),(66,111),(66,116),(66,119),(67,112),(67,117),(67,119),(68,113),(68,118),(68,119),(69,99),(69,114),(69,117),(70,100),(70,115),(70,117),(71,101),(71,116),(71,117),(72,102),(72,114),(72,116),(73,103),(73,115),(73,116),(74,104),(74,114),(74,115),(75,105),(75,114),(75,118),(76,106),(76,115),(76,118),(77,107),(77,116),(77,118),(78,108),(78,117),(78,118),(79,99),(79,109),(79,112),(80,100),(80,110),(80,112),(81,101),(81,111),(81,112),(82,102),(82,109),(82,111),(83,103),(83,110),(83,111),(84,104),(84,109),(84,110),(85,105),(85,109),(85,113),(86,106),(86,110),(86,113),(87,107),(87,111),(87,113),(88,108),(88,112),(88,113),(89,99),(89,105),(89,108),(90,100),(90,106),(90,108),(91,101),(91,107),(91,108),(92,102),(92,105),(92,107),(93,103),(93,106),(93,107),(94,104),(94,105),(94,106),(95,99),(95,101),(95,102),(96,100),(96,101),(96,103),(97,99),(97,100),(97,104),(98,102),(98,103),(98,104),(99,120),(99,123),(100,121),(100,123),(101,122),(101,123),(102,120),(102,122),(103,121),(103,122),(104,120),(104,121),(105,120),(105,124),(106,121),(106,124),(107,122),(107,124),(108,123),(108,124),(109,120),(109,125),(110,121),(110,125),(111,122),(111,125),(112,123),(112,125),(113,124),(113,125),(114,120),(114,126),(115,121),(115,126),(116,122),(116,126),(117,123),(117,126),(118,124),(118,126),(119,125),(119,126),(120,127),(121,127),(122,127),(123,127),(124,127),(125,127),(126,127)],128)

[[2,2,2,2,2],[1,1,1,1]] => ([],1) => ([],1)

[[3,3,3,3,2],[2,2,2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,2,2],[2,2,2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,4,3,2],[3,3,3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,2,2,2],[2,2,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,4,3,3,2],[3,3,2,2]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,3,2,2],[3,3,2,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,5,4,3,2],[4,4,3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,2,2,2,2],[2,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,3,2],[3,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,2,2],[3,2,2,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,4,3,2],[4,3,3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,3,2,2,2],[3,2,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,3,3,2],[4,3,2,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[5,4,3,2,2],[4,3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[6,5,4,3,2],[5,4,3,2]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,23),(1,24),(1,25),(1,26),(1,27),(1,28),(2,18),(2,19),(2,20),(2,21),(2,22),(2,28),(3,14),(3,15),(3,16),(3,17),(3,22),(3,27),(4,11),(4,12),(4,13),(4,17),(4,21),(4,26),(5,9),(5,10),(5,13),(5,16),(5,20),(5,25),(6,8),(6,10),(6,12),(6,15),(6,19),(6,24),(7,8),(7,9),(7,11),(7,14),(7,18),(7,23),(8,29),(8,32),(8,35),(8,41),(8,51),(9,29),(9,30),(9,33),(9,39),(9,49),(10,29),(10,31),(10,34),(10,40),(10,50),(11,30),(11,32),(11,36),(11,42),(11,52),(12,31),(12,32),(12,37),(12,43),(12,53),(13,30),(13,31),(13,38),(13,44),(13,54),(14,33),(14,35),(14,36),(14,45),(14,55),(15,34),(15,35),(15,37),(15,46),(15,56),(16,33),(16,34),(16,38),(16,47),(16,57),(17,36),(17,37),(17,38),(17,48),(17,58),(18,39),(18,41),(18,42),(18,45),(18,59),(19,40),(19,41),(19,43),(19,46),(19,60),(20,39),(20,40),(20,44),(20,47),(20,61),(21,42),(21,43),(21,44),(21,48),(21,62),(22,45),(22,46),(22,47),(22,48),(22,63),(23,49),(23,51),(23,52),(23,55),(23,59),(24,50),(24,51),(24,53),(24,56),(24,60),(25,49),(25,50),(25,54),(25,57),(25,61),(26,52),(26,53),(26,54),(26,58),(26,62),(27,55),(27,56),(27,57),(27,58),(27,63),(28,59),(28,60),(28,61),(28,62),(28,63),(29,67),(29,68),(29,78),(29,88),(30,64),(30,68),(30,75),(30,85),(31,65),(31,68),(31,76),(31,86),(32,66),(32,68),(32,77),(32,87),(33,64),(33,67),(33,69),(33,79),(34,65),(34,67),(34,70),(34,80),(35,66),(35,67),(35,71),(35,81),(36,64),(36,66),(36,72),(36,82),(37,65),(37,66),(37,73),(37,83),(38,64),(38,65),(38,74),(38,84),(39,69),(39,75),(39,78),(39,89),(40,70),(40,76),(40,78),(40,90),(41,71),(41,77),(41,78),(41,91),(42,72),(42,75),(42,77),(42,92),(43,73),(43,76),(43,77),(43,93),(44,74),(44,75),(44,76),(44,94),(45,69),(45,71),(45,72),(45,95),(46,70),(46,71),(46,73),(46,96),(47,69),(47,70),(47,74),(47,97),(48,72),(48,73),(48,74),(48,98),(49,79),(49,85),(49,88),(49,89),(50,80),(50,86),(50,88),(50,90),(51,81),(51,87),(51,88),(51,91),(52,82),(52,85),(52,87),(52,92),(53,83),(53,86),(53,87),(53,93),(54,84),(54,85),(54,86),(54,94),(55,79),(55,81),(55,82),(55,95),(56,80),(56,81),(56,83),(56,96),(57,79),(57,80),(57,84),(57,97),(58,82),(58,83),(58,84),(58,98),(59,89),(59,91),(59,92),(59,95),(60,90),(60,91),(60,93),(60,96),(61,89),(61,90),(61,94),(61,97),(62,92),(62,93),(62,94),(62,98),(63,95),(63,96),(63,97),(63,98),(64,109),(64,114),(64,119),(65,110),(65,115),(65,119),(66,111),(66,116),(66,119),(67,112),(67,117),(67,119),(68,113),(68,118),(68,119),(69,99),(69,114),(69,117),(70,100),(70,115),(70,117),(71,101),(71,116),(71,117),(72,102),(72,114),(72,116),(73,103),(73,115),(73,116),(74,104),(74,114),(74,115),(75,105),(75,114),(75,118),(76,106),(76,115),(76,118),(77,107),(77,116),(77,118),(78,108),(78,117),(78,118),(79,99),(79,109),(79,112),(80,100),(80,110),(80,112),(81,101),(81,111),(81,112),(82,102),(82,109),(82,111),(83,103),(83,110),(83,111),(84,104),(84,109),(84,110),(85,105),(85,109),(85,113),(86,106),(86,110),(86,113),(87,107),(87,111),(87,113),(88,108),(88,112),(88,113),(89,99),(89,105),(89,108),(90,100),(90,106),(90,108),(91,101),(91,107),(91,108),(92,102),(92,105),(92,107),(93,103),(93,106),(93,107),(94,104),(94,105),(94,106),(95,99),(95,101),(95,102),(96,100),(96,101),(96,103),(97,99),(97,100),(97,104),(98,102),(98,103),(98,104),(99,120),(99,123),(100,121),(100,123),(101,122),(101,123),(102,120),(102,122),(103,121),(103,122),(104,120),(104,121),(105,120),(105,124),(106,121),(106,124),(107,122),(107,124),(108,123),(108,124),(109,120),(109,125),(110,121),(110,125),(111,122),(111,125),(112,123),(112,125),(113,124),(113,125),(114,120),(114,126),(115,121),(115,126),(116,122),(116,126),(117,123),(117,126),(118,124),(118,126),(119,125),(119,126),(120,127),(121,127),(122,127),(123,127),(124,127),(125,127),(126,127)],128)

[[1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,2,2,2,1],[1,1,1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,3,2,1],[2,2,2,2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[2,2,2,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,3,2,2,1],[2,2,2,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,3,2,1,1],[2,2,2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,4,3,2,1],[3,3,3,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[2,2,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,2,2,2,1],[2,2,1,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,2,2,1,1],[2,2,1,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,3,3,2,1],[3,3,2,2,1]] => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,3,2,1,1,1],[2,2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,2,2,1],[3,3,2,1,1]] => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,4,3,2,1,1],[3,3,2,1]] => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[2,1,1,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,2,2,2,2,1],[2,1,1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,2,2,2,1,1],[2,1,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,3,2,1],[3,2,2,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,2,2,1,1,1],[2,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,2,2,1],[3,2,2,1,1]] => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,3,3,2,1,1],[3,2,2,1]] => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,2,1,1,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,2,2,2,1],[3,2,1,1,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,2,2,1,1],[3,2,1,1]] => ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,3,2,1,1,1],[3,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[7],[]] => ([],1) => ([],1)

[[6,1],[]] => ([],1) => ([],1)

[[7,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,2],[]] => ([],1) => ([],1)

[[6,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[7,2],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,1,1],[]] => ([],1) => ([],1)

[[6,2,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[7,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3],[]] => ([],1) => ([],1)

[[5,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[6,3],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[7,3],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,2,1],[]] => ([],1) => ([],1)

[[5,3,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,2,1],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,3,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[6,2,1],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[7,3,1],[3,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,2,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[6,3,2],[2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[6,2,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[7,3,2],[3,2]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,1,1,1],[]] => ([],1) => ([],1)

[[5,2,2,1],[1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,2,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[6,3,2,1],[2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[6,2,2,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,2,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[7,3,2,1],[3,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4],[1]] => ([],1) => ([],1)

[[5,4],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[6,4],[3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[7,4],[4]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,1],[]] => ([],1) => ([],1)

[[4,4,1],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,3,1],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[6,4,1],[3,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,3,1],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[7,4,1],[4,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,2,2],[]] => ([],1) => ([],1)

[[4,3,2],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,2],[2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,4,2],[3,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,2,2],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,3,2],[3,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[7,4,2],[4,2]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,2,1,1],[]] => ([],1) => ([],1)

[[4,3,2,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,4,2,1],[2,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,2,1,1],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,3,2,1],[2,1,1]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,3,1,1],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,4,2,1],[3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,2,1,1],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[6,3,2,1],[3,1,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[6,3,1,1],[3,1]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,3,3],[2,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,4,3],[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,3,3],[3,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[7,4,3],[4,3]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,3,3,1],[2,2,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[5,3,2,1],[2,2]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,4,3,1],[3,3,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,2,2,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,3,3,1],[3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[6,3,2,1],[3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,2,2,2],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,3,3,2],[2,2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[5,3,2,2],[2,2,1]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,4,3,2],[3,3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,2,2,2],[2,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[6,3,3,2],[3,2,2]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[6,3,2,2],[3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,1,1,1,1],[]] => ([],1) => ([],1)

[[4,2,2,2,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[5,3,3,2,1],[2,2,2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,2,1,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,2,2,1],[2,2,1,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,3,2,1,1],[2,2,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,1,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,2,2,2,1],[2,1,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,2,2,1,1],[2,1,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,2,1,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,5],[3]] => ([],1) => ([],1)

[[6,5],[4]] => ([(0,1)],2) => ([(0,1)],2)

[[7,5],[5]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,1],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,1],[3,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,1],[3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5,1],[4,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[6,4,1],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[7,5,1],[5,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,5,2],[3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,5,2],[4,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,3,2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,4,2],[4,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[7,5,2],[5,2]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,3,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,5,2,1],[3,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,2,1],[3,1,1]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,4,1,1],[3,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,5,2,1],[4,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,3,1,1],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[6,4,2,1],[4,1,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[6,4,1,1],[4,1]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,3],[1,1]] => ([],1) => ([],1)

[[4,4,3],[2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,3],[3,3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,5,3],[4,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,3,3],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,4,3],[4,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[7,5,3],[5,3]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[2,2,2,1],[]] => ([],1) => ([],1)

[[3,3,3,1],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,1],[1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,3,1],[2,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,2,1],[2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,5,3,1],[3,3,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,2,2,1],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,2,1],[2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,4,3,1],[3,2,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,2,1],[3,2]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,2,2,1],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,3,1],[3,1,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[5,3,2,1],[3,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,2,2],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,2],[2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,2,2],[2,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,5,3,2],[3,3,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,3,2,2],[2,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[5,4,3,2],[3,2,2]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,2,2],[3,2,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,3,2,2],[3,1,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[2,2,1,1,1],[]] => ([],1) => ([],1)

[[3,3,2,2,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,2,1,1],[1,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,2,1],[2,2,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,2,2,1],[2,2,1,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,4,2,1,1],[2,2,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[5,5,3,2,1],[3,3,2,1]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,23),(1,24),(1,25),(1,26),(1,27),(1,28),(2,18),(2,19),(2,20),(2,21),(2,22),(2,28),(3,14),(3,15),(3,16),(3,17),(3,22),(3,27),(4,11),(4,12),(4,13),(4,17),(4,21),(4,26),(5,9),(5,10),(5,13),(5,16),(5,20),(5,25),(6,8),(6,10),(6,12),(6,15),(6,19),(6,24),(7,8),(7,9),(7,11),(7,14),(7,18),(7,23),(8,29),(8,32),(8,35),(8,41),(8,51),(9,29),(9,30),(9,33),(9,39),(9,49),(10,29),(10,31),(10,34),(10,40),(10,50),(11,30),(11,32),(11,36),(11,42),(11,52),(12,31),(12,32),(12,37),(12,43),(12,53),(13,30),(13,31),(13,38),(13,44),(13,54),(14,33),(14,35),(14,36),(14,45),(14,55),(15,34),(15,35),(15,37),(15,46),(15,56),(16,33),(16,34),(16,38),(16,47),(16,57),(17,36),(17,37),(17,38),(17,48),(17,58),(18,39),(18,41),(18,42),(18,45),(18,59),(19,40),(19,41),(19,43),(19,46),(19,60),(20,39),(20,40),(20,44),(20,47),(20,61),(21,42),(21,43),(21,44),(21,48),(21,62),(22,45),(22,46),(22,47),(22,48),(22,63),(23,49),(23,51),(23,52),(23,55),(23,59),(24,50),(24,51),(24,53),(24,56),(24,60),(25,49),(25,50),(25,54),(25,57),(25,61),(26,52),(26,53),(26,54),(26,58),(26,62),(27,55),(27,56),(27,57),(27,58),(27,63),(28,59),(28,60),(28,61),(28,62),(28,63),(29,67),(29,68),(29,78),(29,88),(30,64),(30,68),(30,75),(30,85),(31,65),(31,68),(31,76),(31,86),(32,66),(32,68),(32,77),(32,87),(33,64),(33,67),(33,69),(33,79),(34,65),(34,67),(34,70),(34,80),(35,66),(35,67),(35,71),(35,81),(36,64),(36,66),(36,72),(36,82),(37,65),(37,66),(37,73),(37,83),(38,64),(38,65),(38,74),(38,84),(39,69),(39,75),(39,78),(39,89),(40,70),(40,76),(40,78),(40,90),(41,71),(41,77),(41,78),(41,91),(42,72),(42,75),(42,77),(42,92),(43,73),(43,76),(43,77),(43,93),(44,74),(44,75),(44,76),(44,94),(45,69),(45,71),(45,72),(45,95),(46,70),(46,71),(46,73),(46,96),(47,69),(47,70),(47,74),(47,97),(48,72),(48,73),(48,74),(48,98),(49,79),(49,85),(49,88),(49,89),(50,80),(50,86),(50,88),(50,90),(51,81),(51,87),(51,88),(51,91),(52,82),(52,85),(52,87),(52,92),(53,83),(53,86),(53,87),(53,93),(54,84),(54,85),(54,86),(54,94),(55,79),(55,81),(55,82),(55,95),(56,80),(56,81),(56,83),(56,96),(57,79),(57,80),(57,84),(57,97),(58,82),(58,83),(58,84),(58,98),(59,89),(59,91),(59,92),(59,95),(60,90),(60,91),(60,93),(60,96),(61,89),(61,90),(61,94),(61,97),(62,92),(62,93),(62,94),(62,98),(63,95),(63,96),(63,97),(63,98),(64,109),(64,114),(64,119),(65,110),(65,115),(65,119),(66,111),(66,116),(66,119),(67,112),(67,117),(67,119),(68,113),(68,118),(68,119),(69,99),(69,114),(69,117),(70,100),(70,115),(70,117),(71,101),(71,116),(71,117),(72,102),(72,114),(72,116),(73,103),(73,115),(73,116),(74,104),(74,114),(74,115),(75,105),(75,114),(75,118),(76,106),(76,115),(76,118),(77,107),(77,116),(77,118),(78,108),(78,117),(78,118),(79,99),(79,109),(79,112),(80,100),(80,110),(80,112),(81,101),(81,111),(81,112),(82,102),(82,109),(82,111),(83,103),(83,110),(83,111),(84,104),(84,109),(84,110),(85,105),(85,109),(85,113),(86,106),(86,110),(86,113),(87,107),(87,111),(87,113),(88,108),(88,112),(88,113),(89,99),(89,105),(89,108),(90,100),(90,106),(90,108),(91,101),(91,107),(91,108),(92,102),(92,105),(92,107),(93,103),(93,106),(93,107),(94,104),(94,105),(94,106),(95,99),(95,101),(95,102),(96,100),(96,101),(96,103),(97,99),(97,100),(97,104),(98,102),(98,103),(98,104),(99,120),(99,123),(100,121),(100,123),(101,122),(101,123),(102,120),(102,122),(103,121),(103,122),(104,120),(104,121),(105,120),(105,124),(106,121),(106,124),(107,122),(107,124),(108,123),(108,124),(109,120),(109,125),(110,121),(110,125),(111,122),(111,125),(112,123),(112,125),(113,124),(113,125),(114,120),(114,126),(115,121),(115,126),(116,122),(116,126),(117,123),(117,126),(118,124),(118,126),(119,125),(119,126),(120,127),(121,127),(122,127),(123,127),(124,127),(125,127),(126,127)],128)

[[3,2,1,1,1],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,2,2,1],[2,1,1,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,3,2,1,1],[2,1,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,1,1,1],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,2,1,1,1],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,2,2,1],[3,1,1,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,3,1,1,1],[3,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,4],[3,3]] => ([(0,1)],2) => ([(0,1)],2)

[[6,5,4],[4,4]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[6,4,4],[4,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[7,5,4],[5,4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,1],[2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[5,4,4,1],[3,3,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[5,4,3,1],[3,3]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,5,4,1],[4,4,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,3,3,1],[3,2]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,4,4,1],[4,3,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[6,4,3,1],[4,3]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,2,2,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,3,3,2],[2,2,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[5,4,4,2],[3,3,2]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,3,2,2],[2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,3,2],[3,3,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,2,2,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,3,2],[3,2,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,3,2,2],[3,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,2,2,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[4,3,3,2,1],[2,2,1,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,3,3,1,1],[2,2,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,4,4,2,1],[3,3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,1,1],[2,2]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,2,2,1,1],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,3,2,1,1],[3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,3,3],[2,2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[5,4,4,3],[3,3,3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,4,3,3],[3,3,2]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,5,4,3],[4,4,3]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,3,3,3],[3,2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[6,4,4,3],[4,3,3]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[6,4,3,3],[4,3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,2,2,2,1],[1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,3,1],[2,2,2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[4,3,3,2,1],[2,2,2]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,4,4,3,1],[3,3,3,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,2,1],[2,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,2,2,2,1],[2,1,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,3,3,3,1],[3,2,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,2,2,2,2],[1,1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,3,3,3,2],[2,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,3,2,2],[2,2,2,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,4,4,3,2],[3,3,3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,2,2],[2,2,1,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,2,2,2,2],[2,1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,3,3,2],[3,2,2,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,3,2,2,2],[3,2,1,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[2,1,1,1,1,1],[]] => ([],1) => ([],1)

[[3,2,2,2,2,1],[1,1,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,3,3,3,2,1],[2,2,2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,2,2,1,1,1],[1,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,2,2,1],[2,2,2,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,3,2,1,1],[2,2,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,2,1,1,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,2,2,2,1],[2,2,1,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,1,1,1],[2,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,1,1,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,2,2,2,2,1],[2,1,1,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,2,2,2,1,1],[2,1,1,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,2,2,1,1,1],[2,1,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,2,1,1,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,6],[5]] => ([],1) => ([],1)

[[7,6],[6]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,1],[4]] => ([(0,1)],2) => ([(0,1)],2)

[[6,6,1],[5,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5,1],[5]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[7,6,1],[6,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,2],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,2],[4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,6,2],[5,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[5,4,2],[4]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5,2],[5,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[7,6,2],[6,2]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,1,1],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,2,1],[4,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[5,5,1,1],[4,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[6,6,2,1],[5,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,1,1],[4]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5,2,1],[5,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,5,1,1],[5,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[7,6,2,1],[6,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,3],[2]] => ([],1) => ([],1)

[[4,4,3],[3,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,3],[4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[6,6,3],[5,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,4,3],[4,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[6,5,3],[5,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[7,6,3],[6,3]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,2,1],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,3,1],[3,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,2,1],[3,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[5,5,3,1],[4,2,1]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,5,2,1],[4,2]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,6,3,1],[5,3,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,1],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,4,3,1],[4,1,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,2,1],[4,1]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,5,3,1],[5,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[6,5,2,1],[5,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,2,2],[3,1,1]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[5,5,3,2],[4,2,2]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,5,2,2],[4,2,1]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,6,3,2],[5,3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,2,2],[4,1,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[6,5,3,2],[5,2,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[6,5,2,2],[5,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,1,1,1],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2,2,1],[3,1,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[4,4,2,1,1],[3,1,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,5,3,2,1],[4,2,2,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,1,1,1],[3,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,5,2,2,1],[4,2,1,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,5,2,1,1],[4,2,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,1,1,1],[3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,2,2,1],[4,1,1,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,4,2,1,1],[4,1,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,1,1,1],[4,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,4],[3,2]] => ([],1) => ([],1)

[[5,5,4],[4,3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,6,4],[5,4]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,4,4],[4,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5,4],[5,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[7,6,4],[6,4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,3,1],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,1],[3,2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,3,1],[3,2]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[5,5,4,1],[4,3,1]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,5,3,1],[4,3]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,6,4,1],[5,4,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,3,1],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,4,1],[4,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,3,1],[4,2]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,5,4,1],[5,3,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[6,5,3,1],[5,3]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[2,2,2,2],[1]] => ([],1) => ([],1)

[[3,3,3,2],[2,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,2],[3,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,2,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,3,2],[3,2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,5,4,2],[4,3,2]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,2,2],[3,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,5,3,2],[4,3,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,2,2,2],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,3,3,2],[3,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,4,2],[4,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,3,2,2],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,3,2],[4,2,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,2,2],[4,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[2,2,2,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,2,1],[2,1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,3,1,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,4,2,1],[3,2,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,2,1],[3,2,1,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,3,1,1],[3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,2,1,1],[3,2]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[3,2,2,1,1],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,2,1],[3,1,1,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,3,1,1],[3,1,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[5,4,4,2,1],[4,2,2,1]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,23),(1,24),(1,25),(1,26),(1,27),(1,28),(2,18),(2,19),(2,20),(2,21),(2,22),(2,28),(3,14),(3,15),(3,16),(3,17),(3,22),(3,27),(4,11),(4,12),(4,13),(4,17),(4,21),(4,26),(5,9),(5,10),(5,13),(5,16),(5,20),(5,25),(6,8),(6,10),(6,12),(6,15),(6,19),(6,24),(7,8),(7,9),(7,11),(7,14),(7,18),(7,23),(8,29),(8,32),(8,35),(8,41),(8,51),(9,29),(9,30),(9,33),(9,39),(9,49),(10,29),(10,31),(10,34),(10,40),(10,50),(11,30),(11,32),(11,36),(11,42),(11,52),(12,31),(12,32),(12,37),(12,43),(12,53),(13,30),(13,31),(13,38),(13,44),(13,54),(14,33),(14,35),(14,36),(14,45),(14,55),(15,34),(15,35),(15,37),(15,46),(15,56),(16,33),(16,34),(16,38),(16,47),(16,57),(17,36),(17,37),(17,38),(17,48),(17,58),(18,39),(18,41),(18,42),(18,45),(18,59),(19,40),(19,41),(19,43),(19,46),(19,60),(20,39),(20,40),(20,44),(20,47),(20,61),(21,42),(21,43),(21,44),(21,48),(21,62),(22,45),(22,46),(22,47),(22,48),(22,63),(23,49),(23,51),(23,52),(23,55),(23,59),(24,50),(24,51),(24,53),(24,56),(24,60),(25,49),(25,50),(25,54),(25,57),(25,61),(26,52),(26,53),(26,54),(26,58),(26,62),(27,55),(27,56),(27,57),(27,58),(27,63),(28,59),(28,60),(28,61),(28,62),(28,63),(29,67),(29,68),(29,78),(29,88),(30,64),(30,68),(30,75),(30,85),(31,65),(31,68),(31,76),(31,86),(32,66),(32,68),(32,77),(32,87),(33,64),(33,67),(33,69),(33,79),(34,65),(34,67),(34,70),(34,80),(35,66),(35,67),(35,71),(35,81),(36,64),(36,66),(36,72),(36,82),(37,65),(37,66),(37,73),(37,83),(38,64),(38,65),(38,74),(38,84),(39,69),(39,75),(39,78),(39,89),(40,70),(40,76),(40,78),(40,90),(41,71),(41,77),(41,78),(41,91),(42,72),(42,75),(42,77),(42,92),(43,73),(43,76),(43,77),(43,93),(44,74),(44,75),(44,76),(44,94),(45,69),(45,71),(45,72),(45,95),(46,70),(46,71),(46,73),(46,96),(47,69),(47,70),(47,74),(47,97),(48,72),(48,73),(48,74),(48,98),(49,79),(49,85),(49,88),(49,89),(50,80),(50,86),(50,88),(50,90),(51,81),(51,87),(51,88),(51,91),(52,82),(52,85),(52,87),(52,92),(53,83),(53,86),(53,87),(53,93),(54,84),(54,85),(54,86),(54,94),(55,79),(55,81),(55,82),(55,95),(56,80),(56,81),(56,83),(56,96),(57,79),(57,80),(57,84),(57,97),(58,82),(58,83),(58,84),(58,98),(59,89),(59,91),(59,92),(59,95),(60,90),(60,91),(60,93),(60,96),(61,89),(61,90),(61,94),(61,97),(62,92),(62,93),(62,94),(62,98),(63,95),(63,96),(63,97),(63,98),(64,109),(64,114),(64,119),(65,110),(65,115),(65,119),(66,111),(66,116),(66,119),(67,112),(67,117),(67,119),(68,113),(68,118),(68,119),(69,99),(69,114),(69,117),(70,100),(70,115),(70,117),(71,101),(71,116),(71,117),(72,102),(72,114),(72,116),(73,103),(73,115),(73,116),(74,104),(74,114),(74,115),(75,105),(75,114),(75,118),(76,106),(76,115),(76,118),(77,107),(77,116),(77,118),(78,108),(78,117),(78,118),(79,99),(79,109),(79,112),(80,100),(80,110),(80,112),(81,101),(81,111),(81,112),(82,102),(82,109),(82,111),(83,103),(83,110),(83,111),(84,104),(84,109),(84,110),(85,105),(85,109),(85,113),(86,106),(86,110),(86,113),(87,107),(87,111),(87,113),(88,108),(88,112),(88,113),(89,99),(89,105),(89,108),(90,100),(90,106),(90,108),(91,101),(91,107),(91,108),(92,102),(92,105),(92,107),(93,103),(93,106),(93,107),(94,104),(94,105),(94,106),(95,99),(95,101),(95,102),(96,100),(96,101),(96,103),(97,99),(97,100),(97,104),(98,102),(98,103),(98,104),(99,120),(99,123),(100,121),(100,123),(101,122),(101,123),(102,120),(102,122),(103,121),(103,122),(104,120),(104,121),(105,120),(105,124),(106,121),(106,124),(107,122),(107,124),(108,123),(108,124),(109,120),(109,125),(110,121),(110,125),(111,122),(111,125),(112,123),(112,125),(113,124),(113,125),(114,120),(114,126),(115,121),(115,126),(116,122),(116,126),(117,123),(117,126),(118,124),(118,126),(119,125),(119,126),(120,127),(121,127),(122,127),(123,127),(124,127),(125,127),(126,127)],128)

[[4,3,2,1,1],[3,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,4,2,1,1],[4,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,3,3],[3,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,4,3],[4,3,3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,5,3,3],[4,3,2]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,6,4,3],[5,4,3]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,3,3],[4,2,2]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[6,5,4,3],[5,3,3]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[6,5,3,3],[5,3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,3,1],[3,2,2,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,4,3,2,1],[3,2,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,2,2,1],[3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,2,1],[3,1,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,4,3,3,1],[4,2,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,2,2,2],[2,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,3,3,2],[3,2,2,2]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,2,2],[3,2,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,2,2,2],[3,2,1,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,3,2,2,2],[3,1,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[5,4,3,3,2],[4,2,2,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,2,2,2],[4,2,1,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[2,2,1,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,2,2,1],[2,1,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[3,3,2,2,1,1],[2,1,1,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,3,3,2,1],[3,2,2,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,2,1,1,1],[2,1,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,1,1,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,2,2,2,1],[3,2,1,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,2,1,1,1],[3,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,2,1,1,1,1],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,2,2,2,1],[3,1,1,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,2,2,1,1],[3,1,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,1,1,1],[3,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,1,1,1,1],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,5,5],[4,4]] => ([],1) => ([],1)

[[6,6,5],[5,5]] => ([(0,1)],2) => ([(0,1)],2)

[[6,5,5],[5,4]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[7,6,5],[6,5]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,4,1],[3,3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5,1],[4,4,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,4,1],[4,4]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[6,6,5,1],[5,5,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,4,1],[4,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[6,5,5,1],[5,4,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,5,4,1],[5,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[7,6,5,1],[6,5,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,3,2],[2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,2],[3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,5,2],[4,4,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[4,4,3,2],[3,3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,5,4,2],[4,4,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,6,5,2],[5,5,2]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,3,2],[3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,4,2],[4,3,1]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,5,5,2],[5,4,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,3,2],[4,3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[6,5,4,2],[5,4,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,3,1,1],[2,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,2,1],[3,3,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[4,4,4,1,1],[3,3,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[5,5,5,2,1],[4,4,2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,4,3,1,1],[3,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[5,5,4,2,1],[4,4,1,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,5,4,1,1],[4,4,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,3,1,1],[3,2]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[5,4,4,2,1],[4,3,1,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,4,1,1],[4,3,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,3,1,1],[4,3]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[3,3,3,3],[2,2,1]] => ([],1) => ([],1)

[[4,4,4,3],[3,3,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,5,3],[4,4,3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,3,3],[3,3,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,5,4,3],[4,4,2]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,6,5,3],[5,5,3]] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,3,3],[3,2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,4,4,3],[4,3,2]] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,5,5,3],[5,4,3]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,3,3],[4,3,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[6,5,4,3],[5,4,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[2,2,2,2,1],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,1],[2,2,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,2,1],[2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,4,3,1],[3,3,2,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,4,4,2,1],[3,3,2]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,5,5,3,1],[4,4,3,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,2,2,1],[2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,3,1],[3,3,1,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,4,3,2,1],[3,3,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,2,2,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,3,3,1],[3,2,1,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,3,2,1],[3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,2,1],[3,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,3,3,1],[4,3,1,1]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,23),(1,24),(1,25),(1,26),(1,27),(1,28),(2,18),(2,19),(2,20),(2,21),(2,22),(2,28),(3,14),(3,15),(3,16),(3,17),(3,22),(3,27),(4,11),(4,12),(4,13),(4,17),(4,21),(4,26),(5,9),(5,10),(5,13),(5,16),(5,20),(5,25),(6,8),(6,10),(6,12),(6,15),(6,19),(6,24),(7,8),(7,9),(7,11),(7,14),(7,18),(7,23),(8,29),(8,32),(8,35),(8,41),(8,51),(9,29),(9,30),(9,33),(9,39),(9,49),(10,29),(10,31),(10,34),(10,40),(10,50),(11,30),(11,32),(11,36),(11,42),(11,52),(12,31),(12,32),(12,37),(12,43),(12,53),(13,30),(13,31),(13,38),(13,44),(13,54),(14,33),(14,35),(14,36),(14,45),(14,55),(15,34),(15,35),(15,37),(15,46),(15,56),(16,33),(16,34),(16,38),(16,47),(16,57),(17,36),(17,37),(17,38),(17,48),(17,58),(18,39),(18,41),(18,42),(18,45),(18,59),(19,40),(19,41),(19,43),(19,46),(19,60),(20,39),(20,40),(20,44),(20,47),(20,61),(21,42),(21,43),(21,44),(21,48),(21,62),(22,45),(22,46),(22,47),(22,48),(22,63),(23,49),(23,51),(23,52),(23,55),(23,59),(24,50),(24,51),(24,53),(24,56),(24,60),(25,49),(25,50),(25,54),(25,57),(25,61),(26,52),(26,53),(26,54),(26,58),(26,62),(27,55),(27,56),(27,57),(27,58),(27,63),(28,59),(28,60),(28,61),(28,62),(28,63),(29,67),(29,68),(29,78),(29,88),(30,64),(30,68),(30,75),(30,85),(31,65),(31,68),(31,76),(31,86),(32,66),(32,68),(32,77),(32,87),(33,64),(33,67),(33,69),(33,79),(34,65),(34,67),(34,70),(34,80),(35,66),(35,67),(35,71),(35,81),(36,64),(36,66),(36,72),(36,82),(37,65),(37,66),(37,73),(37,83),(38,64),(38,65),(38,74),(38,84),(39,69),(39,75),(39,78),(39,89),(40,70),(40,76),(40,78),(40,90),(41,71),(41,77),(41,78),(41,91),(42,72),(42,75),(42,77),(42,92),(43,73),(43,76),(43,77),(43,93),(44,74),(44,75),(44,76),(44,94),(45,69),(45,71),(45,72),(45,95),(46,70),(46,71),(46,73),(46,96),(47,69),(47,70),(47,74),(47,97),(48,72),(48,73),(48,74),(48,98),(49,79),(49,85),(49,88),(49,89),(50,80),(50,86),(50,88),(50,90),(51,81),(51,87),(51,88),(51,91),(52,82),(52,85),(52,87),(52,92),(53,83),(53,86),(53,87),(53,93),(54,84),(54,85),(54,86),(54,94),(55,79),(55,81),(55,82),(55,95),(56,80),(56,81),(56,83),(56,96),(57,79),(57,80),(57,84),(57,97),(58,82),(58,83),(58,84),(58,98),(59,89),(59,91),(59,92),(59,95),(60,90),(60,91),(60,93),(60,96),(61,89),(61,90),(61,94),(61,97),(62,92),(62,93),(62,94),(62,98),(63,95),(63,96),(63,97),(63,98),(64,109),(64,114),(64,119),(65,110),(65,115),(65,119),(66,111),(66,116),(66,119),(67,112),(67,117),(67,119),(68,113),(68,118),(68,119),(69,99),(69,114),(69,117),(70,100),(70,115),(70,117),(71,101),(71,116),(71,117),(72,102),(72,114),(72,116),(73,103),(73,115),(73,116),(74,104),(74,114),(74,115),(75,105),(75,114),(75,118),(76,106),(76,115),(76,118),(77,107),(77,116),(77,118),(78,108),(78,117),(78,118),(79,99),(79,109),(79,112),(80,100),(80,110),(80,112),(81,101),(81,111),(81,112),(82,102),(82,109),(82,111),(83,103),(83,110),(83,111),(84,104),(84,109),(84,110),(85,105),(85,109),(85,113),(86,106),(86,110),(86,113),(87,107),(87,111),(87,113),(88,108),(88,112),(88,113),(89,99),(89,105),(89,108),(90,100),(90,106),(90,108),(91,101),(91,107),(91,108),(92,102),(92,105),(92,107),(93,103),(93,106),(93,107),(94,104),(94,105),(94,106),(95,99),(95,101),(95,102),(96,100),(96,101),(96,103),(97,99),(97,100),(97,104),(98,102),(98,103),(98,104),(99,120),(99,123),(100,121),(100,123),(101,122),(101,123),(102,120),(102,122),(103,121),(103,122),(104,120),(104,121),(105,120),(105,124),(106,121),(106,124),(107,122),(107,124),(108,123),(108,124),(109,120),(109,125),(110,121),(110,125),(111,122),(111,125),(112,123),(112,125),(113,124),(113,125),(114,120),(114,126),(115,121),(115,126),(116,122),(116,126),(117,123),(117,126),(118,124),(118,126),(119,125),(119,126),(120,127),(121,127),(122,127),(123,127),(124,127),(125,127),(126,127)],128)

[[3,3,3,2,2],[2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[4,4,4,3,2],[3,3,2,2]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,4,2,2],[3,3,2,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,5,5,3,2],[4,4,3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,3,2,2],[3,3,1,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,3,3,2,2],[3,2,1,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,4,3,2,2],[4,3,1,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[2,2,2,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,2,2,1],[2,2,1,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,3,2,1,1],[2,2,1,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,4,3,2,1],[3,3,2,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,3,1,1,1],[2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,4,2,2,1],[3,3,2,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,4,2,1,1],[3,3,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,2,1,1,1],[2,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,4,3,2,2,1],[3,3,1,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,3,1,1,1],[3,3,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,2,2,1,1,1],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,3,3,2,2,1],[3,2,1,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,3,1,1,1],[3,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,1,1,1],[3,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,4,4],[3,3,3]] => ([],1) => ([],1)

[[5,5,5,4],[4,4,4]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,4,4],[4,4,3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[6,6,5,4],[5,5,4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,4,4],[4,3,3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5,5,4],[5,4,4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,5,4,4],[5,4,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[7,6,5,4],[6,5,4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,3,3,1],[2,2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4,1],[3,3,3,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,3,1],[3,3,3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,5,5,4,1],[4,4,4,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,3,1],[3,3,2]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,5,4,4,1],[4,4,3,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,5,4,3,1],[4,4,3]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,3,3,1],[3,2,2]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[5,4,4,4,1],[4,3,3,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,4,4,3,1],[4,3,3]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,3,3,1],[4,3,2]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[2,2,2,2,2],[1,1,1]] => ([],1) => ([],1)

[[3,3,3,3,2],[2,2,2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,4,2],[3,3,3,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,3,2,2],[2,2,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,3,2],[3,3,3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,5,5,4,2],[4,4,4,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,2,2,2],[2,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,3,2],[3,3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,3,2,2],[3,3,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,2,2,2,2],[2,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,3,2],[3,2,2,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,4,4,4,2],[4,3,3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,3,2,2],[3,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[4,3,2,2,2],[3,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,4,3,2,2],[4,3,2]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,23),(1,24),(1,25),(1,26),(1,27),(1,28),(2,18),(2,19),(2,20),(2,21),(2,22),(2,28),(3,14),(3,15),(3,16),(3,17),(3,22),(3,27),(4,11),(4,12),(4,13),(4,17),(4,21),(4,26),(5,9),(5,10),(5,13),(5,16),(5,20),(5,25),(6,8),(6,10),(6,12),(6,15),(6,19),(6,24),(7,8),(7,9),(7,11),(7,14),(7,18),(7,23),(8,29),(8,32),(8,35),(8,41),(8,51),(9,29),(9,30),(9,33),(9,39),(9,49),(10,29),(10,31),(10,34),(10,40),(10,50),(11,30),(11,32),(11,36),(11,42),(11,52),(12,31),(12,32),(12,37),(12,43),(12,53),(13,30),(13,31),(13,38),(13,44),(13,54),(14,33),(14,35),(14,36),(14,45),(14,55),(15,34),(15,35),(15,37),(15,46),(15,56),(16,33),(16,34),(16,38),(16,47),(16,57),(17,36),(17,37),(17,38),(17,48),(17,58),(18,39),(18,41),(18,42),(18,45),(18,59),(19,40),(19,41),(19,43),(19,46),(19,60),(20,39),(20,40),(20,44),(20,47),(20,61),(21,42),(21,43),(21,44),(21,48),(21,62),(22,45),(22,46),(22,47),(22,48),(22,63),(23,49),(23,51),(23,52),(23,55),(23,59),(24,50),(24,51),(24,53),(24,56),(24,60),(25,49),(25,50),(25,54),(25,57),(25,61),(26,52),(26,53),(26,54),(26,58),(26,62),(27,55),(27,56),(27,57),(27,58),(27,63),(28,59),(28,60),(28,61),(28,62),(28,63),(29,67),(29,68),(29,78),(29,88),(30,64),(30,68),(30,75),(30,85),(31,65),(31,68),(31,76),(31,86),(32,66),(32,68),(32,77),(32,87),(33,64),(33,67),(33,69),(33,79),(34,65),(34,67),(34,70),(34,80),(35,66),(35,67),(35,71),(35,81),(36,64),(36,66),(36,72),(36,82),(37,65),(37,66),(37,73),(37,83),(38,64),(38,65),(38,74),(38,84),(39,69),(39,75),(39,78),(39,89),(40,70),(40,76),(40,78),(40,90),(41,71),(41,77),(41,78),(41,91),(42,72),(42,75),(42,77),(42,92),(43,73),(43,76),(43,77),(43,93),(44,74),(44,75),(44,76),(44,94),(45,69),(45,71),(45,72),(45,95),(46,70),(46,71),(46,73),(46,96),(47,69),(47,70),(47,74),(47,97),(48,72),(48,73),(48,74),(48,98),(49,79),(49,85),(49,88),(49,89),(50,80),(50,86),(50,88),(50,90),(51,81),(51,87),(51,88),(51,91),(52,82),(52,85),(52,87),(52,92),(53,83),(53,86),(53,87),(53,93),(54,84),(54,85),(54,86),(54,94),(55,79),(55,81),(55,82),(55,95),(56,80),(56,81),(56,83),(56,96),(57,79),(57,80),(57,84),(57,97),(58,82),(58,83),(58,84),(58,98),(59,89),(59,91),(59,92),(59,95),(60,90),(60,91),(60,93),(60,96),(61,89),(61,90),(61,94),(61,97),(62,92),(62,93),(62,94),(62,98),(63,95),(63,96),(63,97),(63,98),(64,109),(64,114),(64,119),(65,110),(65,115),(65,119),(66,111),(66,116),(66,119),(67,112),(67,117),(67,119),(68,113),(68,118),(68,119),(69,99),(69,114),(69,117),(70,100),(70,115),(70,117),(71,101),(71,116),(71,117),(72,102),(72,114),(72,116),(73,103),(73,115),(73,116),(74,104),(74,114),(74,115),(75,105),(75,114),(75,118),(76,106),(76,115),(76,118),(77,107),(77,116),(77,118),(78,108),(78,117),(78,118),(79,99),(79,109),(79,112),(80,100),(80,110),(80,112),(81,101),(81,111),(81,112),(82,102),(82,109),(82,111),(83,103),(83,110),(83,111),(84,104),(84,109),(84,110),(85,105),(85,109),(85,113),(86,106),(86,110),(86,113),(87,107),(87,111),(87,113),(88,108),(88,112),(88,113),(89,99),(89,105),(89,108),(90,100),(90,106),(90,108),(91,101),(91,107),(91,108),(92,102),(92,105),(92,107),(93,103),(93,106),(93,107),(94,104),(94,105),(94,106),(95,99),(95,101),(95,102),(96,100),(96,101),(96,103),(97,99),(97,100),(97,104),(98,102),(98,103),(98,104),(99,120),(99,123),(100,121),(100,123),(101,122),(101,123),(102,120),(102,122),(103,121),(103,122),(104,120),(104,121),(105,120),(105,124),(106,121),(106,124),(107,122),(107,124),(108,123),(108,124),(109,120),(109,125),(110,121),(110,125),(111,122),(111,125),(112,123),(112,125),(113,124),(113,125),(114,120),(114,126),(115,121),(115,126),(116,122),(116,126),(117,123),(117,126),(118,124),(118,126),(119,125),(119,126),(120,127),(121,127),(122,127),(123,127),(124,127),(125,127),(126,127)],128)

[[2,2,2,2,1,1],[1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,3,2,1],[2,2,2,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[3,3,3,3,1,1],[2,2,2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,4,4,4,2,1],[3,3,3,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,3,2,1,1],[2,2,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,4,3,2,1],[3,3,3,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,4,3,1,1],[3,3,3,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,2,2,1,1],[2,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,3,2,1,1],[3,3,2]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,2,2,2,1,1],[2,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,3,2,1],[3,2,2,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,3,3,1,1],[3,2,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,3,2,1,1],[3,2,2]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,2,1,1],[3,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,3,3,3],[2,2,2,2]] => ([],1) => ([],1)

[[4,4,4,4,3],[3,3,3,3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3,3],[3,3,3,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,5,5,4,3],[4,4,4,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,3,3],[3,3,2,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[5,5,4,4,3],[4,4,3,3]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,5,4,3,3],[4,4,3,2]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,3,3,3],[3,2,2,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,4,4,3],[4,3,3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,4,4,3,3],[4,3,3,2]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[5,4,3,3,3],[4,3,2,2]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[2,2,2,2,2,1],[1,1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3,1],[2,2,2,2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,3,2,1],[2,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,4,4,3,1],[3,3,3,3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,3,2,2,1],[2,2,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,4,3,3,1],[3,3,3,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,4,3,2,1],[3,3,3,2]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,2,2,2,1],[2,2,1,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,3,3,3,1],[3,3,2,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,2,2,2,2,1],[2,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,3,3,3,3,1],[3,2,2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,3,2,1],[3,2,2,2]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,2,2,1],[3,2,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[2,2,2,2,2,2],[1,1,1,1,1]] => ([],1) => ([],1)

[[3,3,3,3,3,2],[2,2,2,2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,2,2],[2,2,2,2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,4,4,3,2],[3,3,3,3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,3,2,2,2],[2,2,2,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,4,3,3,2],[3,3,3,2,2]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,4,3,2,2],[3,3,3,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,3,2,2,2,2],[2,2,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,4,3,3,3,2],[3,3,2,2,2]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,3,2,2,2],[3,3,2,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[3,2,2,2,2,2],[2,1,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,3,3,2],[3,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,3,2,2],[3,2,2,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,3,2,2,2],[3,2,2,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,3,2,2,2,2],[3,2,1,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,2,2,2,1,1],[1,1,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[2,2,2,2,1,1,1],[1,1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,3,3,2,1,1],[2,2,2,2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[2,2,2,1,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,3,2,2,1,1],[2,2,2,1,1]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,3,3,2,1,1,1],[2,2,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[2,2,1,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,2,2,2,1,1],[2,2,1,1,1]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,3,2,2,1,1,1],[2,2,1,1]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,19),(1,20),(1,21),(2,13),(2,14),(2,15),(2,16),(2,21),(3,10),(3,11),(3,12),(3,16),(3,20),(4,8),(4,9),(4,12),(4,15),(4,19),(5,7),(5,9),(5,11),(5,14),(5,18),(6,7),(6,8),(6,10),(6,13),(6,17),(7,22),(7,25),(7,28),(7,34),(8,22),(8,23),(8,26),(8,32),(9,22),(9,24),(9,27),(9,33),(10,23),(10,25),(10,29),(10,35),(11,24),(11,25),(11,30),(11,36),(12,23),(12,24),(12,31),(12,37),(13,26),(13,28),(13,29),(13,38),(14,27),(14,28),(14,30),(14,39),(15,26),(15,27),(15,31),(15,40),(16,29),(16,30),(16,31),(16,41),(17,32),(17,34),(17,35),(17,38),(18,33),(18,34),(18,36),(18,39),(19,32),(19,33),(19,37),(19,40),(20,35),(20,36),(20,37),(20,41),(21,38),(21,39),(21,40),(21,41),(22,45),(22,46),(22,56),(23,42),(23,46),(23,53),(24,43),(24,46),(24,54),(25,44),(25,46),(25,55),(26,42),(26,45),(26,47),(27,43),(27,45),(27,48),(28,44),(28,45),(28,49),(29,42),(29,44),(29,50),(30,43),(30,44),(30,51),(31,42),(31,43),(31,52),(32,47),(32,53),(32,56),(33,48),(33,54),(33,56),(34,49),(34,55),(34,56),(35,50),(35,53),(35,55),(36,51),(36,54),(36,55),(37,52),(37,53),(37,54),(38,47),(38,49),(38,50),(39,48),(39,49),(39,51),(40,47),(40,48),(40,52),(41,50),(41,51),(41,52),(42,57),(42,62),(43,58),(43,62),(44,59),(44,62),(45,60),(45,62),(46,61),(46,62),(47,57),(47,60),(48,58),(48,60),(49,59),(49,60),(50,57),(50,59),(51,58),(51,59),(52,57),(52,58),(53,57),(53,61),(54,58),(54,61),(55,59),(55,61),(56,60),(56,61),(57,63),(58,63),(59,63),(60,63),(61,63),(62,63)],64)

[[3,3,2,1,1,1,1],[2,2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[2,1,1,1,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,2,2,2,2,1,1],[2,1,1,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,2,2,2,1,1,1],[2,1,1,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,2,2,1,1,1,1],[2,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,2,1,1,1,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,2,1,1,1,1],[3,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[8],[]] => ([],1) => ([],1)

[[7,1],[]] => ([],1) => ([],1)

[[6,2],[]] => ([],1) => ([],1)

[[6,1,1],[]] => ([],1) => ([],1)

[[5,3],[]] => ([],1) => ([],1)

[[5,2,1],[]] => ([],1) => ([],1)

[[5,1,1,1],[]] => ([],1) => ([],1)

[[4,4],[]] => ([],1) => ([],1)

[[4,3,1],[]] => ([],1) => ([],1)

[[4,2,2],[]] => ([],1) => ([],1)

[[4,2,1,1],[]] => ([],1) => ([],1)

[[4,1,1,1,1],[]] => ([],1) => ([],1)

[[3,3,2],[]] => ([],1) => ([],1)

[[3,3,1,1],[]] => ([],1) => ([],1)

[[3,2,2,1],[]] => ([],1) => ([],1)

[[3,2,1,1,1],[]] => ([],1) => ([],1)

[[3,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,2,2],[]] => ([],1) => ([],1)

[[2,2,2,1,1],[]] => ([],1) => ([],1)

[[2,2,1,1,1,1],[]] => ([],1) => ([],1)

[[2,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[1,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[9],[]] => ([],1) => ([],1)

[[8,1],[]] => ([],1) => ([],1)

[[7,2],[]] => ([],1) => ([],1)

[[7,1,1],[]] => ([],1) => ([],1)

[[6,3],[]] => ([],1) => ([],1)

[[6,2,1],[]] => ([],1) => ([],1)

[[6,1,1,1],[]] => ([],1) => ([],1)

[[5,4],[]] => ([],1) => ([],1)

[[5,3,1],[]] => ([],1) => ([],1)

[[5,2,2],[]] => ([],1) => ([],1)

[[5,2,1,1],[]] => ([],1) => ([],1)

[[5,1,1,1,1],[]] => ([],1) => ([],1)

[[4,4,1],[]] => ([],1) => ([],1)

[[4,3,2],[]] => ([],1) => ([],1)

[[4,3,1,1],[]] => ([],1) => ([],1)

[[4,2,2,1],[]] => ([],1) => ([],1)

[[4,2,1,1,1],[]] => ([],1) => ([],1)

[[4,1,1,1,1,1],[]] => ([],1) => ([],1)

[[3,3,3],[]] => ([],1) => ([],1)

[[3,3,2,1],[]] => ([],1) => ([],1)

[[3,3,1,1,1],[]] => ([],1) => ([],1)

[[3,2,2,2],[]] => ([],1) => ([],1)

[[3,2,2,1,1],[]] => ([],1) => ([],1)

[[3,2,1,1,1,1],[]] => ([],1) => ([],1)

[[3,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,2,2,1],[]] => ([],1) => ([],1)

[[2,2,2,1,1,1],[]] => ([],1) => ([],1)

[[2,2,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[1,1,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[10],[]] => ([],1) => ([],1)

[[9,1],[]] => ([],1) => ([],1)

[[8,2],[]] => ([],1) => ([],1)

[[8,1,1],[]] => ([],1) => ([],1)

[[7,3],[]] => ([],1) => ([],1)

[[7,2,1],[]] => ([],1) => ([],1)

[[7,1,1,1],[]] => ([],1) => ([],1)

[[6,4],[]] => ([],1) => ([],1)

[[6,3,1],[]] => ([],1) => ([],1)

[[6,2,2],[]] => ([],1) => ([],1)

[[6,2,1,1],[]] => ([],1) => ([],1)

[[6,1,1,1,1],[]] => ([],1) => ([],1)

[[5,5],[]] => ([],1) => ([],1)

[[5,4,1],[]] => ([],1) => ([],1)

[[5,3,2],[]] => ([],1) => ([],1)

[[5,3,1,1],[]] => ([],1) => ([],1)

[[5,2,2,1],[]] => ([],1) => ([],1)

[[5,2,1,1,1],[]] => ([],1) => ([],1)

[[5,1,1,1,1,1],[]] => ([],1) => ([],1)

[[4,4,2],[]] => ([],1) => ([],1)

[[4,4,1,1],[]] => ([],1) => ([],1)

[[4,3,3],[]] => ([],1) => ([],1)

[[4,3,2,1],[]] => ([],1) => ([],1)

[[4,3,1,1,1],[]] => ([],1) => ([],1)

[[4,2,2,2],[]] => ([],1) => ([],1)

[[4,2,2,1,1],[]] => ([],1) => ([],1)

[[4,2,1,1,1,1],[]] => ([],1) => ([],1)

[[4,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[3,3,3,1],[]] => ([],1) => ([],1)

[[3,3,2,2],[]] => ([],1) => ([],1)

[[3,3,2,1,1],[]] => ([],1) => ([],1)

[[3,3,1,1,1,1],[]] => ([],1) => ([],1)

[[3,2,2,2,1],[]] => ([],1) => ([],1)

[[3,2,2,1,1,1],[]] => ([],1) => ([],1)

[[3,2,1,1,1,1,1],[]] => ([],1) => ([],1)

[[3,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,2,2,2],[]] => ([],1) => ([],1)

[[2,2,2,2,1,1],[]] => ([],1) => ([],1)

[[2,2,2,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,1,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[1,1,1,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[6,5],[]] => ([],1) => ([],1)

[[5,5,1],[]] => ([],1) => ([],1)

[[5,4,2],[]] => ([],1) => ([],1)

[[5,3,3],[]] => ([],1) => ([],1)

[[4,4,3],[]] => ([],1) => ([],1)

[[4,4,2,1],[]] => ([],1) => ([],1)

[[4,3,3,1],[]] => ([],1) => ([],1)

[[4,3,2,2],[]] => ([],1) => ([],1)

[[3,3,3,2],[]] => ([],1) => ([],1)

[[3,2,2,2,2],[]] => ([],1) => ([],1)

[[6,6],[]] => ([],1) => ([],1)

[[5,5,2],[]] => ([],1) => ([],1)

[[5,4,3],[]] => ([],1) => ([],1)

[[4,4,4],[]] => ([],1) => ([],1)

[[4,4,3,1],[]] => ([],1) => ([],1)

[[4,4,2,2],[]] => ([],1) => ([],1)

[[4,3,3,2],[]] => ([],1) => ([],1)

[[3,3,3,3],[]] => ([],1) => ([],1)

[[3,3,3,2,1],[]] => ([],1) => ([],1)

[[3,3,2,2,2],[]] => ([],1) => ([],1)

[[2,2,2,2,2,2],[]] => ([],1) => ([],1)

[[5,5,3],[]] => ([],1) => ([],1)

[[5,4,4],[]] => ([],1) => ([],1)

[[4,4,4,1],[]] => ([],1) => ([],1)

[[4,4,3,2],[]] => ([],1) => ([],1)

[[4,3,3,3],[]] => ([],1) => ([],1)

[[3,3,3,3,1],[]] => ([],1) => ([],1)

[[3,3,3,2,2],[]] => ([],1) => ([],1)

[[5,5,4],[]] => ([],1) => ([],1)

[[4,4,4,2],[]] => ([],1) => ([],1)

[[4,4,3,3],[]] => ([],1) => ([],1)

[[3,3,3,3,2],[]] => ([],1) => ([],1)

[[5,5,5],[]] => ([],1) => ([],1)

[[5,5,4,1],[]] => ([],1) => ([],1)

[[4,4,4,3],[]] => ([],1) => ([],1)

[[3,3,3,3,3],[]] => ([],1) => ([],1)

[[5,5,5,1],[]] => ([],1) => ([],1)

[[4,4,4,4],[]] => ([],1) => ([],1)

[[4,4,4,3,1],[]] => ([],1) => ([],1)

[[3,3,3,3,3,1],[]] => ([],1) => ([],1)

[[4,4,4,4,1],[]] => ([],1) => ([],1)

[[2,2,1,1,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,2,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,2,1,1,1,1],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[2,2,2,2,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,2,2,1,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,1,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[2,2,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,2,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],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)

[[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[3,3,3,2,1,1],[2,2,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,3,2,1,1],[2,1]] => ([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,2,1,1],[3,1]] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,3,3,1,1],[2,2]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[4,4,3,1,1],[3,2]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[2,2,2,2,2,2,1],[1,1,1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,2,2,2,2,1],[1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[3,3,3,2,2,1],[2,2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[4,4,2,2,1],[3,1,1]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[3,3,3,3,2,1],[2,2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[5,3,2,1],[2,1]] => ([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,4,2,1],[3,3,1]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,3,3,3,1],[2,2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[4,4,3,3,1],[3,2,2]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,3,3,1],[2,2]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[4,4,4,3,1],[3,3,2]] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,5,3,1],[4,2]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,4,4,4,1],[3,3,3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,4,4,1],[3,3]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[5,5,4,1],[4,3]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],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)

[[3,2,2,2,2,2],[1,1,1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,2,2,2],[2,1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,2,2,2],[2,2,1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],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)

[[4,3,2,2,2],[2,1,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[4,4,2,2,2],[3,1,1,1]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[3,3,3,3,2,2],[2,2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[4,3,3,2,2],[2,2,1,1]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,3,2,2],[2,1,1]] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,4,4,2,2],[3,3,1,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[5,4,2,2],[3,1,1]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[3,3,3,3,3,2],[2,2,2,2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,3,2],[2,2,2,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[5,3,3,2],[2,2,1]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[4,4,4,3,2],[3,3,2,1]] => ([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[4,4,4,4,2],[3,3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,4,2],[3,3,1]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,5,5,2],[4,4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,4,3,3,3],[3,2,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,3,3,3],[2,2,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,3,3],[3,3,2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[5,4,3,3],[3,2,2]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,5,3,3],[4,2,2]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[[4,4,4,4,3],[3,3,3,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,4,3],[3,3,2]] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)

[[5,5,4,3],[4,3,2]] => ([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,15),(1,16),(1,19),(2,14),(2,16),(2,18),(3,14),(3,15),(3,17),(4,5),(4,6),(4,17),(4,18),(4,19),(5,10),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(6,13),(7,24),(7,27),(7,29),(8,25),(8,28),(8,29),(9,26),(9,27),(9,28),(10,24),(10,30),(10,32),(11,25),(11,31),(11,32),(12,26),(12,30),(12,31),(13,24),(13,25),(13,26),(14,20),(14,23),(15,20),(15,21),(16,20),(16,22),(17,7),(17,10),(17,21),(17,23),(18,8),(18,11),(18,22),(18,23),(19,9),(19,12),(19,21),(19,22),(20,38),(21,27),(21,30),(21,38),(22,28),(22,31),(22,38),(23,29),(23,32),(23,38),(24,35),(24,37),(25,36),(25,37),(26,35),(26,36),(27,33),(27,35),(28,33),(28,36),(29,33),(29,37),(30,34),(30,35),(31,34),(31,36),(32,34),(32,37),(33,39),(34,39),(35,39),(36,39),(37,39),(38,33),(38,34)],40)

[[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[5,5,5,3],[4,4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)

[[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],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)

[[4,4,4,4,4],[3,3,3,3]] => ([],1) => ([],1)

[[5,4,4,4],[3,3,3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,4,4],[4,3,3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,4,4],[3,3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,5,4],[4,4,3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[6,6,4],[5,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[7,4],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[3,3,3],[1]] => ([],1) => ([],1)

[[3,3,3,1],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,1],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[2,2,2,2,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,1],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,2],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4],[2,2]] => ([],1) => ([],1)

[[5,5],[2]] => ([],1) => ([],1)

[[4,4,3],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,3],[2,1,1]] => ([],1) => ([],1)

[[4,3,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3],[1,1,1]] => ([],1) => ([],1)

[[4,4,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4],[3,1]] => ([],1) => ([],1)

[[5,4],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4],[2,1]] => ([],1) => ([],1)

[[5,5],[1]] => ([],1) => ([],1)

[[4,4,4],[1,1]] => ([],1) => ([],1)

[[3,3,2,2],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,2],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,2],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,2],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,2,2,2],[1,1]] => ([],1) => ([],1)

[[3,2,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,2],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,2,2,2],[1]] => ([],1) => ([],1)

[[3,3,3,2],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3],[2,2]] => ([],1) => ([],1)

[[4,3,3],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3],[2,1]] => ([],1) => ([],1)

[[4,3,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3],[1,1]] => ([],1) => ([],1)

[[4,4,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4],[3]] => ([],1) => ([],1)

[[4,4,4],[2]] => ([],1) => ([],1)

[[4,4,4],[1]] => ([],1) => ([],1)

[[3,3,3,3],[2]] => ([],1) => ([],1)

[[3,3,3,3],[1]] => ([],1) => ([],1)

[[4,4,4,1],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,1],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,2],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[6,6],[4]] => ([],1) => ([],1)

[[6,5],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5],[3,3]] => ([],1) => ([],1)

[[6,6],[3]] => ([],1) => ([],1)

[[6,4],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,4],[3,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,4],[2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[2,2,2]] => ([],1) => ([],1)

[[5,5,4],[2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[6,5],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5],[3,2]] => ([],1) => ([],1)

[[6,6],[2]] => ([],1) => ([],1)

[[5,5,5],[2,2]] => ([],1) => ([],1)

[[6,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,3],[3,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[5,4,3],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(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)

[[4,4,4,3],[2,2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,3,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,3],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,3],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3],[1,1,1,1]] => ([],1) => ([],1)

[[4,4,3,3],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,4,3],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,3],[2,1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[6,4],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,4],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,4],[2,2,1]] => ([],1) => ([],1)

[[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5],[3,1]] => ([],1) => ([],1)

[[6,6],[1]] => ([],1) => ([],1)

[[5,5,5],[2,1]] => ([],1) => ([],1)

[[4,4,4,4],[3,1,1]] => ([],1) => ([],1)

[[5,4,4],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[2,1,1]] => ([],1) => ([],1)

[[5,5,4],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[1,1,1]] => ([],1) => ([],1)

[[5,5,5],[1,1]] => ([],1) => ([],1)

[[5,5,2],[3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,2],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(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)

[[4,4,4,2],[2,2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,2],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,3,2],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,3,2],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)

[[4,3,3,2],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,3,2],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,4,2],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[5,5,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2,2],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,2,2],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,2,2],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,3,2],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,3,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,2],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,2],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,2],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,3],[3]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,4,4,3],[2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,3],[2]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,3,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(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)

[[4,3,3,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3],[1,1,1]] => ([],1) => ([],1)

[[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,3],[1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,5,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,4],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[3,2]] => ([],1) => ([],1)

[[5,4,4],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[2,2]] => ([],1) => ([],1)

[[5,5,4],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5],[4]] => ([],1) => ([],1)

[[5,5,5],[3]] => ([],1) => ([],1)

[[5,5,5],[2]] => ([],1) => ([],1)

[[4,4,4,4],[3,1]] => ([],1) => ([],1)

[[5,4,4],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[2,1]] => ([],1) => ([],1)

[[5,5,4],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[1,1]] => ([],1) => ([],1)

[[5,5,5],[1]] => ([],1) => ([],1)

[[4,3,3,3],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,3],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,3],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3],[2,1]] => ([],1) => ([],1)

[[4,3,3,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3],[1,1]] => ([],1) => ([],1)

[[4,4,3,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3],[2]] => ([],1) => ([],1)

[[3,3,3,3,3],[1]] => ([],1) => ([],1)

[[4,4,4,4],[3]] => ([],1) => ([],1)

[[4,4,4,4],[2]] => ([],1) => ([],1)

[[4,4,4,4],[1]] => ([],1) => ([],1)

[[5,5,5,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5,5],[4,1]] => ([],1) => ([],1)

[[3,3,3,3,3,3],[2]] => ([],1) => ([],1)

[[4,4,4,4,3],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5,4],[4]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4,4],[3,1]] => ([],1) => ([],1)

[[5,5,5,5],[4]] => ([],1) => ([],1)

[[4,4,4,4,4],[3]] => ([],1) => ([],1)

[[5,5,5,5,5],[4]] => ([],1) => ([],1)

[[5,5,5,5,1],[]] => ([],1) => ([],1)

[[5,5,5,5,5,5],[4]] => ([],1) => ([],1)

[[4,4,4,4,4,4],[3]] => ([],1) => ([],1)

[[4,4,4,4,4,1],[]] => ([],1) => ([],1)

[[5,5,5,5,5,1],[]] => ([],1) => ([],1)

[[6,6,6,6,6,6],[5]] => ([],1) => ([],1)

[[6,6,6,6,6],[5]] => ([],1) => ([],1)

[[5,5,5,5,4],[4]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5,5,5],[4,1]] => ([],1) => ([],1)

[[5,5,5,4,1],[]] => ([],1) => ([],1)

[[5,5,5,5,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[6,6,6,6,1],[]] => ([],1) => ([],1)

[[6,6,6,6,6,1],[]] => ([],1) => ([],1)

Map

dominating sublattice

Description

Return the sublattice of the dominance order induced by the support of the expansion of the skew Schur function into Schur functions.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the subposet of the dominance order whose elements are the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a lattice.
The example $\lambda = (5^2,4^2,1)$ and $\mu=(3,2)$ shows that this lattice is not a sublattice of the dominance order.

Map

lattice of congruences

Description

The lattice of congruences of a lattice.
A congruence of a lattice is an equivalence relation such that $a_1 \cong a_2$ and $b_1 \cong b_2$ implies $a_1 \vee b_1 \cong a_2 \vee b_2$ and $a_1 \wedge b_1 \cong a_2 \wedge b_2$.
The set of congruences ordered by refinement forms a lattice.