Identifier
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
Images
[1] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4)
[2] => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[1,1] => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[3] => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[2,1] => 1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[1,1,1] => 1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[4] => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[3,1] => 10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
[2,2] => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
[2,1,1] => 10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
[1,1,1,1] => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[5] => 100000 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[4,1] => 100010 => ([(0,3),(0,4),(1,2),(1,11),(1,15),(2,7),(2,12),(3,13),(3,14),(4,1),(4,13),(4,14),(6,9),(7,10),(8,6),(9,5),(10,5),(11,7),(12,9),(12,10),(13,8),(13,15),(14,8),(14,11),(15,6),(15,12)],16)
[3,2] => 10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
[3,1,1] => 100110 => ([(0,3),(0,4),(1,11),(1,16),(2,10),(2,15),(3,2),(3,13),(3,14),(4,1),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,15),(13,16),(14,10),(14,11),(15,6),(15,12),(16,7),(16,12)],17)
[2,2,1] => 11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
[2,1,1,1] => 101110 => ([(0,3),(0,4),(1,2),(1,11),(1,15),(2,7),(2,12),(3,13),(3,14),(4,1),(4,13),(4,14),(6,9),(7,10),(8,6),(9,5),(10,5),(11,7),(12,9),(12,10),(13,8),(13,15),(14,8),(14,11),(15,6),(15,12)],16)
[1,1,1,1,1] => 111110 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[6] => 1000000 => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14)
[5,1] => 1000010 => ([(0,4),(0,5),(1,3),(1,9),(1,17),(2,14),(2,19),(3,2),(3,13),(3,18),(4,15),(4,16),(5,1),(5,15),(5,16),(7,11),(8,7),(9,13),(10,8),(11,6),(12,6),(13,14),(14,12),(15,9),(15,10),(16,10),(16,17),(17,8),(17,18),(18,7),(18,19),(19,11),(19,12)],20)
[4,2] => 100100 => ([(0,2),(0,3),(1,11),(1,12),(2,13),(2,14),(3,1),(3,13),(3,14),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,9),(11,6),(11,9),(12,5),(12,6),(13,10),(13,11),(14,10),(14,12)],15)
[4,1,1] => 1000110 => ([(0,4),(0,5),(1,13),(1,20),(2,3),(2,14),(2,21),(3,8),(3,16),(4,1),(4,17),(4,18),(5,2),(5,17),(5,18),(7,9),(8,10),(9,11),(10,12),(11,6),(12,6),(13,7),(14,8),(15,9),(15,19),(16,10),(16,19),(17,20),(17,21),(18,13),(18,14),(19,11),(19,12),(20,7),(20,15),(21,15),(21,16)],22)
[3,3] => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[3,2,1] => 101010 => ([(0,1),(0,2),(1,10),(1,11),(2,10),(2,11),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12)
[3,1,1,1] => 1001110 => ([(0,4),(0,5),(1,13),(1,20),(2,3),(2,14),(2,21),(3,8),(3,16),(4,1),(4,17),(4,18),(5,2),(5,17),(5,18),(7,9),(8,10),(9,11),(10,12),(11,6),(12,6),(13,7),(14,8),(15,9),(15,19),(16,10),(16,19),(17,20),(17,21),(18,13),(18,14),(19,11),(19,12),(20,7),(20,15),(21,15),(21,16)],22)
[2,2,2] => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[2,2,1,1] => 110110 => ([(0,2),(0,3),(1,11),(1,12),(2,13),(2,14),(3,1),(3,13),(3,14),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,9),(11,6),(11,9),(12,5),(12,6),(13,10),(13,11),(14,10),(14,12)],15)
[2,1,1,1,1] => 1011110 => ([(0,4),(0,5),(1,3),(1,9),(1,17),(2,14),(2,19),(3,2),(3,13),(3,18),(4,15),(4,16),(5,1),(5,15),(5,16),(7,11),(8,7),(9,13),(10,8),(11,6),(12,6),(13,14),(14,12),(15,9),(15,10),(16,10),(16,17),(17,8),(17,18),(18,7),(18,19),(19,11),(19,12)],20)
[1,1,1,1,1,1] => 1111110 => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14)
[7] => 10000000 => ([(0,2),(0,8),(1,10),(2,9),(3,5),(3,11),(4,3),(4,13),(5,7),(5,12),(6,4),(6,15),(7,1),(7,14),(8,6),(8,9),(9,15),(11,12),(12,14),(13,11),(14,10),(15,13)],16)
[6,1] => 10000010 => ([(0,5),(0,6),(1,4),(1,11),(1,20),(2,16),(2,22),(3,2),(3,17),(3,23),(4,3),(4,15),(4,21),(5,18),(5,19),(6,1),(6,18),(6,19),(8,9),(9,13),(10,8),(11,15),(12,10),(13,7),(14,7),(15,17),(16,14),(17,16),(18,11),(18,12),(19,12),(19,20),(20,10),(20,21),(21,8),(21,23),(22,13),(22,14),(23,9),(23,22)],24)
[5,2] => 1000100 => ([(0,3),(0,4),(1,2),(1,18),(1,19),(2,7),(2,14),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,17),(15,19),(16,17),(16,18),(17,6),(17,13),(18,13),(18,14),(19,6),(19,7)],20)
[5,1,1] => 10000110 => ([(0,5),(0,6),(1,4),(1,16),(1,26),(2,17),(2,25),(3,10),(3,22),(4,3),(4,8),(4,18),(5,1),(5,20),(5,21),(6,2),(6,20),(6,21),(8,10),(9,11),(10,13),(11,12),(12,14),(13,15),(14,7),(15,7),(16,8),(17,9),(18,22),(18,23),(19,11),(19,23),(20,25),(20,26),(21,16),(21,17),(22,13),(22,24),(23,12),(23,24),(24,14),(24,15),(25,9),(25,19),(26,18),(26,19)],27)
[4,3] => 101000 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
[4,2,1] => 1001010 => ([(0,2),(0,3),(1,5),(1,12),(2,18),(2,19),(3,1),(3,18),(3,19),(5,6),(6,7),(7,10),(8,11),(9,8),(10,4),(11,4),(12,6),(12,14),(13,9),(13,15),(14,7),(14,16),(15,8),(15,16),(16,10),(16,11),(17,9),(17,14),(17,15),(18,5),(18,13),(18,17),(19,12),(19,13),(19,17)],20)
[4,1,1,1] => 10001110 => ([(0,5),(0,6),(1,4),(1,17),(1,27),(2,3),(2,16),(2,26),(3,8),(3,19),(4,9),(4,20),(5,2),(5,21),(5,22),(6,1),(6,21),(6,22),(8,10),(9,11),(10,12),(11,13),(12,14),(13,15),(14,7),(15,7),(16,8),(17,9),(18,23),(18,24),(19,10),(19,23),(20,11),(20,24),(21,26),(21,27),(22,16),(22,17),(23,12),(23,25),(24,13),(24,25),(25,14),(25,15),(26,18),(26,19),(27,18),(27,20)],28)
[3,3,1] => 110010 => ([(0,3),(0,4),(1,11),(2,12),(2,13),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,7),(7,9),(8,10),(9,5),(10,5),(11,8),(12,7),(12,14),(13,8),(13,14),(14,9),(14,10),(15,6),(15,12),(16,6),(16,11),(16,13)],17)
[3,2,2] => 101100 => ([(0,3),(0,4),(1,11),(2,12),(2,13),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,7),(7,9),(8,10),(9,5),(10,5),(11,8),(12,7),(12,14),(13,8),(13,14),(14,9),(14,10),(15,6),(15,12),(16,6),(16,11),(16,13)],17)
[3,2,1,1] => 1010110 => ([(0,2),(0,3),(1,5),(1,12),(2,18),(2,19),(3,1),(3,18),(3,19),(5,6),(6,7),(7,10),(8,11),(9,8),(10,4),(11,4),(12,6),(12,14),(13,9),(13,15),(14,7),(14,16),(15,8),(15,16),(16,10),(16,11),(17,9),(17,14),(17,15),(18,5),(18,13),(18,17),(19,12),(19,13),(19,17)],20)
[3,1,1,1,1] => 10011110 => ([(0,5),(0,6),(1,4),(1,16),(1,26),(2,17),(2,25),(3,10),(3,22),(4,3),(4,8),(4,18),(5,1),(5,20),(5,21),(6,2),(6,20),(6,21),(8,10),(9,11),(10,13),(11,12),(12,14),(13,15),(14,7),(15,7),(16,8),(17,9),(18,22),(18,23),(19,11),(19,23),(20,25),(20,26),(21,16),(21,17),(22,13),(22,24),(23,12),(23,24),(24,14),(24,15),(25,9),(25,19),(26,18),(26,19)],27)
[2,2,2,1] => 111010 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
[2,2,1,1,1] => 1101110 => ([(0,3),(0,4),(1,2),(1,18),(1,19),(2,7),(2,14),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,17),(15,19),(16,17),(16,18),(17,6),(17,13),(18,13),(18,14),(19,6),(19,7)],20)
[2,1,1,1,1,1] => 10111110 => ([(0,5),(0,6),(1,4),(1,11),(1,20),(2,16),(2,22),(3,2),(3,17),(3,23),(4,3),(4,15),(4,21),(5,18),(5,19),(6,1),(6,18),(6,19),(8,9),(9,13),(10,8),(11,15),(12,10),(13,7),(14,7),(15,17),(16,14),(17,16),(18,11),(18,12),(19,12),(19,20),(20,10),(20,21),(21,8),(21,23),(22,13),(22,14),(23,9),(23,22)],24)
[1,1,1,1,1,1,1] => 11111110 => ([(0,2),(0,8),(1,10),(2,9),(3,5),(3,11),(4,3),(4,13),(5,7),(5,12),(6,4),(6,15),(7,1),(7,14),(8,6),(8,9),(9,15),(11,12),(12,14),(13,11),(14,10),(15,13)],16)
[8] => 100000000 => ([(0,2),(0,9),(1,11),(2,10),(3,4),(3,13),(4,6),(4,12),(5,3),(5,15),(6,8),(6,14),(7,5),(7,17),(8,1),(8,16),(9,7),(9,10),(10,17),(12,14),(13,12),(14,16),(15,13),(16,11),(17,15)],18)
[7,1] => 100000010 => ([(0,6),(0,7),(1,3),(1,11),(1,21),(2,18),(2,25),(3,4),(3,17),(3,24),(4,5),(4,20),(4,27),(5,2),(5,19),(5,26),(6,22),(6,23),(7,1),(7,22),(7,23),(9,12),(10,9),(11,17),(12,13),(13,14),(14,15),(15,8),(16,8),(17,20),(18,16),(19,18),(20,19),(21,9),(21,24),(22,10),(22,11),(23,10),(23,21),(24,12),(24,27),(25,15),(25,16),(26,14),(26,25),(27,13),(27,26)],28)
[6,2] => 10000100 => ([(0,4),(0,5),(1,3),(1,18),(1,22),(2,14),(2,24),(3,2),(3,13),(3,23),(4,19),(4,20),(5,1),(5,19),(5,20),(7,12),(8,9),(9,10),(10,11),(11,6),(12,6),(13,14),(14,7),(15,9),(15,17),(16,11),(16,12),(17,10),(17,16),(18,15),(18,23),(19,21),(19,22),(20,18),(20,21),(21,8),(21,15),(22,8),(22,13),(23,17),(23,24),(24,7),(24,16)],25)
[6,1,1] => 100000110 => ([(0,6),(0,7),(1,15),(1,25),(2,4),(2,14),(2,24),(3,19),(3,30),(4,5),(4,18),(4,31),(5,3),(5,20),(5,29),(6,2),(6,21),(6,22),(7,1),(7,21),(7,22),(9,17),(10,12),(11,13),(12,11),(13,16),(14,18),(15,10),(16,8),(17,8),(18,20),(19,9),(20,19),(21,14),(21,15),(22,24),(22,25),(23,16),(23,17),(24,28),(24,31),(25,10),(25,28),(26,11),(26,27),(27,13),(27,23),(28,12),(28,26),(29,27),(29,30),(30,9),(30,23),(31,26),(31,29)],32)
[5,3] => 1001000 => ([(0,3),(0,4),(1,11),(2,1),(2,15),(2,19),(3,17),(3,18),(4,2),(4,17),(4,18),(6,10),(7,8),(8,9),(9,5),(10,5),(11,6),(12,8),(12,13),(13,9),(13,10),(14,12),(14,16),(15,7),(15,12),(16,6),(16,13),(17,14),(17,15),(18,14),(18,19),(19,7),(19,11),(19,16)],20)
[5,2,1] => 10001010 => ([(0,3),(0,4),(1,2),(1,14),(1,22),(2,6),(2,15),(3,23),(3,24),(4,1),(4,23),(4,24),(6,8),(7,9),(8,10),(9,13),(10,12),(11,7),(12,5),(13,5),(14,6),(15,8),(15,19),(16,19),(16,20),(17,11),(17,18),(18,7),(18,20),(19,10),(19,21),(20,9),(20,21),(21,12),(21,13),(22,15),(22,16),(23,17),(23,22),(23,25),(24,14),(24,17),(24,25),(25,11),(25,16),(25,18)],26)
[5,1,1,1] => 100001110 => ([(0,6),(0,7),(1,4),(1,11),(1,28),(2,5),(2,12),(2,27),(3,18),(3,33),(4,20),(4,32),(5,3),(5,19),(5,31),(6,1),(6,29),(6,30),(7,2),(7,29),(7,30),(9,13),(10,14),(11,20),(12,19),(13,15),(14,16),(15,17),(16,8),(17,8),(18,10),(19,18),(20,9),(21,22),(21,25),(22,23),(22,26),(23,15),(23,24),(24,16),(24,17),(25,13),(25,23),(26,14),(26,24),(27,21),(27,31),(28,21),(28,32),(29,27),(29,28),(30,11),(30,12),(31,22),(31,33),(32,9),(32,25),(33,10),(33,26)],34)
[4,4] => 110000 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[4,3,1] => 1010010 => ([(0,2),(0,3),(1,12),(1,13),(2,18),(2,19),(3,1),(3,18),(3,19),(5,8),(6,5),(7,10),(8,11),(9,7),(10,4),(11,4),(12,9),(12,15),(13,14),(13,15),(14,8),(14,16),(15,7),(15,16),(16,10),(16,11),(17,5),(17,9),(17,14),(18,6),(18,12),(18,17),(19,6),(19,13),(19,17)],20)
[4,2,2] => 1001100 => ([(0,3),(0,4),(1,18),(1,20),(2,17),(2,19),(3,1),(3,15),(3,16),(4,2),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,19),(15,20),(16,17),(16,18),(17,13),(17,14),(18,6),(18,13),(19,7),(19,14),(20,6),(20,7)],21)
[4,2,1,1] => 10010110 => ([(0,3),(0,4),(1,15),(1,25),(2,14),(2,24),(3,2),(3,26),(3,27),(4,1),(4,26),(4,27),(6,8),(7,9),(8,10),(9,11),(10,12),(11,13),(12,5),(13,5),(14,6),(15,7),(16,18),(16,23),(17,19),(17,23),(18,8),(18,21),(19,9),(19,22),(20,12),(20,13),(21,10),(21,20),(22,11),(22,20),(23,21),(23,22),(24,6),(24,18),(25,7),(25,19),(26,16),(26,17),(26,24),(26,25),(27,14),(27,15),(27,16),(27,17)],28)
[4,1,1,1,1] => 100011110 => ([(0,6),(0,7),(1,4),(1,11),(1,28),(2,5),(2,12),(2,27),(3,18),(3,33),(4,20),(4,32),(5,3),(5,19),(5,31),(6,1),(6,29),(6,30),(7,2),(7,29),(7,30),(9,13),(10,14),(11,20),(12,19),(13,15),(14,16),(15,17),(16,8),(17,8),(18,10),(19,18),(20,9),(21,22),(21,25),(22,23),(22,26),(23,15),(23,24),(24,16),(24,17),(25,13),(25,23),(26,14),(26,24),(27,21),(27,31),(28,21),(28,32),(29,27),(29,28),(30,11),(30,12),(31,22),(31,33),(32,9),(32,25),(33,10),(33,26)],34)
[3,3,2] => 110100 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17)
[3,3,1,1] => 1100110 => ([(0,3),(0,4),(1,18),(1,20),(2,17),(2,19),(3,1),(3,15),(3,16),(4,2),(4,15),(4,16),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,10),(12,11),(13,8),(13,12),(14,9),(14,12),(15,19),(15,20),(16,17),(16,18),(17,13),(17,14),(18,6),(18,13),(19,7),(19,14),(20,6),(20,7)],21)
[3,2,2,1] => 1011010 => ([(0,2),(0,3),(1,12),(1,13),(2,18),(2,19),(3,1),(3,18),(3,19),(5,8),(6,5),(7,10),(8,11),(9,7),(10,4),(11,4),(12,9),(12,15),(13,14),(13,15),(14,8),(14,16),(15,7),(15,16),(16,10),(16,11),(17,5),(17,9),(17,14),(18,6),(18,12),(18,17),(19,6),(19,13),(19,17)],20)
[3,2,1,1,1] => 10101110 => ([(0,3),(0,4),(1,2),(1,14),(1,22),(2,6),(2,15),(3,23),(3,24),(4,1),(4,23),(4,24),(6,8),(7,9),(8,10),(9,13),(10,12),(11,7),(12,5),(13,5),(14,6),(15,8),(15,19),(16,19),(16,20),(17,11),(17,18),(18,7),(18,20),(19,10),(19,21),(20,9),(20,21),(21,12),(21,13),(22,15),(22,16),(23,17),(23,22),(23,25),(24,14),(24,17),(24,25),(25,11),(25,16),(25,18)],26)
[3,1,1,1,1,1] => 100111110 => ([(0,6),(0,7),(1,15),(1,25),(2,4),(2,14),(2,24),(3,19),(3,30),(4,5),(4,18),(4,31),(5,3),(5,20),(5,29),(6,2),(6,21),(6,22),(7,1),(7,21),(7,22),(9,17),(10,12),(11,13),(12,11),(13,16),(14,18),(15,10),(16,8),(17,8),(18,20),(19,9),(20,19),(21,14),(21,15),(22,24),(22,25),(23,16),(23,17),(24,28),(24,31),(25,10),(25,28),(26,11),(26,27),(27,13),(27,23),(28,12),(28,26),(29,27),(29,30),(30,9),(30,23),(31,26),(31,29)],32)
[2,2,2,2] => 111100 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[2,2,2,1,1] => 1110110 => ([(0,3),(0,4),(1,11),(2,1),(2,15),(2,19),(3,17),(3,18),(4,2),(4,17),(4,18),(6,10),(7,8),(8,9),(9,5),(10,5),(11,6),(12,8),(12,13),(13,9),(13,10),(14,12),(14,16),(15,7),(15,12),(16,6),(16,13),(17,14),(17,15),(18,14),(18,19),(19,7),(19,11),(19,16)],20)
[2,2,1,1,1,1] => 11011110 => ([(0,4),(0,5),(1,3),(1,18),(1,22),(2,14),(2,24),(3,2),(3,13),(3,23),(4,19),(4,20),(5,1),(5,19),(5,20),(7,12),(8,9),(9,10),(10,11),(11,6),(12,6),(13,14),(14,7),(15,9),(15,17),(16,11),(16,12),(17,10),(17,16),(18,15),(18,23),(19,21),(19,22),(20,18),(20,21),(21,8),(21,15),(22,8),(22,13),(23,17),(23,24),(24,7),(24,16)],25)
[2,1,1,1,1,1,1] => 101111110 => ([(0,6),(0,7),(1,3),(1,11),(1,21),(2,18),(2,25),(3,4),(3,17),(3,24),(4,5),(4,20),(4,27),(5,2),(5,19),(5,26),(6,22),(6,23),(7,1),(7,22),(7,23),(9,12),(10,9),(11,17),(12,13),(13,14),(14,15),(15,8),(16,8),(17,20),(18,16),(19,18),(20,19),(21,9),(21,24),(22,10),(22,11),(23,10),(23,21),(24,12),(24,27),(25,15),(25,16),(26,14),(26,25),(27,13),(27,26)],28)
[1,1,1,1,1,1,1,1] => 111111110 => ([(0,2),(0,9),(1,11),(2,10),(3,4),(3,13),(4,6),(4,12),(5,3),(5,15),(6,8),(6,14),(7,5),(7,17),(8,1),(8,16),(9,7),(9,10),(10,17),(12,14),(13,12),(14,16),(15,13),(16,11),(17,15)],18)
[9] => 1000000000 => ([(0,2),(0,10),(1,12),(2,11),(3,5),(3,13),(4,3),(4,15),(5,7),(5,14),(6,4),(6,17),(7,9),(7,16),(8,6),(8,19),(9,1),(9,18),(10,8),(10,11),(11,19),(13,14),(14,16),(15,13),(16,18),(17,15),(18,12),(19,17)],20)
[8,1] => 1000000010 => ([(0,7),(0,8),(1,3),(1,12),(1,24),(2,20),(2,28),(3,5),(3,19),(3,27),(4,6),(4,21),(4,29),(5,4),(5,23),(5,31),(6,2),(6,22),(6,30),(7,25),(7,26),(8,1),(8,25),(8,26),(10,15),(11,10),(12,19),(13,14),(14,16),(15,13),(16,17),(17,9),(18,9),(19,23),(20,18),(21,22),(22,20),(23,21),(24,10),(24,27),(25,11),(25,12),(26,11),(26,24),(27,15),(27,31),(28,17),(28,18),(29,14),(29,30),(30,16),(30,28),(31,13),(31,29)],32)
[7,2] => 100000100 => ([(0,5),(0,6),(1,4),(1,21),(1,22),(2,16),(2,28),(3,2),(3,17),(3,29),(4,3),(4,15),(4,27),(5,23),(5,24),(6,1),(6,23),(6,24),(8,13),(9,12),(10,14),(11,10),(12,11),(13,7),(14,7),(15,17),(16,8),(17,16),(18,9),(18,25),(19,10),(19,20),(20,13),(20,14),(21,25),(21,27),(22,9),(22,15),(23,18),(23,22),(24,18),(24,21),(25,12),(25,26),(26,11),(26,19),(27,26),(27,29),(28,8),(28,20),(29,19),(29,28)],30)
[7,1,1] => 1000000110 => ([(0,7),(0,8),(1,17),(1,28),(2,4),(2,16),(2,27),(3,21),(3,35),(4,6),(4,20),(4,36),(5,3),(5,22),(5,34),(6,5),(6,23),(6,33),(7,2),(7,24),(7,25),(8,1),(8,24),(8,25),(10,19),(11,13),(12,14),(13,15),(14,11),(15,18),(16,20),(17,12),(18,9),(19,9),(20,23),(21,10),(22,21),(23,22),(24,16),(24,17),(25,27),(25,28),(26,18),(26,19),(27,32),(27,36),(28,12),(28,32),(29,11),(29,30),(30,13),(30,31),(31,15),(31,26),(32,14),(32,29),(33,30),(33,34),(34,31),(34,35),(35,10),(35,26),(36,29),(36,33)],37)
[6,3] => 10001000 => ([(0,3),(0,4),(1,2),(1,22),(1,23),(2,20),(2,21),(3,17),(3,18),(4,1),(4,17),(4,18),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,16),(12,19),(13,8),(13,15),(14,9),(14,15),(15,10),(15,11),(16,13),(16,14),(17,12),(17,22),(18,12),(18,23),(19,7),(19,14),(20,6),(20,13),(21,6),(21,7),(22,16),(22,20),(23,19),(23,21)],24)
[6,2,1] => 100001010 => ([(0,4),(0,5),(1,3),(1,8),(1,18),(2,17),(2,28),(3,2),(3,16),(3,27),(4,29),(4,30),(5,1),(5,29),(5,30),(7,13),(8,16),(9,11),(10,9),(11,12),(12,15),(13,14),(14,6),(15,6),(16,17),(17,7),(18,22),(18,27),(19,10),(19,21),(20,13),(20,26),(21,9),(21,24),(22,23),(22,24),(23,20),(23,25),(24,11),(24,25),(25,12),(25,26),(26,14),(26,15),(27,23),(27,28),(28,7),(28,20),(29,8),(29,19),(29,31),(30,18),(30,19),(30,31),(31,10),(31,21),(31,22)],32)
[6,1,1,1] => 1000001110 => ([(0,7),(0,8),(1,6),(1,13),(1,33),(2,4),(2,12),(2,32),(3,21),(3,38),(4,23),(4,39),(5,3),(5,20),(5,37),(6,5),(6,22),(6,36),(7,1),(7,34),(7,35),(8,2),(8,34),(8,35),(10,16),(11,14),(12,23),(13,22),(14,15),(15,17),(16,18),(17,19),(18,9),(19,9),(20,21),(21,10),(22,20),(23,11),(24,15),(24,25),(25,17),(25,29),(26,28),(26,30),(27,16),(27,29),(28,14),(28,24),(29,18),(29,19),(30,24),(30,31),(31,25),(31,27),(32,26),(32,39),(33,26),(33,36),(34,32),(34,33),(35,12),(35,13),(36,30),(36,37),(37,31),(37,38),(38,10),(38,27),(39,11),(39,28)],40)
[5,4] => 1010000 => ([(0,4),(0,5),(1,3),(1,14),(2,12),(3,2),(3,18),(4,17),(4,19),(5,1),(5,17),(5,19),(7,8),(8,9),(9,10),(10,6),(11,6),(12,11),(13,8),(13,16),(14,16),(14,18),(15,10),(15,11),(16,9),(16,15),(17,7),(17,13),(18,12),(18,15),(19,7),(19,13),(19,14)],20)
[5,3,1] => 10010010 => ([(0,2),(0,3),(1,14),(1,15),(2,19),(2,20),(3,1),(3,19),(3,20),(5,7),(6,8),(7,4),(8,4),(9,16),(9,18),(10,17),(10,18),(11,16),(11,17),(12,7),(12,8),(13,9),(13,11),(14,9),(14,10),(15,10),(15,11),(16,5),(16,12),(17,6),(17,12),(18,5),(18,6),(19,13),(19,14),(20,13),(20,15)],21)
[5,2,2] => 10001100 => ([(0,4),(0,5),(1,23),(1,25),(2,3),(2,24),(2,26),(3,8),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,10),(12,9),(13,6),(14,6),(15,13),(15,14),(16,12),(16,21),(17,21),(17,22),(18,11),(18,22),(19,23),(19,24),(20,25),(20,26),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,17),(24,18),(25,7),(25,16),(26,7),(26,8)],27)
[5,2,1,1] => 100010110 => ([(0,4),(0,5),(1,18),(1,32),(2,3),(2,17),(2,31),(3,8),(3,30),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,14),(8,11),(9,15),(10,16),(11,12),(12,9),(13,10),(14,13),(15,6),(16,6),(17,8),(18,7),(19,21),(19,22),(20,19),(20,27),(21,10),(21,23),(22,9),(22,23),(23,15),(23,16),(24,19),(24,28),(25,20),(25,29),(26,20),(26,24),(27,13),(27,21),(28,12),(28,22),(29,14),(29,27),(30,11),(30,28),(31,24),(31,30),(32,7),(32,29),(33,25),(33,26),(33,31),(33,32),(34,17),(34,18),(34,25),(34,26)],35)
[5,1,1,1,1] => 1000011110 => ([(0,7),(0,8),(1,6),(1,13),(1,34),(2,5),(2,12),(2,33),(3,20),(3,39),(4,21),(4,40),(5,3),(5,22),(5,37),(6,4),(6,23),(6,38),(7,2),(7,35),(7,36),(8,1),(8,35),(8,36),(10,14),(11,15),(12,22),(13,23),(14,16),(15,17),(16,18),(17,19),(18,9),(19,9),(20,10),(21,11),(22,20),(23,21),(24,16),(24,30),(25,17),(25,30),(26,24),(26,25),(27,31),(27,32),(28,14),(28,24),(29,15),(29,25),(30,18),(30,19),(31,26),(31,28),(32,26),(32,29),(33,27),(33,37),(34,27),(34,38),(35,33),(35,34),(36,12),(36,13),(37,31),(37,39),(38,32),(38,40),(39,10),(39,28),(40,11),(40,29)],41)
[4,4,1] => 1100010 => ([(0,4),(0,5),(1,14),(2,3),(2,19),(2,20),(3,15),(3,16),(4,1),(4,17),(4,21),(5,2),(5,17),(5,21),(7,10),(8,9),(9,12),(10,13),(11,7),(12,6),(13,6),(14,8),(15,10),(15,18),(16,9),(16,18),(17,11),(17,20),(18,12),(18,13),(19,8),(19,16),(20,7),(20,15),(21,11),(21,14),(21,19)],22)
[4,3,2] => 1010100 => ([(0,2),(0,3),(1,10),(2,14),(2,17),(3,1),(3,14),(3,17),(5,8),(6,5),(7,9),(8,4),(9,4),(10,6),(11,13),(11,16),(12,8),(12,9),(13,7),(13,12),(14,11),(14,15),(15,6),(15,13),(15,16),(16,5),(16,7),(16,12),(17,10),(17,11),(17,15)],18)
[4,3,1,1] => 10100110 => ([(0,3),(0,4),(1,23),(1,25),(2,15),(2,24),(3,1),(3,26),(3,27),(4,2),(4,26),(4,27),(6,10),(7,8),(8,9),(9,11),(10,12),(11,14),(12,13),(13,5),(14,5),(15,6),(16,20),(16,21),(17,10),(17,20),(18,8),(18,19),(19,9),(19,21),(20,12),(20,22),(21,11),(21,22),(22,13),(22,14),(23,16),(23,19),(24,6),(24,17),(25,16),(25,17),(26,7),(26,18),(26,24),(26,25),(27,7),(27,15),(27,18),(27,23)],28)
[4,2,2,1] => 10011010 => ([(0,3),(0,4),(1,23),(1,25),(2,15),(2,24),(3,1),(3,26),(3,27),(4,2),(4,26),(4,27),(6,10),(7,8),(8,9),(9,11),(10,12),(11,14),(12,13),(13,5),(14,5),(15,6),(16,20),(16,21),(17,10),(17,20),(18,8),(18,19),(19,9),(19,21),(20,12),(20,22),(21,11),(21,22),(22,13),(22,14),(23,16),(23,19),(24,6),(24,17),(25,16),(25,17),(26,7),(26,18),(26,24),(26,25),(27,7),(27,15),(27,18),(27,23)],28)
[4,2,1,1,1] => 100101110 => ([(0,4),(0,5),(1,18),(1,32),(2,3),(2,17),(2,31),(3,8),(3,30),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,14),(8,11),(9,15),(10,16),(11,12),(12,9),(13,10),(14,13),(15,6),(16,6),(17,8),(18,7),(19,21),(19,22),(20,19),(20,27),(21,10),(21,23),(22,9),(22,23),(23,15),(23,16),(24,19),(24,28),(25,20),(25,29),(26,20),(26,24),(27,13),(27,21),(28,12),(28,22),(29,14),(29,27),(30,11),(30,28),(31,24),(31,30),(32,7),(32,29),(33,25),(33,26),(33,31),(33,32),(34,17),(34,18),(34,25),(34,26)],35)
[4,1,1,1,1,1] => 1000111110 => ([(0,7),(0,8),(1,6),(1,13),(1,33),(2,4),(2,12),(2,32),(3,21),(3,38),(4,23),(4,39),(5,3),(5,20),(5,37),(6,5),(6,22),(6,36),(7,1),(7,34),(7,35),(8,2),(8,34),(8,35),(10,16),(11,14),(12,23),(13,22),(14,15),(15,17),(16,18),(17,19),(18,9),(19,9),(20,21),(21,10),(22,20),(23,11),(24,15),(24,25),(25,17),(25,29),(26,28),(26,30),(27,16),(27,29),(28,14),(28,24),(29,18),(29,19),(30,24),(30,31),(31,25),(31,27),(32,26),(32,39),(33,26),(33,36),(34,32),(34,33),(35,12),(35,13),(36,30),(36,37),(37,31),(37,38),(38,10),(38,27),(39,11),(39,28)],40)
[3,3,3] => 111000 => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
[3,3,2,1] => 1101010 => ([(0,2),(0,3),(1,10),(2,14),(2,17),(3,1),(3,14),(3,17),(5,8),(6,5),(7,9),(8,4),(9,4),(10,6),(11,13),(11,16),(12,8),(12,9),(13,7),(13,12),(14,11),(14,15),(15,6),(15,13),(15,16),(16,5),(16,7),(16,12),(17,10),(17,11),(17,15)],18)
[3,3,1,1,1] => 11001110 => ([(0,4),(0,5),(1,23),(1,25),(2,3),(2,24),(2,26),(3,8),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,10),(12,9),(13,6),(14,6),(15,13),(15,14),(16,12),(16,21),(17,21),(17,22),(18,11),(18,22),(19,23),(19,24),(20,25),(20,26),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,17),(24,18),(25,7),(25,16),(26,7),(26,8)],27)
[3,2,2,2] => 1011100 => ([(0,4),(0,5),(1,14),(2,3),(2,19),(2,20),(3,15),(3,16),(4,1),(4,17),(4,21),(5,2),(5,17),(5,21),(7,10),(8,9),(9,12),(10,13),(11,7),(12,6),(13,6),(14,8),(15,10),(15,18),(16,9),(16,18),(17,11),(17,20),(18,12),(18,13),(19,8),(19,16),(20,7),(20,15),(21,11),(21,14),(21,19)],22)
[3,2,2,1,1] => 10110110 => ([(0,2),(0,3),(1,14),(1,15),(2,19),(2,20),(3,1),(3,19),(3,20),(5,7),(6,8),(7,4),(8,4),(9,16),(9,18),(10,17),(10,18),(11,16),(11,17),(12,7),(12,8),(13,9),(13,11),(14,9),(14,10),(15,10),(15,11),(16,5),(16,12),(17,6),(17,12),(18,5),(18,6),(19,13),(19,14),(20,13),(20,15)],21)
[3,2,1,1,1,1] => 101011110 => ([(0,4),(0,5),(1,3),(1,8),(1,18),(2,17),(2,28),(3,2),(3,16),(3,27),(4,29),(4,30),(5,1),(5,29),(5,30),(7,13),(8,16),(9,11),(10,9),(11,12),(12,15),(13,14),(14,6),(15,6),(16,17),(17,7),(18,22),(18,27),(19,10),(19,21),(20,13),(20,26),(21,9),(21,24),(22,23),(22,24),(23,20),(23,25),(24,11),(24,25),(25,12),(25,26),(26,14),(26,15),(27,23),(27,28),(28,7),(28,20),(29,8),(29,19),(29,31),(30,18),(30,19),(30,31),(31,10),(31,21),(31,22)],32)
[3,1,1,1,1,1,1] => 1001111110 => ([(0,7),(0,8),(1,17),(1,28),(2,4),(2,16),(2,27),(3,21),(3,35),(4,6),(4,20),(4,36),(5,3),(5,22),(5,34),(6,5),(6,23),(6,33),(7,2),(7,24),(7,25),(8,1),(8,24),(8,25),(10,19),(11,13),(12,14),(13,15),(14,11),(15,18),(16,20),(17,12),(18,9),(19,9),(20,23),(21,10),(22,21),(23,22),(24,16),(24,17),(25,27),(25,28),(26,18),(26,19),(27,32),(27,36),(28,12),(28,32),(29,11),(29,30),(30,13),(30,31),(31,15),(31,26),(32,14),(32,29),(33,30),(33,34),(34,31),(34,35),(35,10),(35,26),(36,29),(36,33)],37)
[2,2,2,2,1] => 1111010 => ([(0,4),(0,5),(1,3),(1,14),(2,12),(3,2),(3,18),(4,17),(4,19),(5,1),(5,17),(5,19),(7,8),(8,9),(9,10),(10,6),(11,6),(12,11),(13,8),(13,16),(14,16),(14,18),(15,10),(15,11),(16,9),(16,15),(17,7),(17,13),(18,12),(18,15),(19,7),(19,13),(19,14)],20)
[2,2,2,1,1,1] => 11101110 => ([(0,3),(0,4),(1,2),(1,22),(1,23),(2,20),(2,21),(3,17),(3,18),(4,1),(4,17),(4,18),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,16),(12,19),(13,8),(13,15),(14,9),(14,15),(15,10),(15,11),(16,13),(16,14),(17,12),(17,22),(18,12),(18,23),(19,7),(19,14),(20,6),(20,13),(21,6),(21,7),(22,16),(22,20),(23,19),(23,21)],24)
[2,2,1,1,1,1,1] => 110111110 => ([(0,5),(0,6),(1,4),(1,21),(1,22),(2,16),(2,28),(3,2),(3,17),(3,29),(4,3),(4,15),(4,27),(5,23),(5,24),(6,1),(6,23),(6,24),(8,13),(9,12),(10,14),(11,10),(12,11),(13,7),(14,7),(15,17),(16,8),(17,16),(18,9),(18,25),(19,10),(19,20),(20,13),(20,14),(21,25),(21,27),(22,9),(22,15),(23,18),(23,22),(24,18),(24,21),(25,12),(25,26),(26,11),(26,19),(27,26),(27,29),(28,8),(28,20),(29,19),(29,28)],30)
[2,1,1,1,1,1,1,1] => 1011111110 => ([(0,7),(0,8),(1,3),(1,12),(1,24),(2,20),(2,28),(3,5),(3,19),(3,27),(4,6),(4,21),(4,29),(5,4),(5,23),(5,31),(6,2),(6,22),(6,30),(7,25),(7,26),(8,1),(8,25),(8,26),(10,15),(11,10),(12,19),(13,14),(14,16),(15,13),(16,17),(17,9),(18,9),(19,23),(20,18),(21,22),(22,20),(23,21),(24,10),(24,27),(25,11),(25,12),(26,11),(26,24),(27,15),(27,31),(28,17),(28,18),(29,14),(29,30),(30,16),(30,28),(31,13),(31,29)],32)
[1,1,1,1,1,1,1,1,1] => 1111111110 => ([(0,2),(0,10),(1,12),(2,11),(3,5),(3,13),(4,3),(4,15),(5,7),(5,14),(6,4),(6,17),(7,9),(7,16),(8,6),(8,19),(9,1),(9,18),(10,8),(10,11),(11,19),(13,14),(14,16),(15,13),(16,18),(17,15),(18,12),(19,17)],20)
[10] => 10000000000 => ([(0,2),(0,11),(1,13),(2,12),(3,4),(3,15),(4,6),(4,14),(5,3),(5,17),(6,8),(6,16),(7,5),(7,19),(8,10),(8,18),(9,7),(9,21),(10,1),(10,20),(11,9),(11,12),(12,21),(14,16),(15,14),(16,18),(17,15),(18,20),(19,17),(20,13),(21,19)],22)
[9,1] => 10000000010 => ([(0,8),(0,9),(1,3),(1,13),(1,27),(2,22),(2,31),(3,6),(3,21),(3,30),(4,5),(4,24),(4,33),(5,7),(5,23),(5,32),(6,4),(6,26),(6,35),(7,2),(7,25),(7,34),(8,28),(8,29),(9,1),(9,28),(9,29),(11,17),(12,11),(13,21),(14,16),(15,14),(16,18),(17,15),(18,19),(19,10),(20,10),(21,26),(22,20),(23,25),(24,23),(25,22),(26,24),(27,11),(27,30),(28,12),(28,13),(29,12),(29,27),(30,17),(30,35),(31,19),(31,20),(32,16),(32,34),(33,14),(33,32),(34,18),(34,31),(35,15),(35,33)],36)
[8,2] => 1000000100 => ([(0,6),(0,7),(1,5),(1,24),(1,25),(2,18),(2,32),(3,4),(3,20),(3,34),(4,2),(4,19),(4,33),(5,3),(5,17),(5,31),(6,26),(6,27),(7,1),(7,26),(7,27),(9,15),(10,14),(11,16),(12,13),(13,11),(14,12),(15,8),(16,8),(17,20),(18,9),(19,18),(20,19),(21,10),(21,28),(22,11),(22,23),(23,15),(23,16),(24,28),(24,31),(25,10),(25,17),(26,21),(26,25),(27,21),(27,24),(28,14),(28,29),(29,12),(29,30),(30,13),(30,22),(31,29),(31,34),(32,9),(32,23),(33,22),(33,32),(34,30),(34,33)],35)
[8,1,1] => 10000000110 => ([(0,8),(0,9),(1,19),(1,31),(2,4),(2,18),(2,30),(3,23),(3,37),(4,5),(4,22),(4,41),(5,6),(5,26),(5,38),(6,7),(6,24),(6,40),(7,3),(7,25),(7,39),(8,2),(8,27),(8,28),(9,1),(9,27),(9,28),(11,21),(12,13),(13,17),(14,12),(15,16),(16,14),(17,20),(18,22),(19,15),(20,10),(21,10),(22,26),(23,11),(24,25),(25,23),(26,24),(27,18),(27,19),(28,30),(28,31),(29,20),(29,21),(30,36),(30,41),(31,15),(31,36),(32,14),(32,34),(33,13),(33,35),(34,12),(34,33),(35,17),(35,29),(36,16),(36,32),(37,11),(37,29),(38,34),(38,40),(39,35),(39,37),(40,33),(40,39),(41,32),(41,38)],42)
[7,3] => 100001000 => ([(0,4),(0,5),(1,3),(1,21),(1,22),(2,14),(2,28),(3,2),(3,27),(3,29),(4,23),(4,24),(5,1),(5,23),(5,24),(7,11),(8,9),(9,12),(10,13),(11,10),(12,6),(13,6),(14,8),(15,17),(15,20),(16,15),(16,18),(17,11),(17,25),(18,7),(18,17),(19,12),(19,13),(20,25),(20,26),(21,18),(21,29),(22,15),(22,27),(23,16),(23,22),(24,16),(24,21),(25,10),(25,19),(26,9),(26,19),(27,20),(27,28),(28,8),(28,26),(29,7),(29,14)],30)
>>> Load all 311 entries. <<<
[7,2,1] => 1000001010 => ([(0,5),(0,6),(1,4),(1,8),(1,27),(2,19),(2,33),(3,2),(3,20),(3,34),(4,3),(4,18),(4,32),(5,35),(5,36),(6,1),(6,35),(6,36),(8,18),(9,12),(10,13),(11,17),(12,16),(13,14),(14,15),(15,11),(16,7),(17,7),(18,20),(19,9),(20,19),(21,11),(21,22),(22,16),(22,17),(23,12),(23,22),(24,21),(24,23),(25,24),(25,30),(26,25),(26,29),(27,26),(27,32),(28,10),(28,31),(29,14),(29,30),(30,15),(30,21),(31,13),(31,29),(32,25),(32,34),(33,9),(33,23),(34,24),(34,33),(35,27),(35,28),(35,37),(36,8),(36,28),(36,37),(37,10),(37,26),(37,31)],38)
[7,1,1,1] => 10000001110 => ([(0,8),(0,9),(1,7),(1,11),(1,34),(2,4),(2,12),(2,35),(3,24),(3,43),(4,22),(4,41),(5,6),(5,26),(5,45),(6,3),(6,25),(6,44),(7,5),(7,23),(7,42),(8,1),(8,36),(8,37),(9,2),(9,36),(9,37),(11,23),(12,22),(13,16),(14,19),(15,21),(16,20),(17,18),(18,15),(19,17),(20,10),(21,10),(22,14),(23,26),(24,13),(25,24),(26,25),(27,33),(27,40),(28,15),(28,29),(29,20),(29,21),(30,31),(30,39),(31,28),(31,32),(32,16),(32,29),(33,30),(33,38),(34,27),(34,42),(35,27),(35,41),(36,34),(36,35),(37,11),(37,12),(38,17),(38,39),(39,18),(39,28),(40,19),(40,38),(41,14),(41,40),(42,33),(42,45),(43,13),(43,32),(44,31),(44,43),(45,30),(45,44)],46)
[6,4] => 10010000 => ([(0,4),(0,5),(1,2),(1,21),(2,7),(3,1),(3,17),(3,24),(4,22),(4,23),(5,3),(5,22),(5,23),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,11),(14,19),(15,12),(15,13),(16,14),(16,18),(17,8),(17,14),(18,19),(18,20),(19,9),(19,15),(20,10),(20,15),(21,7),(21,20),(22,16),(22,17),(23,16),(23,24),(24,8),(24,18),(24,21)],25)
[6,3,1] => 100010010 => ([(0,3),(0,4),(1,2),(1,28),(1,29),(2,7),(2,26),(3,20),(3,21),(4,1),(4,20),(4,21),(6,12),(7,10),(8,13),(9,14),(10,11),(11,8),(12,9),(13,5),(14,5),(15,8),(15,17),(16,9),(16,17),(17,13),(17,14),(18,22),(18,27),(19,15),(19,16),(20,18),(20,28),(21,18),(21,29),(22,19),(22,24),(23,6),(23,24),(24,12),(24,16),(25,11),(25,15),(26,10),(26,25),(27,6),(27,19),(27,25),(28,7),(28,22),(28,23),(29,23),(29,26),(29,27)],30)
[6,2,2] => 100001100 => ([(0,5),(0,6),(1,29),(1,31),(2,3),(2,30),(2,32),(3,4),(3,9),(3,23),(4,14),(4,27),(5,1),(5,24),(5,25),(6,2),(6,24),(6,25),(8,15),(9,14),(10,16),(11,17),(12,10),(13,11),(14,12),(15,13),(16,7),(17,7),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,16),(21,17),(22,18),(22,26),(23,18),(23,27),(24,29),(24,30),(25,31),(25,32),(26,13),(26,20),(27,12),(27,19),(28,15),(28,26),(29,22),(29,28),(30,22),(30,23),(31,8),(31,28),(32,8),(32,9)],33)
[6,2,1,1] => 1000010110 => ([(0,5),(0,6),(1,21),(1,39),(2,3),(2,20),(2,38),(3,4),(3,9),(3,30),(4,16),(4,36),(5,1),(5,40),(5,41),(6,2),(6,40),(6,41),(8,17),(9,16),(10,18),(11,19),(12,14),(13,15),(14,10),(15,11),(16,12),(17,13),(18,7),(19,7),(20,9),(21,8),(22,26),(22,27),(23,22),(23,35),(24,22),(24,33),(25,23),(25,34),(26,10),(26,28),(27,11),(27,28),(28,18),(28,19),(29,23),(29,24),(30,24),(30,36),(31,25),(31,37),(32,25),(32,29),(33,14),(33,26),(34,13),(34,35),(35,15),(35,27),(36,12),(36,33),(37,17),(37,34),(38,29),(38,30),(39,8),(39,37),(40,31),(40,32),(40,38),(40,39),(41,20),(41,21),(41,31),(41,32)],42)
[6,1,1,1,1] => 10000011110 => ([(0,8),(0,9),(1,6),(1,12),(1,37),(2,7),(2,11),(2,36),(3,25),(3,45),(4,24),(4,46),(5,4),(5,26),(5,47),(6,5),(6,23),(6,43),(7,3),(7,22),(7,44),(8,1),(8,38),(8,39),(9,2),(9,38),(9,39),(11,22),(12,23),(13,18),(14,19),(15,20),(16,21),(17,16),(18,17),(19,15),(20,10),(21,10),(22,25),(23,26),(24,14),(25,13),(26,24),(27,30),(27,31),(28,27),(28,40),(29,33),(29,34),(30,16),(30,32),(31,15),(31,32),(32,20),(32,21),(33,28),(33,35),(34,28),(34,42),(35,27),(35,41),(36,29),(36,44),(37,29),(37,43),(38,36),(38,37),(39,11),(39,12),(40,17),(40,30),(41,19),(41,31),(42,18),(42,40),(43,33),(43,47),(44,34),(44,45),(45,13),(45,42),(46,14),(46,41),(47,35),(47,46)],48)
[5,5] => 1100000 => ([(0,6),(0,7),(1,11),(2,5),(2,15),(3,13),(4,3),(4,17),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(9,12),(10,9),(11,10),(12,8),(13,8),(14,11),(14,15),(15,10),(15,16),(16,9),(16,17),(17,12),(17,13)],18)
[5,4,1] => 10100010 => ([(0,3),(0,4),(1,2),(1,21),(1,22),(2,16),(2,17),(3,23),(3,24),(4,1),(4,23),(4,24),(6,10),(7,9),(8,6),(9,11),(10,12),(11,13),(12,14),(13,5),(14,5),(15,10),(15,19),(16,18),(16,19),(17,9),(17,18),(18,11),(18,20),(19,12),(19,20),(20,13),(20,14),(21,7),(21,17),(22,15),(22,16),(23,8),(23,22),(23,25),(24,8),(24,21),(24,25),(25,6),(25,7),(25,15)],26)
[5,3,2] => 10010100 => ([(0,2),(0,3),(1,17),(1,18),(2,22),(2,23),(3,1),(3,22),(3,23),(5,10),(6,9),(7,11),(8,12),(9,8),(10,7),(11,4),(12,4),(13,11),(13,12),(14,10),(14,20),(15,20),(15,21),(16,9),(16,21),(17,5),(17,14),(18,5),(18,6),(19,15),(19,16),(20,7),(20,13),(21,8),(21,13),(22,17),(22,19),(22,24),(23,18),(23,19),(23,24),(24,6),(24,14),(24,15),(24,16)],25)
[5,3,1,1] => 100100110 => ([(0,3),(0,4),(1,27),(1,31),(2,15),(2,26),(3,1),(3,29),(3,30),(4,2),(4,29),(4,30),(6,12),(7,11),(8,13),(9,14),(10,8),(11,9),(12,10),(13,5),(14,5),(15,6),(16,21),(16,23),(17,8),(17,19),(18,9),(18,19),(19,13),(19,14),(20,7),(20,23),(21,17),(21,18),(22,16),(22,20),(23,11),(23,18),(24,12),(24,25),(25,10),(25,17),(26,6),(26,24),(27,16),(27,28),(28,7),(28,21),(28,25),(29,22),(29,26),(29,31),(30,15),(30,22),(30,27),(31,20),(31,24),(31,28)],32)
[5,2,2,1] => 100011010 => ([(0,4),(0,5),(1,30),(1,31),(2,3),(2,18),(2,32),(3,7),(3,28),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,15),(8,12),(9,16),(10,17),(11,13),(12,11),(13,10),(14,9),(15,14),(16,6),(17,6),(18,7),(19,20),(19,21),(20,10),(20,22),(21,9),(21,22),(22,16),(22,17),(23,19),(23,25),(24,19),(24,26),(25,13),(25,20),(26,14),(26,21),(27,11),(27,25),(28,15),(28,26),(29,12),(29,27),(30,23),(30,24),(31,23),(31,27),(32,24),(32,28),(33,8),(33,29),(33,30),(33,32),(34,8),(34,18),(34,29),(34,31)],35)
[5,2,1,1,1] => 1000101110 => ([(0,5),(0,6),(1,4),(1,21),(1,40),(2,3),(2,20),(2,39),(3,8),(3,37),(4,9),(4,38),(5,2),(5,41),(5,42),(6,1),(6,41),(6,42),(8,16),(9,17),(10,18),(11,19),(12,14),(13,15),(14,10),(15,11),(16,12),(17,13),(18,7),(19,7),(20,8),(21,9),(22,26),(22,27),(23,22),(23,35),(24,22),(24,36),(25,23),(25,24),(26,10),(26,28),(27,11),(27,28),(28,18),(28,19),(29,23),(29,33),(30,24),(30,34),(31,25),(31,29),(32,25),(32,30),(33,12),(33,35),(34,13),(34,36),(35,14),(35,26),(36,15),(36,27),(37,16),(37,33),(38,17),(38,34),(39,29),(39,37),(40,30),(40,38),(41,31),(41,32),(41,39),(41,40),(42,20),(42,21),(42,31),(42,32)],43)
[5,1,1,1,1,1] => 10000111110 => ([(0,8),(0,9),(1,6),(1,12),(1,37),(2,7),(2,11),(2,36),(3,25),(3,45),(4,24),(4,46),(5,4),(5,26),(5,47),(6,5),(6,23),(6,43),(7,3),(7,22),(7,44),(8,1),(8,38),(8,39),(9,2),(9,38),(9,39),(11,22),(12,23),(13,18),(14,19),(15,20),(16,21),(17,16),(18,17),(19,15),(20,10),(21,10),(22,25),(23,26),(24,14),(25,13),(26,24),(27,30),(27,31),(28,27),(28,40),(29,33),(29,34),(30,16),(30,32),(31,15),(31,32),(32,20),(32,21),(33,28),(33,35),(34,28),(34,42),(35,27),(35,41),(36,29),(36,44),(37,29),(37,43),(38,36),(38,37),(39,11),(39,12),(40,17),(40,30),(41,19),(41,31),(42,18),(42,40),(43,33),(43,47),(44,34),(44,45),(45,13),(45,42),(46,14),(46,41),(47,35),(47,46)],48)
[4,4,2] => 1100100 => ([(0,3),(0,4),(1,12),(2,14),(2,19),(3,2),(3,18),(3,20),(4,1),(4,18),(4,20),(6,8),(7,10),(8,11),(9,7),(10,5),(11,5),(12,6),(13,9),(13,16),(14,15),(14,16),(15,8),(15,17),(16,7),(16,17),(17,10),(17,11),(18,13),(18,14),(19,6),(19,9),(19,15),(20,12),(20,13),(20,19)],21)
[4,4,1,1] => 11000110 => ([(0,4),(0,5),(1,24),(1,26),(2,3),(2,23),(2,25),(3,17),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,9),(12,10),(13,6),(14,6),(15,13),(15,14),(16,12),(16,22),(17,21),(17,22),(18,11),(18,21),(19,25),(19,26),(20,23),(20,24),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,7),(24,16),(25,8),(25,18),(26,7),(26,8)],27)
[4,3,3] => 1011000 => ([(0,4),(0,5),(1,13),(2,1),(2,15),(3,14),(3,16),(4,2),(4,20),(4,21),(5,3),(5,20),(5,21),(7,8),(8,9),(9,11),(10,12),(11,6),(12,6),(13,10),(14,8),(14,18),(15,13),(15,17),(16,17),(16,18),(17,10),(17,19),(18,9),(18,19),(19,11),(19,12),(20,7),(20,14),(21,7),(21,15),(21,16)],22)
[4,3,2,1] => 10101010 => ([(0,1),(0,2),(1,14),(1,15),(2,14),(2,15),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,12),(8,13),(9,12),(9,13),(10,6),(10,7),(11,6),(11,7),(12,4),(12,5),(13,4),(13,5),(14,10),(14,11),(15,10),(15,11)],16)
[4,3,1,1,1] => 101001110 => ([(0,4),(0,5),(1,30),(1,31),(2,3),(2,18),(2,32),(3,7),(3,28),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,15),(8,12),(9,16),(10,17),(11,13),(12,11),(13,10),(14,9),(15,14),(16,6),(17,6),(18,7),(19,20),(19,21),(20,10),(20,22),(21,9),(21,22),(22,16),(22,17),(23,19),(23,25),(24,19),(24,26),(25,13),(25,20),(26,14),(26,21),(27,11),(27,25),(28,15),(28,26),(29,12),(29,27),(30,23),(30,24),(31,23),(31,27),(32,24),(32,28),(33,8),(33,29),(33,30),(33,32),(34,8),(34,18),(34,29),(34,31)],35)
[4,2,2,2] => 10011100 => ([(0,4),(0,5),(1,24),(1,26),(2,3),(2,23),(2,25),(3,17),(3,18),(4,1),(4,19),(4,20),(5,2),(5,19),(5,20),(7,12),(8,11),(9,13),(10,14),(11,9),(12,10),(13,6),(14,6),(15,13),(15,14),(16,12),(16,22),(17,21),(17,22),(18,11),(18,21),(19,25),(19,26),(20,23),(20,24),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,7),(24,16),(25,8),(25,18),(26,7),(26,8)],27)
[4,2,2,1,1] => 100110110 => ([(0,3),(0,4),(1,27),(1,31),(2,15),(2,26),(3,1),(3,29),(3,30),(4,2),(4,29),(4,30),(6,12),(7,11),(8,13),(9,14),(10,8),(11,9),(12,10),(13,5),(14,5),(15,6),(16,21),(16,23),(17,8),(17,19),(18,9),(18,19),(19,13),(19,14),(20,7),(20,23),(21,17),(21,18),(22,16),(22,20),(23,11),(23,18),(24,12),(24,25),(25,10),(25,17),(26,6),(26,24),(27,16),(27,28),(28,7),(28,21),(28,25),(29,22),(29,26),(29,31),(30,15),(30,22),(30,27),(31,20),(31,24),(31,28)],32)
[4,2,1,1,1,1] => 1001011110 => ([(0,5),(0,6),(1,21),(1,39),(2,3),(2,20),(2,38),(3,4),(3,9),(3,30),(4,16),(4,36),(5,1),(5,40),(5,41),(6,2),(6,40),(6,41),(8,17),(9,16),(10,18),(11,19),(12,14),(13,15),(14,10),(15,11),(16,12),(17,13),(18,7),(19,7),(20,9),(21,8),(22,26),(22,27),(23,22),(23,35),(24,22),(24,33),(25,23),(25,34),(26,10),(26,28),(27,11),(27,28),(28,18),(28,19),(29,23),(29,24),(30,24),(30,36),(31,25),(31,37),(32,25),(32,29),(33,14),(33,26),(34,13),(34,35),(35,15),(35,27),(36,12),(36,33),(37,17),(37,34),(38,29),(38,30),(39,8),(39,37),(40,31),(40,32),(40,38),(40,39),(41,20),(41,21),(41,31),(41,32)],42)
[4,1,1,1,1,1,1] => 10001111110 => ([(0,8),(0,9),(1,7),(1,11),(1,34),(2,4),(2,12),(2,35),(3,24),(3,43),(4,22),(4,41),(5,6),(5,26),(5,45),(6,3),(6,25),(6,44),(7,5),(7,23),(7,42),(8,1),(8,36),(8,37),(9,2),(9,36),(9,37),(11,23),(12,22),(13,16),(14,19),(15,21),(16,20),(17,18),(18,15),(19,17),(20,10),(21,10),(22,14),(23,26),(24,13),(25,24),(26,25),(27,33),(27,40),(28,15),(28,29),(29,20),(29,21),(30,31),(30,39),(31,28),(31,32),(32,16),(32,29),(33,30),(33,38),(34,27),(34,42),(35,27),(35,41),(36,34),(36,35),(37,11),(37,12),(38,17),(38,39),(39,18),(39,28),(40,19),(40,38),(41,14),(41,40),(42,33),(42,45),(43,13),(43,32),(44,31),(44,43),(45,30),(45,44)],46)
[3,3,3,1] => 1110010 => ([(0,4),(0,5),(1,13),(2,1),(2,15),(3,14),(3,16),(4,2),(4,20),(4,21),(5,3),(5,20),(5,21),(7,8),(8,9),(9,11),(10,12),(11,6),(12,6),(13,10),(14,8),(14,18),(15,13),(15,17),(16,17),(16,18),(17,10),(17,19),(18,9),(18,19),(19,11),(19,12),(20,7),(20,14),(21,7),(21,15),(21,16)],22)
[3,3,2,2] => 1101100 => ([(0,3),(0,4),(1,12),(2,14),(2,19),(3,2),(3,18),(3,20),(4,1),(4,18),(4,20),(6,8),(7,10),(8,11),(9,7),(10,5),(11,5),(12,6),(13,9),(13,16),(14,15),(14,16),(15,8),(15,17),(16,7),(16,17),(17,10),(17,11),(18,13),(18,14),(19,6),(19,9),(19,15),(20,12),(20,13),(20,19)],21)
[3,3,2,1,1] => 11010110 => ([(0,2),(0,3),(1,17),(1,18),(2,22),(2,23),(3,1),(3,22),(3,23),(5,10),(6,9),(7,11),(8,12),(9,8),(10,7),(11,4),(12,4),(13,11),(13,12),(14,10),(14,20),(15,20),(15,21),(16,9),(16,21),(17,5),(17,14),(18,5),(18,6),(19,15),(19,16),(20,7),(20,13),(21,8),(21,13),(22,17),(22,19),(22,24),(23,18),(23,19),(23,24),(24,6),(24,14),(24,15),(24,16)],25)
[3,3,1,1,1,1] => 110011110 => ([(0,5),(0,6),(1,29),(1,31),(2,3),(2,30),(2,32),(3,4),(3,9),(3,23),(4,14),(4,27),(5,1),(5,24),(5,25),(6,2),(6,24),(6,25),(8,15),(9,14),(10,16),(11,17),(12,10),(13,11),(14,12),(15,13),(16,7),(17,7),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,16),(21,17),(22,18),(22,26),(23,18),(23,27),(24,29),(24,30),(25,31),(25,32),(26,13),(26,20),(27,12),(27,19),(28,15),(28,26),(29,22),(29,28),(30,22),(30,23),(31,8),(31,28),(32,8),(32,9)],33)
[3,2,2,2,1] => 10111010 => ([(0,3),(0,4),(1,2),(1,21),(1,22),(2,16),(2,17),(3,23),(3,24),(4,1),(4,23),(4,24),(6,10),(7,9),(8,6),(9,11),(10,12),(11,13),(12,14),(13,5),(14,5),(15,10),(15,19),(16,18),(16,19),(17,9),(17,18),(18,11),(18,20),(19,12),(19,20),(20,13),(20,14),(21,7),(21,17),(22,15),(22,16),(23,8),(23,22),(23,25),(24,8),(24,21),(24,25),(25,6),(25,7),(25,15)],26)
[3,2,2,1,1,1] => 101101110 => ([(0,3),(0,4),(1,2),(1,28),(1,29),(2,7),(2,26),(3,20),(3,21),(4,1),(4,20),(4,21),(6,12),(7,10),(8,13),(9,14),(10,11),(11,8),(12,9),(13,5),(14,5),(15,8),(15,17),(16,9),(16,17),(17,13),(17,14),(18,22),(18,27),(19,15),(19,16),(20,18),(20,28),(21,18),(21,29),(22,19),(22,24),(23,6),(23,24),(24,12),(24,16),(25,11),(25,15),(26,10),(26,25),(27,6),(27,19),(27,25),(28,7),(28,22),(28,23),(29,23),(29,26),(29,27)],30)
[3,2,1,1,1,1,1] => 1010111110 => ([(0,5),(0,6),(1,4),(1,8),(1,27),(2,19),(2,33),(3,2),(3,20),(3,34),(4,3),(4,18),(4,32),(5,35),(5,36),(6,1),(6,35),(6,36),(8,18),(9,12),(10,13),(11,17),(12,16),(13,14),(14,15),(15,11),(16,7),(17,7),(18,20),(19,9),(20,19),(21,11),(21,22),(22,16),(22,17),(23,12),(23,22),(24,21),(24,23),(25,24),(25,30),(26,25),(26,29),(27,26),(27,32),(28,10),(28,31),(29,14),(29,30),(30,15),(30,21),(31,13),(31,29),(32,25),(32,34),(33,9),(33,23),(34,24),(34,33),(35,27),(35,28),(35,37),(36,8),(36,28),(36,37),(37,10),(37,26),(37,31)],38)
[3,1,1,1,1,1,1,1] => 10011111110 => ([(0,8),(0,9),(1,19),(1,31),(2,4),(2,18),(2,30),(3,23),(3,37),(4,5),(4,22),(4,41),(5,6),(5,26),(5,38),(6,7),(6,24),(6,40),(7,3),(7,25),(7,39),(8,2),(8,27),(8,28),(9,1),(9,27),(9,28),(11,21),(12,13),(13,17),(14,12),(15,16),(16,14),(17,20),(18,22),(19,15),(20,10),(21,10),(22,26),(23,11),(24,25),(25,23),(26,24),(27,18),(27,19),(28,30),(28,31),(29,20),(29,21),(30,36),(30,41),(31,15),(31,36),(32,14),(32,34),(33,13),(33,35),(34,12),(34,33),(35,17),(35,29),(36,16),(36,32),(37,11),(37,29),(38,34),(38,40),(39,35),(39,37),(40,33),(40,39),(41,32),(41,38)],42)
[2,2,2,2,2] => 1111100 => ([(0,6),(0,7),(1,11),(2,5),(2,15),(3,13),(4,3),(4,17),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(9,12),(10,9),(11,10),(12,8),(13,8),(14,11),(14,15),(15,10),(15,16),(16,9),(16,17),(17,12),(17,13)],18)
[2,2,2,2,1,1] => 11110110 => ([(0,4),(0,5),(1,2),(1,21),(2,7),(3,1),(3,17),(3,24),(4,22),(4,23),(5,3),(5,22),(5,23),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,11),(14,19),(15,12),(15,13),(16,14),(16,18),(17,8),(17,14),(18,19),(18,20),(19,9),(19,15),(20,10),(20,15),(21,7),(21,20),(22,16),(22,17),(23,16),(23,24),(24,8),(24,18),(24,21)],25)
[2,2,2,1,1,1,1] => 111011110 => ([(0,4),(0,5),(1,3),(1,21),(1,22),(2,14),(2,28),(3,2),(3,27),(3,29),(4,23),(4,24),(5,1),(5,23),(5,24),(7,11),(8,9),(9,12),(10,13),(11,10),(12,6),(13,6),(14,8),(15,17),(15,20),(16,15),(16,18),(17,11),(17,25),(18,7),(18,17),(19,12),(19,13),(20,25),(20,26),(21,18),(21,29),(22,15),(22,27),(23,16),(23,22),(24,16),(24,21),(25,10),(25,19),(26,9),(26,19),(27,20),(27,28),(28,8),(28,26),(29,7),(29,14)],30)
[2,2,1,1,1,1,1,1] => 1101111110 => ([(0,6),(0,7),(1,5),(1,24),(1,25),(2,18),(2,32),(3,4),(3,20),(3,34),(4,2),(4,19),(4,33),(5,3),(5,17),(5,31),(6,26),(6,27),(7,1),(7,26),(7,27),(9,15),(10,14),(11,16),(12,13),(13,11),(14,12),(15,8),(16,8),(17,20),(18,9),(19,18),(20,19),(21,10),(21,28),(22,11),(22,23),(23,15),(23,16),(24,28),(24,31),(25,10),(25,17),(26,21),(26,25),(27,21),(27,24),(28,14),(28,29),(29,12),(29,30),(30,13),(30,22),(31,29),(31,34),(32,9),(32,23),(33,22),(33,32),(34,30),(34,33)],35)
[2,1,1,1,1,1,1,1,1] => 10111111110 => ([(0,8),(0,9),(1,3),(1,13),(1,27),(2,22),(2,31),(3,6),(3,21),(3,30),(4,5),(4,24),(4,33),(5,7),(5,23),(5,32),(6,4),(6,26),(6,35),(7,2),(7,25),(7,34),(8,28),(8,29),(9,1),(9,28),(9,29),(11,17),(12,11),(13,21),(14,16),(15,14),(16,18),(17,15),(18,19),(19,10),(20,10),(21,26),(22,20),(23,25),(24,23),(25,22),(26,24),(27,11),(27,30),(28,12),(28,13),(29,12),(29,27),(30,17),(30,35),(31,19),(31,20),(32,16),(32,34),(33,14),(33,32),(34,18),(34,31),(35,15),(35,33)],36)
[1,1,1,1,1,1,1,1,1,1] => 11111111110 => ([(0,2),(0,11),(1,13),(2,12),(3,4),(3,15),(4,6),(4,14),(5,3),(5,17),(6,8),(6,16),(7,5),(7,19),(8,10),(8,18),(9,7),(9,21),(10,1),(10,20),(11,9),(11,12),(12,21),(14,16),(15,14),(16,18),(17,15),(18,20),(19,17),(20,13),(21,19)],22)
[7,4] => 100010000 => ([(0,4),(0,5),(1,14),(2,3),(2,27),(2,28),(3,1),(3,21),(3,29),(4,22),(4,23),(5,2),(5,22),(5,23),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,16),(15,20),(16,17),(16,24),(17,25),(17,26),(18,11),(18,25),(19,12),(19,13),(20,17),(20,18),(21,8),(21,18),(22,15),(22,28),(23,15),(23,27),(24,7),(24,26),(25,9),(25,19),(26,10),(26,19),(27,20),(27,21),(28,16),(28,29),(29,8),(29,14),(29,24)],30)
[6,5] => 10100000 => ([(0,5),(0,6),(1,4),(1,17),(2,14),(3,2),(3,22),(4,3),(4,21),(5,20),(5,23),(6,1),(6,20),(6,23),(8,11),(9,13),(10,9),(11,10),(12,7),(13,7),(14,12),(15,12),(15,13),(16,9),(16,15),(17,18),(17,21),(18,10),(18,16),(19,11),(19,18),(20,8),(20,19),(21,16),(21,22),(22,14),(22,15),(23,8),(23,17),(23,19)],24)
[6,4,1] => 100100010 => ([(0,3),(0,4),(1,2),(1,28),(1,29),(2,23),(2,24),(3,20),(3,21),(4,1),(4,20),(4,21),(6,11),(7,12),(8,13),(9,14),(10,8),(11,9),(12,10),(13,5),(14,5),(15,16),(15,17),(16,8),(16,18),(17,9),(17,18),(18,13),(18,14),(19,22),(19,27),(20,19),(20,28),(21,19),(21,29),(22,15),(22,26),(23,15),(23,25),(24,6),(24,25),(25,11),(25,17),(26,10),(26,16),(27,6),(27,12),(27,26),(28,7),(28,22),(28,23),(29,7),(29,24),(29,27)],30)
[6,3,2] => 100010100 => ([(0,3),(0,4),(1,2),(1,27),(1,28),(2,6),(2,25),(3,29),(3,30),(4,1),(4,29),(4,30),(6,13),(7,10),(8,14),(9,15),(10,11),(11,8),(12,9),(13,12),(14,5),(15,5),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,14),(19,15),(20,16),(20,24),(21,16),(21,23),(22,20),(22,26),(23,12),(23,17),(24,11),(24,18),(25,13),(25,23),(26,10),(26,24),(27,21),(27,25),(28,6),(28,7),(29,22),(29,27),(29,31),(30,22),(30,28),(30,31),(31,7),(31,20),(31,21),(31,26)],32)
[5,5,1] => 11000010 => ([(0,5),(0,6),(1,17),(2,4),(2,20),(2,21),(3,23),(3,24),(4,3),(4,22),(4,25),(5,2),(5,19),(5,26),(6,1),(6,19),(6,26),(8,10),(9,11),(10,15),(11,16),(12,9),(13,8),(14,12),(15,7),(16,7),(17,13),(18,15),(18,16),(19,14),(19,21),(20,13),(20,25),(21,12),(21,22),(22,9),(22,23),(23,11),(23,18),(24,10),(24,18),(25,8),(25,24),(26,14),(26,17),(26,20)],27)
[5,4,2] => 10100100 => ([(0,2),(0,3),(1,13),(1,14),(2,22),(2,23),(3,1),(3,22),(3,23),(5,6),(6,7),(7,8),(8,11),(9,12),(10,9),(11,4),(12,4),(13,18),(13,21),(14,15),(14,18),(15,10),(15,19),(16,8),(16,17),(17,11),(17,12),(18,16),(18,19),(19,9),(19,17),(20,6),(20,15),(20,21),(21,7),(21,10),(21,16),(22,5),(22,13),(22,20),(23,5),(23,14),(23,20)],24)
[5,4,1,1] => 101000110 => ([(0,4),(0,5),(1,18),(1,32),(2,3),(2,30),(2,31),(3,23),(3,24),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,15),(8,12),(9,16),(10,17),(11,13),(12,11),(13,10),(14,9),(15,14),(16,6),(17,6),(18,7),(19,20),(19,21),(20,9),(20,22),(21,10),(21,22),(22,16),(22,17),(23,19),(23,25),(24,19),(24,26),(25,14),(25,20),(26,13),(26,21),(27,11),(27,26),(28,15),(28,25),(29,12),(29,27),(30,23),(30,28),(31,24),(31,27),(32,7),(32,28),(33,8),(33,29),(33,30),(33,32),(34,8),(34,18),(34,29),(34,31)],35)
[5,3,3] => 10011000 => ([(0,4),(0,5),(1,14),(2,23),(2,24),(3,1),(3,25),(3,26),(4,2),(4,18),(4,19),(5,3),(5,18),(5,19),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,12),(15,13),(16,21),(16,22),(17,11),(17,21),(18,23),(18,25),(19,24),(19,26),(20,7),(20,22),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,16),(24,20),(25,8),(25,17),(26,8),(26,14),(26,20)],27)
[5,3,2,1] => 100101010 => ([(0,2),(0,3),(1,5),(1,15),(2,26),(2,27),(3,1),(3,26),(3,27),(5,9),(6,7),(7,10),(8,11),(9,6),(10,12),(11,13),(12,4),(13,4),(14,21),(14,24),(15,9),(15,18),(16,10),(16,22),(17,11),(17,22),(18,6),(18,19),(19,7),(19,16),(20,8),(20,17),(21,20),(21,25),(22,12),(22,13),(23,18),(23,21),(23,24),(24,19),(24,20),(24,25),(25,8),(25,16),(25,17),(26,14),(26,15),(26,23),(27,5),(27,14),(27,23)],28)
[5,2,2,2] => 100011100 => ([(0,5),(0,6),(1,4),(1,30),(1,33),(2,3),(2,31),(2,32),(3,23),(3,29),(4,9),(4,28),(5,1),(5,24),(5,25),(6,2),(6,24),(6,25),(8,15),(9,12),(10,16),(11,17),(12,13),(13,10),(14,11),(15,14),(16,7),(17,7),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,16),(21,17),(22,18),(22,26),(23,18),(23,27),(24,30),(24,31),(25,32),(25,33),(26,13),(26,19),(27,14),(27,20),(28,12),(28,26),(29,15),(29,27),(30,22),(30,28),(31,22),(31,23),(32,8),(32,29),(33,8),(33,9)],34)
[4,4,3] => 1101000 => ([(0,4),(0,5),(1,13),(2,3),(2,20),(3,7),(4,1),(4,19),(4,21),(5,2),(5,19),(5,21),(7,9),(8,11),(9,12),(10,8),(11,6),(12,6),(13,10),(14,10),(14,17),(15,16),(15,17),(16,9),(16,18),(17,8),(17,18),(18,11),(18,12),(19,14),(19,15),(20,7),(20,16),(21,13),(21,14),(21,15),(21,20)],22)
[4,4,2,1] => 11001010 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,6),(11,7),(12,5),(13,5),(14,10),(15,11),(15,18),(16,19),(16,23),(17,10),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27)
[4,4,1,1,1] => 110001110 => ([(0,5),(0,6),(1,4),(1,30),(1,33),(2,3),(2,31),(2,32),(3,23),(3,29),(4,9),(4,28),(5,1),(5,24),(5,25),(6,2),(6,24),(6,25),(8,15),(9,12),(10,16),(11,17),(12,13),(13,10),(14,11),(15,14),(16,7),(17,7),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,16),(21,17),(22,18),(22,26),(23,18),(23,27),(24,30),(24,31),(25,32),(25,33),(26,13),(26,19),(27,14),(27,20),(28,12),(28,26),(29,15),(29,27),(30,22),(30,28),(31,22),(31,23),(32,8),(32,29),(33,8),(33,9)],34)
[4,3,3,1] => 10110010 => ([(0,3),(0,4),(1,23),(1,25),(2,22),(2,24),(3,2),(3,26),(3,27),(4,1),(4,26),(4,27),(6,10),(7,11),(8,6),(9,7),(10,12),(11,13),(12,14),(13,15),(14,5),(15,5),(16,19),(16,20),(17,10),(17,19),(18,11),(18,20),(19,12),(19,21),(20,13),(20,21),(21,14),(21,15),(22,6),(22,17),(23,7),(23,18),(24,16),(24,17),(25,16),(25,18),(26,8),(26,9),(26,24),(26,25),(27,8),(27,9),(27,22),(27,23)],28)
[4,3,2,2] => 10101100 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,6),(11,7),(12,5),(13,5),(14,10),(15,11),(15,18),(16,19),(16,23),(17,10),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27)
[4,3,2,1,1] => 101010110 => ([(0,2),(0,3),(1,5),(1,15),(2,26),(2,27),(3,1),(3,26),(3,27),(5,9),(6,7),(7,10),(8,11),(9,6),(10,12),(11,13),(12,4),(13,4),(14,21),(14,24),(15,9),(15,18),(16,10),(16,22),(17,11),(17,22),(18,6),(18,19),(19,7),(19,16),(20,8),(20,17),(21,20),(21,25),(22,12),(22,13),(23,18),(23,21),(23,24),(24,19),(24,20),(24,25),(25,8),(25,16),(25,17),(26,14),(26,15),(26,23),(27,5),(27,14),(27,23)],28)
[4,2,2,2,1] => 100111010 => ([(0,4),(0,5),(1,18),(1,32),(2,3),(2,30),(2,31),(3,23),(3,24),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,15),(8,12),(9,16),(10,17),(11,13),(12,11),(13,10),(14,9),(15,14),(16,6),(17,6),(18,7),(19,20),(19,21),(20,9),(20,22),(21,10),(21,22),(22,16),(22,17),(23,19),(23,25),(24,19),(24,26),(25,14),(25,20),(26,13),(26,21),(27,11),(27,26),(28,15),(28,25),(29,12),(29,27),(30,23),(30,28),(31,24),(31,27),(32,7),(32,28),(33,8),(33,29),(33,30),(33,32),(34,8),(34,18),(34,29),(34,31)],35)
[3,3,3,2] => 1110100 => ([(0,4),(0,5),(1,13),(2,3),(2,20),(3,7),(4,1),(4,19),(4,21),(5,2),(5,19),(5,21),(7,9),(8,11),(9,12),(10,8),(11,6),(12,6),(13,10),(14,10),(14,17),(15,16),(15,17),(16,9),(16,18),(17,8),(17,18),(18,11),(18,12),(19,14),(19,15),(20,7),(20,16),(21,13),(21,14),(21,15),(21,20)],22)
[3,3,3,1,1] => 11100110 => ([(0,4),(0,5),(1,14),(2,23),(2,24),(3,1),(3,25),(3,26),(4,2),(4,18),(4,19),(5,3),(5,18),(5,19),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,12),(15,13),(16,21),(16,22),(17,11),(17,21),(18,23),(18,25),(19,24),(19,26),(20,7),(20,22),(21,9),(21,15),(22,10),(22,15),(23,16),(23,17),(24,16),(24,20),(25,8),(25,17),(26,8),(26,14),(26,20)],27)
[3,3,2,2,1] => 11011010 => ([(0,2),(0,3),(1,13),(1,14),(2,22),(2,23),(3,1),(3,22),(3,23),(5,6),(6,7),(7,8),(8,11),(9,12),(10,9),(11,4),(12,4),(13,18),(13,21),(14,15),(14,18),(15,10),(15,19),(16,8),(16,17),(17,11),(17,12),(18,16),(18,19),(19,9),(19,17),(20,6),(20,15),(20,21),(21,7),(21,10),(21,16),(22,5),(22,13),(22,20),(23,5),(23,14),(23,20)],24)
[3,3,2,1,1,1] => 110101110 => ([(0,3),(0,4),(1,2),(1,27),(1,28),(2,6),(2,25),(3,29),(3,30),(4,1),(4,29),(4,30),(6,13),(7,10),(8,14),(9,15),(10,11),(11,8),(12,9),(13,12),(14,5),(15,5),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,14),(19,15),(20,16),(20,24),(21,16),(21,23),(22,20),(22,26),(23,12),(23,17),(24,11),(24,18),(25,13),(25,23),(26,10),(26,24),(27,21),(27,25),(28,6),(28,7),(29,22),(29,27),(29,31),(30,22),(30,28),(30,31),(31,7),(31,20),(31,21),(31,26)],32)
[3,2,2,2,2] => 10111100 => ([(0,5),(0,6),(1,17),(2,4),(2,20),(2,21),(3,23),(3,24),(4,3),(4,22),(4,25),(5,2),(5,19),(5,26),(6,1),(6,19),(6,26),(8,10),(9,11),(10,15),(11,16),(12,9),(13,8),(14,12),(15,7),(16,7),(17,13),(18,15),(18,16),(19,14),(19,21),(20,13),(20,25),(21,12),(21,22),(22,9),(22,23),(23,11),(23,18),(24,10),(24,18),(25,8),(25,24),(26,14),(26,17),(26,20)],27)
[3,2,2,2,1,1] => 101110110 => ([(0,3),(0,4),(1,2),(1,28),(1,29),(2,23),(2,24),(3,20),(3,21),(4,1),(4,20),(4,21),(6,11),(7,12),(8,13),(9,14),(10,8),(11,9),(12,10),(13,5),(14,5),(15,16),(15,17),(16,8),(16,18),(17,9),(17,18),(18,13),(18,14),(19,22),(19,27),(20,19),(20,28),(21,19),(21,29),(22,15),(22,26),(23,15),(23,25),(24,6),(24,25),(25,11),(25,17),(26,10),(26,16),(27,6),(27,12),(27,26),(28,7),(28,22),(28,23),(29,7),(29,24),(29,27)],30)
[2,2,2,2,2,1] => 11111010 => ([(0,5),(0,6),(1,4),(1,17),(2,14),(3,2),(3,22),(4,3),(4,21),(5,20),(5,23),(6,1),(6,20),(6,23),(8,11),(9,13),(10,9),(11,10),(12,7),(13,7),(14,12),(15,12),(15,13),(16,9),(16,15),(17,18),(17,21),(18,10),(18,16),(19,11),(19,18),(20,8),(20,19),(21,16),(21,22),(22,14),(22,15),(23,8),(23,17),(23,19)],24)
[2,2,2,2,1,1,1] => 111101110 => ([(0,4),(0,5),(1,14),(2,3),(2,27),(2,28),(3,1),(3,21),(3,29),(4,22),(4,23),(5,2),(5,22),(5,23),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,16),(15,20),(16,17),(16,24),(17,25),(17,26),(18,11),(18,25),(19,12),(19,13),(20,17),(20,18),(21,8),(21,18),(22,15),(22,28),(23,15),(23,27),(24,7),(24,26),(25,9),(25,19),(26,10),(26,19),(27,20),(27,21),(28,16),(28,29),(29,8),(29,14),(29,24)],30)
[7,5] => 100100000 => ([(0,5),(0,6),(1,3),(1,23),(2,15),(3,2),(3,28),(4,1),(4,21),(4,29),(5,26),(5,27),(6,4),(6,26),(6,27),(8,13),(9,12),(10,14),(11,10),(12,11),(13,7),(14,7),(15,8),(16,17),(16,20),(17,10),(17,18),(18,13),(18,14),(19,22),(19,24),(20,8),(20,18),(21,9),(21,24),(22,16),(22,25),(23,16),(23,28),(24,12),(24,25),(25,11),(25,17),(26,19),(26,21),(27,19),(27,29),(28,15),(28,20),(29,9),(29,22),(29,23)],30)
[6,6] => 11000000 => ([(0,7),(0,8),(1,11),(2,4),(2,16),(3,15),(4,5),(4,18),(5,6),(5,20),(6,3),(6,19),(7,2),(7,17),(8,1),(8,17),(10,12),(11,10),(12,13),(13,14),(14,9),(15,9),(16,10),(16,18),(17,11),(17,16),(18,12),(18,20),(19,14),(19,15),(20,13),(20,19)],21)
[6,5,1] => 101000010 => ([(0,4),(0,5),(1,3),(1,19),(1,20),(2,25),(2,26),(3,2),(3,27),(3,28),(4,30),(4,31),(5,1),(5,30),(5,31),(7,9),(8,13),(9,15),(10,8),(11,14),(12,7),(13,11),(14,17),(15,16),(16,6),(17,6),(18,15),(18,24),(19,12),(19,28),(20,21),(20,27),(21,13),(21,22),(22,11),(22,23),(23,14),(23,24),(24,16),(24,17),(25,9),(25,18),(26,18),(26,23),(27,22),(27,26),(28,7),(28,25),(29,8),(29,12),(29,21),(30,10),(30,19),(30,29),(31,10),(31,20),(31,29)],32)
[6,4,2] => 100100100 => ([(0,2),(0,3),(1,17),(1,18),(2,22),(2,23),(3,1),(3,22),(3,23),(5,7),(6,8),(7,4),(8,4),(9,12),(9,14),(10,12),(10,13),(11,13),(11,14),(12,19),(12,21),(13,20),(13,21),(14,19),(14,20),(15,7),(15,8),(16,9),(16,10),(17,9),(17,11),(18,10),(18,11),(19,5),(19,15),(20,6),(20,15),(21,5),(21,6),(22,16),(22,17),(23,16),(23,18)],24)
[6,3,3] => 100011000 => ([(0,4),(0,5),(1,28),(1,29),(2,3),(2,30),(2,31),(3,22),(3,23),(4,1),(4,24),(4,25),(5,2),(5,24),(5,25),(7,11),(8,12),(9,13),(10,14),(11,9),(12,10),(13,6),(14,6),(15,26),(15,27),(16,11),(16,26),(17,12),(17,27),(18,13),(18,14),(19,15),(19,16),(20,15),(20,17),(21,7),(21,16),(22,8),(22,17),(23,7),(23,8),(24,28),(24,30),(25,29),(25,31),(26,9),(26,18),(27,10),(27,18),(28,19),(28,21),(29,19),(29,20),(30,21),(30,23),(31,20),(31,22)],32)
[5,5,2] => 11000100 => ([(0,4),(0,5),(1,15),(2,3),(2,24),(2,26),(3,16),(3,17),(4,1),(4,18),(4,25),(5,2),(5,18),(5,25),(7,9),(8,10),(9,11),(10,14),(11,13),(12,8),(13,6),(14,6),(15,7),(16,9),(16,21),(17,21),(17,22),(18,20),(18,24),(19,8),(19,22),(20,12),(20,19),(21,11),(21,23),(22,10),(22,23),(23,13),(23,14),(24,17),(24,19),(25,15),(25,20),(25,26),(26,7),(26,12),(26,16)],27)
[5,5,1,1] => 110000110 => ([(0,5),(0,6),(1,30),(1,32),(2,3),(2,29),(2,31),(3,4),(3,22),(3,28),(4,18),(4,26),(5,1),(5,23),(5,24),(6,2),(6,23),(6,24),(8,15),(9,14),(10,16),(11,17),(12,10),(13,11),(14,13),(15,12),(16,7),(17,7),(18,19),(18,20),(19,11),(19,21),(20,10),(20,21),(21,16),(21,17),(22,18),(22,25),(23,31),(23,32),(24,29),(24,30),(25,13),(25,19),(26,12),(26,20),(27,14),(27,25),(28,15),(28,26),(29,22),(29,27),(30,9),(30,27),(31,8),(31,28),(32,8),(32,9)],33)
[5,4,3] => 10101000 => ([(0,3),(0,4),(1,2),(1,20),(2,6),(3,19),(3,23),(4,1),(4,19),(4,23),(6,10),(7,8),(8,11),(9,12),(10,9),(11,5),(12,5),(13,11),(13,12),(14,15),(14,22),(15,7),(15,18),(16,10),(16,17),(17,9),(17,13),(18,8),(18,13),(19,14),(19,21),(20,6),(20,16),(21,15),(21,16),(21,22),(22,7),(22,17),(22,18),(23,14),(23,20),(23,21)],24)
[5,4,2,1] => 101001010 => ([(0,2),(0,3),(1,22),(1,23),(2,27),(2,28),(3,1),(3,27),(3,28),(5,10),(6,9),(7,11),(8,12),(9,7),(10,8),(11,4),(12,4),(13,14),(13,15),(14,25),(14,26),(15,10),(15,26),(16,9),(16,25),(17,11),(17,12),(18,14),(18,16),(19,6),(19,16),(20,5),(20,15),(21,5),(21,6),(22,13),(22,20),(23,13),(23,18),(24,19),(24,21),(25,7),(25,17),(26,8),(26,17),(27,22),(27,24),(27,29),(28,23),(28,24),(28,29),(29,18),(29,19),(29,20),(29,21)],30)
[5,3,3,1] => 100110010 => ([(0,3),(0,4),(1,27),(1,31),(2,25),(2,26),(3,1),(3,28),(3,29),(4,2),(4,28),(4,29),(6,12),(7,13),(8,14),(9,15),(10,11),(11,8),(12,9),(13,10),(14,5),(15,5),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,14),(19,15),(20,6),(20,23),(21,16),(21,23),(22,16),(22,24),(23,12),(23,17),(24,11),(24,18),(25,21),(25,22),(26,20),(26,21),(27,22),(27,30),(28,7),(28,26),(28,31),(29,7),(29,25),(29,27),(30,6),(30,10),(30,24),(31,13),(31,20),(31,30)],32)
[5,3,2,2] => 100101100 => ([(0,3),(0,4),(1,30),(1,31),(2,28),(2,29),(3,1),(3,32),(3,33),(4,2),(4,32),(4,33),(6,13),(7,12),(8,14),(9,15),(10,8),(11,9),(12,11),(13,10),(14,5),(15,5),(16,18),(16,19),(17,16),(17,24),(18,8),(18,20),(19,9),(19,20),(20,14),(20,15),(21,16),(21,25),(22,17),(22,26),(23,17),(23,21),(24,10),(24,18),(25,11),(25,19),(26,13),(26,24),(27,12),(27,25),(28,21),(28,27),(29,7),(29,27),(30,6),(30,26),(31,6),(31,7),(32,22),(32,23),(32,29),(32,31),(33,22),(33,23),(33,28),(33,30)],34)
[4,4,4] => 1110000 => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)
[4,4,3,1] => 11010010 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,7),(11,6),(12,5),(13,5),(14,10),(15,10),(15,18),(16,11),(16,23),(17,19),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27)
[4,4,2,2] => 11001100 => ([(0,3),(0,4),(1,22),(1,24),(2,21),(2,23),(3,2),(3,16),(3,17),(4,1),(4,16),(4,17),(6,8),(7,9),(8,10),(9,11),(10,5),(11,5),(12,8),(12,14),(13,9),(13,14),(14,10),(14,11),(15,12),(15,13),(16,21),(16,22),(17,23),(17,24),(18,6),(18,12),(19,7),(19,13),(20,6),(20,7),(21,15),(21,18),(22,15),(22,19),(23,18),(23,20),(24,19),(24,20)],25)
[4,4,2,1,1] => 110010110 => ([(0,3),(0,4),(1,30),(1,31),(2,28),(2,29),(3,1),(3,32),(3,33),(4,2),(4,32),(4,33),(6,13),(7,12),(8,14),(9,15),(10,8),(11,9),(12,11),(13,10),(14,5),(15,5),(16,18),(16,19),(17,16),(17,24),(18,8),(18,20),(19,9),(19,20),(20,14),(20,15),(21,16),(21,25),(22,17),(22,26),(23,17),(23,21),(24,10),(24,18),(25,11),(25,19),(26,13),(26,24),(27,12),(27,25),(28,21),(28,27),(29,7),(29,27),(30,6),(30,26),(31,6),(31,7),(32,22),(32,23),(32,29),(32,31),(33,22),(33,23),(33,28),(33,30)],34)
[4,3,3,2] => 10110100 => ([(0,3),(0,4),(1,14),(2,16),(2,17),(3,2),(3,25),(3,26),(4,1),(4,25),(4,26),(6,8),(7,9),(8,12),(9,13),(10,7),(11,6),(12,5),(13,5),(14,10),(15,10),(15,18),(16,11),(16,23),(17,19),(17,23),(18,7),(18,22),(19,21),(19,22),(20,12),(20,13),(21,8),(21,20),(22,9),(22,20),(23,6),(23,21),(24,11),(24,18),(24,19),(25,15),(25,16),(25,24),(26,14),(26,15),(26,17),(26,24)],27)
[4,3,3,1,1] => 101100110 => ([(0,3),(0,4),(1,27),(1,31),(2,25),(2,26),(3,1),(3,28),(3,29),(4,2),(4,28),(4,29),(6,12),(7,13),(8,14),(9,15),(10,11),(11,8),(12,9),(13,10),(14,5),(15,5),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,14),(19,15),(20,6),(20,23),(21,16),(21,23),(22,16),(22,24),(23,12),(23,17),(24,11),(24,18),(25,21),(25,22),(26,20),(26,21),(27,22),(27,30),(28,7),(28,26),(28,31),(29,7),(29,25),(29,27),(30,6),(30,10),(30,24),(31,13),(31,20),(31,30)],32)
[4,3,2,2,1] => 101011010 => ([(0,2),(0,3),(1,22),(1,23),(2,27),(2,28),(3,1),(3,27),(3,28),(5,10),(6,9),(7,11),(8,12),(9,7),(10,8),(11,4),(12,4),(13,14),(13,15),(14,25),(14,26),(15,10),(15,26),(16,9),(16,25),(17,11),(17,12),(18,14),(18,16),(19,6),(19,16),(20,5),(20,15),(21,5),(21,6),(22,13),(22,20),(23,13),(23,18),(24,19),(24,21),(25,7),(25,17),(26,8),(26,17),(27,22),(27,24),(27,29),(28,23),(28,24),(28,29),(29,18),(29,19),(29,20),(29,21)],30)
[4,2,2,2,2] => 100111100 => ([(0,5),(0,6),(1,30),(1,32),(2,3),(2,29),(2,31),(3,4),(3,22),(3,28),(4,18),(4,26),(5,1),(5,23),(5,24),(6,2),(6,23),(6,24),(8,15),(9,14),(10,16),(11,17),(12,10),(13,11),(14,13),(15,12),(16,7),(17,7),(18,19),(18,20),(19,11),(19,21),(20,10),(20,21),(21,16),(21,17),(22,18),(22,25),(23,31),(23,32),(24,29),(24,30),(25,13),(25,19),(26,12),(26,20),(27,14),(27,25),(28,15),(28,26),(29,22),(29,27),(30,9),(30,27),(31,8),(31,28),(32,8),(32,9)],33)
[3,3,3,3] => 1111000 => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)
[3,3,3,2,1] => 11101010 => ([(0,3),(0,4),(1,2),(1,20),(2,6),(3,19),(3,23),(4,1),(4,19),(4,23),(6,10),(7,8),(8,11),(9,12),(10,9),(11,5),(12,5),(13,11),(13,12),(14,15),(14,22),(15,7),(15,18),(16,10),(16,17),(17,9),(17,13),(18,8),(18,13),(19,14),(19,21),(20,6),(20,16),(21,15),(21,16),(21,22),(22,7),(22,17),(22,18),(23,14),(23,20),(23,21)],24)
[3,3,3,1,1,1] => 111001110 => ([(0,4),(0,5),(1,28),(1,29),(2,3),(2,30),(2,31),(3,22),(3,23),(4,1),(4,24),(4,25),(5,2),(5,24),(5,25),(7,11),(8,12),(9,13),(10,14),(11,9),(12,10),(13,6),(14,6),(15,26),(15,27),(16,11),(16,26),(17,12),(17,27),(18,13),(18,14),(19,15),(19,16),(20,15),(20,17),(21,7),(21,16),(22,8),(22,17),(23,7),(23,8),(24,28),(24,30),(25,29),(25,31),(26,9),(26,18),(27,10),(27,18),(28,19),(28,21),(29,19),(29,20),(30,21),(30,23),(31,20),(31,22)],32)
[3,3,2,2,2] => 11011100 => ([(0,4),(0,5),(1,15),(2,3),(2,24),(2,26),(3,16),(3,17),(4,1),(4,18),(4,25),(5,2),(5,18),(5,25),(7,9),(8,10),(9,11),(10,14),(11,13),(12,8),(13,6),(14,6),(15,7),(16,9),(16,21),(17,21),(17,22),(18,20),(18,24),(19,8),(19,22),(20,12),(20,19),(21,11),(21,23),(22,10),(22,23),(23,13),(23,14),(24,17),(24,19),(25,15),(25,20),(25,26),(26,7),(26,12),(26,16)],27)
[3,3,2,2,1,1] => 110110110 => ([(0,2),(0,3),(1,17),(1,18),(2,22),(2,23),(3,1),(3,22),(3,23),(5,7),(6,8),(7,4),(8,4),(9,12),(9,14),(10,12),(10,13),(11,13),(11,14),(12,19),(12,21),(13,20),(13,21),(14,19),(14,20),(15,7),(15,8),(16,9),(16,10),(17,9),(17,11),(18,10),(18,11),(19,5),(19,15),(20,6),(20,15),(21,5),(21,6),(22,16),(22,17),(23,16),(23,18)],24)
[3,2,2,2,2,1] => 101111010 => ([(0,4),(0,5),(1,3),(1,19),(1,20),(2,25),(2,26),(3,2),(3,27),(3,28),(4,30),(4,31),(5,1),(5,30),(5,31),(7,9),(8,13),(9,15),(10,8),(11,14),(12,7),(13,11),(14,17),(15,16),(16,6),(17,6),(18,15),(18,24),(19,12),(19,28),(20,21),(20,27),(21,13),(21,22),(22,11),(22,23),(23,14),(23,24),(24,16),(24,17),(25,9),(25,18),(26,18),(26,23),(27,22),(27,26),(28,7),(28,25),(29,8),(29,12),(29,21),(30,10),(30,19),(30,29),(31,10),(31,20),(31,29)],32)
[2,2,2,2,2,2] => 11111100 => ([(0,7),(0,8),(1,11),(2,4),(2,16),(3,15),(4,5),(4,18),(5,6),(5,20),(6,3),(6,19),(7,2),(7,17),(8,1),(8,17),(10,12),(11,10),(12,13),(13,14),(14,9),(15,9),(16,10),(16,18),(17,11),(17,16),(18,12),(18,20),(19,14),(19,15),(20,13),(20,19)],21)
[2,2,2,2,2,1,1] => 111110110 => ([(0,5),(0,6),(1,3),(1,23),(2,15),(3,2),(3,28),(4,1),(4,21),(4,29),(5,26),(5,27),(6,4),(6,26),(6,27),(8,13),(9,12),(10,14),(11,10),(12,11),(13,7),(14,7),(15,8),(16,17),(16,20),(17,10),(17,18),(18,13),(18,14),(19,22),(19,24),(20,8),(20,18),(21,9),(21,24),(22,16),(22,25),(23,16),(23,28),(24,12),(24,25),(25,11),(25,17),(26,19),(26,21),(27,19),(27,29),(28,15),(28,20),(29,9),(29,22),(29,23)],30)
[7,6] => 101000000 => ([(0,6),(0,7),(1,5),(1,19),(2,16),(3,4),(3,25),(4,2),(4,26),(5,3),(5,24),(6,23),(6,27),(7,1),(7,23),(7,27),(9,13),(10,15),(11,12),(12,10),(13,11),(14,8),(15,8),(16,14),(17,14),(17,15),(18,10),(18,17),(19,20),(19,24),(20,11),(20,21),(21,12),(21,18),(22,13),(22,20),(23,9),(23,22),(24,21),(24,25),(25,18),(25,26),(26,16),(26,17),(27,9),(27,19),(27,22)],28)
[6,6,1] => 110000010 => ([(0,6),(0,7),(1,20),(2,4),(2,21),(2,23),(3,27),(3,28),(4,5),(4,25),(4,26),(5,3),(5,29),(5,30),(6,2),(6,22),(6,31),(7,1),(7,22),(7,31),(9,15),(10,13),(11,10),(12,16),(13,14),(14,17),(15,12),(16,18),(17,19),(18,8),(19,8),(20,9),(21,10),(21,26),(22,11),(22,21),(23,9),(23,25),(24,18),(24,19),(25,15),(25,30),(26,13),(26,29),(27,16),(27,24),(28,17),(28,24),(29,14),(29,28),(30,12),(30,27),(31,11),(31,20),(31,23)],32)
[6,5,2] => 101000100 => ([(0,3),(0,4),(1,2),(1,25),(1,26),(2,21),(2,22),(3,27),(3,28),(4,1),(4,27),(4,28),(6,13),(7,10),(8,14),(9,15),(10,11),(11,12),(12,8),(13,9),(14,5),(15,5),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,14),(19,15),(20,6),(20,23),(21,16),(21,23),(22,16),(22,24),(23,13),(23,17),(24,12),(24,18),(25,20),(25,21),(26,22),(26,29),(27,7),(27,25),(27,30),(28,7),(28,26),(28,30),(29,6),(29,11),(29,24),(30,10),(30,20),(30,29)],31)
[6,4,3] => 100101000 => ([(0,3),(0,4),(1,15),(2,1),(2,23),(2,28),(3,29),(3,30),(4,2),(4,29),(4,30),(6,12),(7,10),(8,13),(9,14),(10,11),(11,8),(12,9),(13,5),(14,5),(15,6),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,13),(19,14),(20,16),(20,25),(21,16),(21,26),(22,6),(22,25),(23,7),(23,27),(24,20),(24,21),(25,12),(25,17),(26,11),(26,18),(27,10),(27,26),(28,7),(28,15),(28,22),(29,23),(29,24),(29,31),(30,24),(30,28),(30,31),(31,20),(31,21),(31,22),(31,27)],32)
[5,5,3] => 11001000 => ([(0,4),(0,5),(1,15),(2,8),(3,1),(3,16),(3,26),(4,2),(4,24),(4,25),(5,3),(5,24),(5,25),(7,9),(8,7),(9,10),(10,13),(11,14),(12,11),(13,6),(14,6),(15,12),(16,19),(16,23),(17,18),(17,23),(18,12),(18,22),(19,9),(19,21),(20,13),(20,14),(21,10),(21,20),(22,11),(22,20),(23,21),(23,22),(24,16),(24,17),(25,8),(25,17),(25,26),(26,7),(26,15),(26,18),(26,19)],27)
[5,5,2,1] => 110001010 => ([(0,4),(0,5),(1,17),(2,3),(2,29),(2,30),(3,22),(3,27),(4,1),(4,31),(4,33),(5,2),(5,31),(5,33),(7,14),(8,11),(9,15),(10,16),(11,12),(12,9),(13,10),(14,13),(15,6),(16,6),(17,7),(18,19),(18,20),(19,10),(19,21),(20,9),(20,21),(21,15),(21,16),(22,18),(22,25),(23,18),(23,26),(24,8),(24,28),(25,13),(25,19),(26,12),(26,20),(27,14),(27,25),(28,11),(28,26),(29,7),(29,27),(30,22),(30,23),(31,24),(31,30),(31,32),(32,8),(32,23),(32,28),(33,17),(33,24),(33,29),(33,32)],34)
[5,4,4] => 10110000 => ([(0,5),(0,6),(1,3),(1,20),(2,15),(3,2),(3,25),(4,21),(4,23),(5,1),(5,24),(5,26),(6,4),(6,24),(6,26),(8,13),(9,12),(10,14),(11,10),(12,11),(13,7),(14,7),(15,8),(16,17),(16,19),(17,10),(17,18),(18,13),(18,14),(19,8),(19,18),(20,16),(20,25),(21,16),(21,22),(22,11),(22,17),(23,12),(23,22),(24,9),(24,23),(25,15),(25,19),(26,9),(26,20),(26,21)],27)
[5,4,3,1] => 101010010 => ([(0,2),(0,3),(1,20),(1,21),(2,27),(2,28),(3,1),(3,27),(3,28),(5,11),(6,9),(7,12),(8,13),(9,10),(10,7),(11,8),(12,4),(13,4),(14,8),(14,16),(15,7),(15,16),(16,12),(16,13),(17,14),(17,15),(18,17),(18,24),(19,5),(19,25),(20,18),(20,23),(21,6),(21,23),(22,19),(22,26),(23,9),(23,24),(24,10),(24,15),(25,11),(25,14),(26,5),(26,17),(26,25),(27,20),(27,22),(27,29),(28,21),(28,22),(28,29),(29,6),(29,18),(29,19),(29,26)],30)
[5,4,2,2] => 101001100 => ([(0,3),(0,4),(1,28),(1,29),(2,30),(2,31),(3,1),(3,32),(3,33),(4,2),(4,32),(4,33),(6,14),(7,11),(8,15),(9,16),(10,12),(11,13),(12,8),(13,9),(14,10),(15,5),(16,5),(17,18),(17,19),(18,9),(18,20),(19,8),(19,20),(20,15),(20,16),(21,17),(21,23),(22,17),(22,24),(23,13),(23,18),(24,12),(24,19),(25,11),(25,23),(26,14),(26,27),(27,10),(27,24),(28,7),(28,25),(29,21),(29,25),(30,21),(30,22),(31,7),(31,22),(31,27),(32,6),(32,26),(32,29),(32,30),(33,6),(33,26),(33,28),(33,31)],34)
[5,3,3,2] => 100110100 => ([(0,3),(0,4),(1,28),(1,29),(2,30),(2,31),(3,1),(3,32),(3,33),(4,2),(4,32),(4,33),(6,13),(7,10),(8,14),(9,15),(10,11),(11,8),(12,9),(13,12),(14,5),(15,5),(16,17),(16,18),(17,8),(17,19),(18,9),(18,19),(19,14),(19,15),(20,16),(20,26),(21,16),(21,24),(22,20),(22,25),(23,6),(23,25),(24,11),(24,17),(25,13),(25,26),(26,12),(26,18),(27,10),(27,24),(28,21),(28,27),(29,20),(29,21),(30,7),(30,27),(31,6),(31,7),(32,22),(32,23),(32,28),(32,30),(33,22),(33,23),(33,29),(33,31)],34)
[4,4,4,1] => 11100010 => ([(0,5),(0,6),(1,2),(1,24),(2,8),(3,4),(3,25),(3,26),(4,20),(4,23),(5,1),(5,21),(5,27),(6,3),(6,21),(6,27),(8,14),(9,12),(10,15),(11,16),(12,13),(13,10),(14,11),(15,7),(16,7),(17,10),(17,19),(18,11),(18,19),(19,15),(19,16),(20,17),(20,18),(21,9),(21,26),(22,14),(22,18),(23,13),(23,17),(24,8),(24,22),(25,20),(25,22),(26,12),(26,23),(27,9),(27,24),(27,25)],28)
[4,4,3,2] => 11010100 => ([(0,3),(0,4),(1,15),(2,14),(3,2),(3,20),(3,24),(4,1),(4,20),(4,24),(6,10),(7,11),(8,6),(9,7),(10,12),(11,13),(12,5),(13,5),(14,8),(15,9),(16,17),(16,18),(17,10),(17,19),(18,11),(18,19),(19,12),(19,13),(20,21),(20,22),(21,8),(21,16),(21,23),(22,9),(22,16),(22,23),(23,6),(23,7),(23,17),(23,18),(24,14),(24,15),(24,21),(24,22)],25)
[4,4,3,1,1] => 110100110 => ([(0,3),(0,4),(1,28),(1,29),(2,30),(2,31),(3,1),(3,32),(3,33),(4,2),(4,32),(4,33),(6,13),(7,10),(8,14),(9,15),(10,11),(11,8),(12,9),(13,12),(14,5),(15,5),(16,17),(16,18),(17,8),(17,19),(18,9),(18,19),(19,14),(19,15),(20,16),(20,26),(21,16),(21,24),(22,20),(22,25),(23,6),(23,25),(24,11),(24,17),(25,13),(25,26),(26,12),(26,18),(27,10),(27,24),(28,21),(28,27),(29,20),(29,21),(30,7),(30,27),(31,6),(31,7),(32,22),(32,23),(32,28),(32,30),(33,22),(33,23),(33,29),(33,31)],34)
[4,4,2,2,1] => 110011010 => ([(0,3),(0,4),(1,28),(1,29),(2,30),(2,31),(3,1),(3,32),(3,33),(4,2),(4,32),(4,33),(6,14),(7,11),(8,15),(9,16),(10,12),(11,13),(12,8),(13,9),(14,10),(15,5),(16,5),(17,18),(17,19),(18,9),(18,20),(19,8),(19,20),(20,15),(20,16),(21,17),(21,23),(22,17),(22,24),(23,13),(23,18),(24,12),(24,19),(25,11),(25,23),(26,14),(26,27),(27,10),(27,24),(28,7),(28,25),(29,21),(29,25),(30,21),(30,22),(31,7),(31,22),(31,27),(32,6),(32,26),(32,29),(32,30),(33,6),(33,26),(33,28),(33,31)],34)
[4,3,3,3] => 10111000 => ([(0,5),(0,6),(1,2),(1,24),(2,8),(3,4),(3,25),(3,26),(4,20),(4,23),(5,1),(5,21),(5,27),(6,3),(6,21),(6,27),(8,14),(9,12),(10,15),(11,16),(12,13),(13,10),(14,11),(15,7),(16,7),(17,10),(17,19),(18,11),(18,19),(19,15),(19,16),(20,17),(20,18),(21,9),(21,26),(22,14),(22,18),(23,13),(23,17),(24,8),(24,22),(25,20),(25,22),(26,12),(26,23),(27,9),(27,24),(27,25)],28)
[4,3,3,2,1] => 101101010 => ([(0,2),(0,3),(1,20),(1,21),(2,27),(2,28),(3,1),(3,27),(3,28),(5,11),(6,9),(7,12),(8,13),(9,10),(10,7),(11,8),(12,4),(13,4),(14,8),(14,16),(15,7),(15,16),(16,12),(16,13),(17,14),(17,15),(18,17),(18,24),(19,5),(19,25),(20,18),(20,23),(21,6),(21,23),(22,19),(22,26),(23,9),(23,24),(24,10),(24,15),(25,11),(25,14),(26,5),(26,17),(26,25),(27,20),(27,22),(27,29),(28,21),(28,22),(28,29),(29,6),(29,18),(29,19),(29,26)],30)
[4,3,2,2,2] => 101011100 => ([(0,4),(0,5),(1,17),(2,3),(2,29),(2,30),(3,22),(3,27),(4,1),(4,31),(4,33),(5,2),(5,31),(5,33),(7,14),(8,11),(9,15),(10,16),(11,12),(12,9),(13,10),(14,13),(15,6),(16,6),(17,7),(18,19),(18,20),(19,10),(19,21),(20,9),(20,21),(21,15),(21,16),(22,18),(22,25),(23,18),(23,26),(24,8),(24,28),(25,13),(25,19),(26,12),(26,20),(27,14),(27,25),(28,11),(28,26),(29,7),(29,27),(30,22),(30,23),(31,24),(31,30),(31,32),(32,8),(32,23),(32,28),(33,17),(33,24),(33,29),(33,32)],34)
[3,3,3,3,1] => 11110010 => ([(0,5),(0,6),(1,3),(1,20),(2,15),(3,2),(3,25),(4,21),(4,23),(5,1),(5,24),(5,26),(6,4),(6,24),(6,26),(8,13),(9,12),(10,14),(11,10),(12,11),(13,7),(14,7),(15,8),(16,17),(16,19),(17,10),(17,18),(18,13),(18,14),(19,8),(19,18),(20,16),(20,25),(21,16),(21,22),(22,11),(22,17),(23,12),(23,22),(24,9),(24,23),(25,15),(25,19),(26,9),(26,20),(26,21)],27)
[3,3,3,2,2] => 11101100 => ([(0,4),(0,5),(1,15),(2,8),(3,1),(3,16),(3,26),(4,2),(4,24),(4,25),(5,3),(5,24),(5,25),(7,9),(8,7),(9,10),(10,13),(11,14),(12,11),(13,6),(14,6),(15,12),(16,19),(16,23),(17,18),(17,23),(18,12),(18,22),(19,9),(19,21),(20,13),(20,14),(21,10),(21,20),(22,11),(22,20),(23,21),(23,22),(24,16),(24,17),(25,8),(25,17),(25,26),(26,7),(26,15),(26,18),(26,19)],27)
[3,3,3,2,1,1] => 111010110 => ([(0,3),(0,4),(1,15),(2,1),(2,23),(2,28),(3,29),(3,30),(4,2),(4,29),(4,30),(6,12),(7,10),(8,13),(9,14),(10,11),(11,8),(12,9),(13,5),(14,5),(15,6),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,13),(19,14),(20,16),(20,25),(21,16),(21,26),(22,6),(22,25),(23,7),(23,27),(24,20),(24,21),(25,12),(25,17),(26,11),(26,18),(27,10),(27,26),(28,7),(28,15),(28,22),(29,23),(29,24),(29,31),(30,24),(30,28),(30,31),(31,20),(31,21),(31,22),(31,27)],32)
[3,3,2,2,2,1] => 110111010 => ([(0,3),(0,4),(1,2),(1,25),(1,26),(2,21),(2,22),(3,27),(3,28),(4,1),(4,27),(4,28),(6,13),(7,10),(8,14),(9,15),(10,11),(11,12),(12,8),(13,9),(14,5),(15,5),(16,17),(16,18),(17,9),(17,19),(18,8),(18,19),(19,14),(19,15),(20,6),(20,23),(21,16),(21,23),(22,16),(22,24),(23,13),(23,17),(24,12),(24,18),(25,20),(25,21),(26,22),(26,29),(27,7),(27,25),(27,30),(28,7),(28,26),(28,30),(29,6),(29,11),(29,24),(30,10),(30,20),(30,29)],31)
[3,2,2,2,2,2] => 101111100 => ([(0,6),(0,7),(1,20),(2,4),(2,21),(2,23),(3,27),(3,28),(4,5),(4,25),(4,26),(5,3),(5,29),(5,30),(6,2),(6,22),(6,31),(7,1),(7,22),(7,31),(9,15),(10,13),(11,10),(12,16),(13,14),(14,17),(15,12),(16,18),(17,19),(18,8),(19,8),(20,9),(21,10),(21,26),(22,11),(22,21),(23,9),(23,25),(24,18),(24,19),(25,15),(25,30),(26,13),(26,29),(27,16),(27,24),(28,17),(28,24),(29,14),(29,28),(30,12),(30,27),(31,11),(31,20),(31,23)],32)
[2,2,2,2,2,2,1] => 111111010 => ([(0,6),(0,7),(1,5),(1,19),(2,16),(3,4),(3,25),(4,2),(4,26),(5,3),(5,24),(6,23),(6,27),(7,1),(7,23),(7,27),(9,13),(10,15),(11,12),(12,10),(13,11),(14,8),(15,8),(16,14),(17,14),(17,15),(18,10),(18,17),(19,20),(19,24),(20,11),(20,21),(21,12),(21,18),(22,13),(22,20),(23,9),(23,22),(24,21),(24,25),(25,18),(25,26),(26,16),(26,17),(27,9),(27,19),(27,22)],28)
[7,7] => 110000000 => ([(0,8),(0,9),(1,12),(2,4),(2,18),(3,17),(4,6),(4,20),(5,7),(5,22),(6,5),(6,23),(7,3),(7,21),(8,2),(8,19),(9,1),(9,19),(11,14),(12,11),(13,15),(14,13),(15,16),(16,10),(17,10),(18,11),(18,20),(19,12),(19,18),(20,14),(20,23),(21,16),(21,17),(22,15),(22,21),(23,13),(23,22)],24)
[6,6,2] => 110000100 => ([(0,5),(0,6),(1,18),(2,4),(2,22),(2,32),(3,28),(3,29),(4,3),(4,27),(4,30),(5,2),(5,23),(5,31),(6,1),(6,23),(6,31),(8,15),(9,12),(10,16),(11,17),(12,14),(13,10),(14,11),(15,13),(16,7),(17,7),(18,9),(19,16),(19,17),(20,10),(20,19),(21,11),(21,19),(22,25),(22,27),(23,22),(23,24),(24,8),(24,25),(25,15),(25,26),(26,13),(26,20),(27,26),(27,28),(28,20),(28,21),(29,14),(29,21),(30,12),(30,29),(31,18),(31,24),(31,32),(32,8),(32,9),(32,30)],33)
[6,5,3] => 101001000 => ([(0,3),(0,4),(1,16),(2,1),(2,17),(2,27),(3,28),(3,29),(4,2),(4,28),(4,29),(6,9),(7,10),(8,11),(9,7),(10,12),(11,13),(12,14),(13,15),(14,5),(15,5),(16,8),(17,20),(17,21),(18,11),(18,23),(19,10),(19,24),(20,18),(20,22),(21,19),(21,22),(22,23),(22,24),(23,13),(23,25),(24,12),(24,25),(25,14),(25,15),(26,9),(26,20),(26,30),(27,16),(27,21),(27,30),(28,6),(28,17),(28,26),(29,6),(29,26),(29,27),(30,7),(30,8),(30,18),(30,19)],31)
[6,4,4] => 100110000 => ([(0,5),(0,6),(1,16),(2,1),(2,26),(3,29),(3,30),(4,2),(4,31),(4,32),(5,3),(5,23),(5,24),(6,4),(6,23),(6,24),(8,11),(9,12),(10,14),(11,15),(12,13),(13,10),(14,7),(15,7),(16,8),(17,13),(17,27),(18,27),(18,28),(19,8),(19,28),(20,14),(20,15),(21,17),(21,18),(22,12),(22,17),(23,29),(23,31),(24,30),(24,32),(25,18),(25,19),(26,16),(26,19),(27,10),(27,20),(28,11),(28,20),(29,21),(29,22),(30,21),(30,25),(31,9),(31,22),(32,9),(32,25),(32,26)],33)
[5,5,4] => 11010000 => ([(0,5),(0,6),(1,15),(2,3),(2,25),(3,4),(3,19),(4,8),(5,1),(5,24),(5,26),(6,2),(6,24),(6,26),(8,11),(9,12),(10,13),(11,14),(12,10),(13,7),(14,7),(15,9),(16,12),(16,22),(17,13),(17,14),(18,22),(18,23),(19,8),(19,23),(20,16),(20,18),(21,9),(21,16),(22,10),(22,17),(23,11),(23,17),(24,20),(24,21),(25,18),(25,19),(26,15),(26,20),(26,21),(26,25)],27)
[5,5,3,1] => 110010010 => ([(0,3),(0,4),(1,14),(2,19),(2,25),(3,2),(3,24),(3,28),(4,1),(4,24),(4,28),(6,9),(7,10),(8,12),(9,13),(10,11),(11,8),(12,5),(13,5),(14,7),(15,22),(15,23),(16,12),(16,13),(17,18),(17,20),(18,15),(18,26),(19,18),(19,27),(20,15),(20,21),(21,6),(21,22),(22,9),(22,16),(23,8),(23,16),(24,17),(24,19),(25,7),(25,20),(25,27),(26,6),(26,11),(26,23),(27,10),(27,21),(27,26),(28,14),(28,17),(28,25)],29)
[5,5,2,2] => 110001100 => ([(0,4),(0,5),(1,28),(1,29),(2,3),(2,30),(2,31),(3,22),(3,23),(4,1),(4,24),(4,25),(5,2),(5,24),(5,25),(7,12),(8,11),(9,13),(10,14),(11,9),(12,10),(13,6),(14,6),(15,26),(15,27),(16,11),(16,26),(17,12),(17,27),(18,13),(18,14),(19,15),(19,16),(20,8),(20,16),(21,7),(21,8),(22,15),(22,17),(23,7),(23,17),(24,28),(24,30),(25,29),(25,31),(26,9),(26,18),(27,10),(27,18),(28,20),(28,21),(29,19),(29,20),(30,21),(30,23),(31,19),(31,22)],32)
[5,4,4,1] => 101100010 => ([(0,4),(0,5),(1,29),(1,31),(2,3),(2,30),(2,32),(3,24),(3,28),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,15),(8,16),(9,17),(10,18),(11,13),(12,14),(13,9),(14,10),(15,11),(16,12),(17,6),(18,6),(19,20),(19,21),(20,9),(20,22),(21,10),(21,22),(22,17),(22,18),(23,19),(23,25),(24,19),(24,26),(25,13),(25,20),(26,14),(26,21),(27,11),(27,25),(28,12),(28,26),(29,23),(29,27),(30,23),(30,24),(31,15),(31,27),(32,16),(32,28),(33,7),(33,8),(33,31),(33,32),(34,7),(34,8),(34,29),(34,30)],35)
[5,4,3,2] => 101010100 => ([(0,2),(0,3),(1,12),(2,18),(2,23),(3,1),(3,18),(3,23),(5,6),(6,10),(7,5),(8,7),(9,11),(10,4),(11,4),(12,8),(13,17),(13,20),(14,10),(14,11),(15,9),(15,14),(16,15),(16,21),(17,16),(17,22),(18,13),(18,19),(19,8),(19,17),(19,20),(20,7),(20,16),(20,22),(21,6),(21,9),(21,14),(22,5),(22,15),(22,21),(23,12),(23,13),(23,19)],24)
[5,3,3,3] => 100111000 => ([(0,5),(0,6),(1,17),(2,4),(2,30),(2,31),(3,1),(3,32),(3,33),(4,22),(4,23),(5,2),(5,24),(5,25),(6,3),(6,24),(6,25),(8,14),(9,12),(10,15),(11,16),(12,13),(13,10),(14,11),(15,7),(16,7),(17,8),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,15),(21,16),(22,18),(22,27),(23,18),(23,28),(24,30),(24,32),(25,31),(25,33),(26,8),(26,28),(27,13),(27,19),(28,14),(28,20),(29,12),(29,27),(30,22),(30,29),(31,23),(31,26),(32,9),(32,29),(33,9),(33,17),(33,26)],34)
[4,4,4,2] => 11100100 => ([(0,4),(0,5),(1,14),(2,1),(2,18),(3,19),(3,25),(4,2),(4,24),(4,26),(5,3),(5,24),(5,26),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,11),(15,22),(16,12),(16,13),(17,8),(17,15),(18,14),(18,21),(19,15),(19,20),(20,22),(20,23),(21,7),(21,23),(22,9),(22,16),(23,10),(23,16),(24,17),(24,19),(25,8),(25,20),(25,21),(26,17),(26,18),(26,25)],27)
[4,4,4,1,1] => 111000110 => ([(0,5),(0,6),(1,17),(2,4),(2,30),(2,31),(3,1),(3,32),(3,33),(4,22),(4,23),(5,2),(5,24),(5,25),(6,3),(6,24),(6,25),(8,14),(9,12),(10,15),(11,16),(12,13),(13,10),(14,11),(15,7),(16,7),(17,8),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,15),(21,16),(22,18),(22,27),(23,18),(23,28),(24,30),(24,32),(25,31),(25,33),(26,8),(26,28),(27,13),(27,19),(28,14),(28,20),(29,12),(29,27),(30,22),(30,29),(31,23),(31,26),(32,9),(32,29),(33,9),(33,17),(33,26)],34)
[4,4,3,3] => 11011000 => ([(0,4),(0,5),(1,14),(2,1),(2,18),(3,19),(3,25),(4,2),(4,24),(4,26),(5,3),(5,24),(5,26),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,11),(15,22),(16,12),(16,13),(17,8),(17,15),(18,14),(18,21),(19,15),(19,20),(20,22),(20,23),(21,7),(21,23),(22,9),(22,16),(23,10),(23,16),(24,17),(24,19),(25,8),(25,20),(25,21),(26,17),(26,18),(26,25)],27)
[4,4,3,2,1] => 110101010 => ([(0,2),(0,3),(1,12),(2,18),(2,23),(3,1),(3,18),(3,23),(5,6),(6,10),(7,5),(8,7),(9,11),(10,4),(11,4),(12,8),(13,17),(13,20),(14,10),(14,11),(15,9),(15,14),(16,15),(16,21),(17,16),(17,22),(18,13),(18,19),(19,8),(19,17),(19,20),(20,7),(20,16),(20,22),(21,6),(21,9),(21,14),(22,5),(22,15),(22,21),(23,12),(23,13),(23,19)],24)
[4,4,2,2,2] => 110011100 => ([(0,4),(0,5),(1,28),(1,29),(2,3),(2,30),(2,31),(3,22),(3,23),(4,1),(4,24),(4,25),(5,2),(5,24),(5,25),(7,12),(8,11),(9,13),(10,14),(11,9),(12,10),(13,6),(14,6),(15,26),(15,27),(16,11),(16,26),(17,12),(17,27),(18,13),(18,14),(19,15),(19,16),(20,8),(20,16),(21,7),(21,8),(22,15),(22,17),(23,7),(23,17),(24,28),(24,30),(25,29),(25,31),(26,9),(26,18),(27,10),(27,18),(28,20),(28,21),(29,19),(29,20),(30,21),(30,23),(31,19),(31,22)],32)
[4,3,3,3,1] => 101110010 => ([(0,4),(0,5),(1,29),(1,31),(2,3),(2,30),(2,32),(3,24),(3,28),(4,1),(4,33),(4,34),(5,2),(5,33),(5,34),(7,15),(8,16),(9,17),(10,18),(11,13),(12,14),(13,9),(14,10),(15,11),(16,12),(17,6),(18,6),(19,20),(19,21),(20,9),(20,22),(21,10),(21,22),(22,17),(22,18),(23,19),(23,25),(24,19),(24,26),(25,13),(25,20),(26,14),(26,21),(27,11),(27,25),(28,12),(28,26),(29,23),(29,27),(30,23),(30,24),(31,15),(31,27),(32,16),(32,28),(33,7),(33,8),(33,31),(33,32),(34,7),(34,8),(34,29),(34,30)],35)
[4,3,3,2,2] => 101101100 => ([(0,3),(0,4),(1,14),(2,19),(2,25),(3,2),(3,24),(3,28),(4,1),(4,24),(4,28),(6,9),(7,10),(8,12),(9,13),(10,11),(11,8),(12,5),(13,5),(14,7),(15,22),(15,23),(16,12),(16,13),(17,18),(17,20),(18,15),(18,26),(19,18),(19,27),(20,15),(20,21),(21,6),(21,22),(22,9),(22,16),(23,8),(23,16),(24,17),(24,19),(25,7),(25,20),(25,27),(26,6),(26,11),(26,23),(27,10),(27,21),(27,26),(28,14),(28,17),(28,25)],29)
[3,3,3,3,2] => 11110100 => ([(0,5),(0,6),(1,15),(2,3),(2,25),(3,4),(3,19),(4,8),(5,1),(5,24),(5,26),(6,2),(6,24),(6,26),(8,11),(9,12),(10,13),(11,14),(12,10),(13,7),(14,7),(15,9),(16,12),(16,22),(17,13),(17,14),(18,22),(18,23),(19,8),(19,23),(20,16),(20,18),(21,9),(21,16),(22,10),(22,17),(23,11),(23,17),(24,20),(24,21),(25,18),(25,19),(26,15),(26,20),(26,21),(26,25)],27)
[3,3,3,3,1,1] => 111100110 => ([(0,5),(0,6),(1,16),(2,1),(2,26),(3,29),(3,30),(4,2),(4,31),(4,32),(5,3),(5,23),(5,24),(6,4),(6,23),(6,24),(8,11),(9,12),(10,14),(11,15),(12,13),(13,10),(14,7),(15,7),(16,8),(17,13),(17,27),(18,27),(18,28),(19,8),(19,28),(20,14),(20,15),(21,17),(21,18),(22,12),(22,17),(23,29),(23,31),(24,30),(24,32),(25,18),(25,19),(26,16),(26,19),(27,10),(27,20),(28,11),(28,20),(29,21),(29,22),(30,21),(30,25),(31,9),(31,22),(32,9),(32,25),(32,26)],33)
[3,3,3,2,2,1] => 111011010 => ([(0,3),(0,4),(1,16),(2,1),(2,17),(2,27),(3,28),(3,29),(4,2),(4,28),(4,29),(6,9),(7,10),(8,11),(9,7),(10,12),(11,13),(12,14),(13,15),(14,5),(15,5),(16,8),(17,20),(17,21),(18,11),(18,23),(19,10),(19,24),(20,18),(20,22),(21,19),(21,22),(22,23),(22,24),(23,13),(23,25),(24,12),(24,25),(25,14),(25,15),(26,9),(26,20),(26,30),(27,16),(27,21),(27,30),(28,6),(28,17),(28,26),(29,6),(29,26),(29,27),(30,7),(30,8),(30,18),(30,19)],31)
[3,3,2,2,2,2] => 110111100 => ([(0,5),(0,6),(1,18),(2,4),(2,22),(2,32),(3,28),(3,29),(4,3),(4,27),(4,30),(5,2),(5,23),(5,31),(6,1),(6,23),(6,31),(8,15),(9,12),(10,16),(11,17),(12,14),(13,10),(14,11),(15,13),(16,7),(17,7),(18,9),(19,16),(19,17),(20,10),(20,19),(21,11),(21,19),(22,25),(22,27),(23,22),(23,24),(24,8),(24,25),(25,15),(25,26),(26,13),(26,20),(27,26),(27,28),(28,20),(28,21),(29,14),(29,21),(30,12),(30,29),(31,18),(31,24),(31,32),(32,8),(32,9),(32,30)],33)
[2,2,2,2,2,2,2] => 111111100 => ([(0,8),(0,9),(1,12),(2,4),(2,18),(3,17),(4,6),(4,20),(5,7),(5,22),(6,5),(6,23),(7,3),(7,21),(8,2),(8,19),(9,1),(9,19),(11,14),(12,11),(13,15),(14,13),(15,16),(16,10),(17,10),(18,11),(18,20),(19,12),(19,18),(20,14),(20,23),(21,16),(21,17),(22,15),(22,21),(23,13),(23,22)],24)
[6,6,3] => 110001000 => ([(0,4),(0,5),(1,16),(2,3),(2,28),(2,31),(3,23),(3,30),(4,1),(4,24),(4,29),(5,2),(5,24),(5,29),(7,13),(8,11),(9,14),(10,15),(11,12),(12,9),(13,10),(14,6),(15,6),(16,8),(17,18),(17,19),(18,10),(18,20),(19,9),(19,20),(20,14),(20,15),(21,7),(21,26),(22,17),(22,26),(23,17),(23,27),(24,25),(24,28),(25,21),(25,22),(26,13),(26,18),(27,12),(27,19),(28,22),(28,23),(29,16),(29,25),(29,31),(30,7),(30,11),(30,27),(31,8),(31,21),(31,30)],32)
[6,5,4] => 101010000 => ([(0,4),(0,5),(1,3),(1,18),(2,14),(3,2),(3,26),(4,25),(4,29),(5,1),(5,25),(5,29),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,12),(15,13),(16,20),(16,28),(17,7),(17,24),(18,19),(18,26),(19,17),(19,21),(20,8),(20,22),(21,23),(21,24),(22,11),(22,23),(23,9),(23,15),(24,10),(24,15),(25,16),(25,27),(26,14),(26,17),(27,19),(27,20),(27,28),(28,8),(28,21),(28,22),(29,16),(29,18),(29,27)],30)
[5,5,5] => 11100000 => ([(0,7),(0,8),(1,6),(1,19),(2,4),(2,18),(3,14),(4,15),(5,3),(5,23),(6,5),(6,22),(7,1),(7,20),(8,2),(8,20),(10,11),(11,12),(12,9),(13,9),(14,13),(15,10),(16,12),(16,13),(17,11),(17,16),(18,15),(18,21),(19,21),(19,22),(20,18),(20,19),(21,10),(21,17),(22,17),(22,23),(23,14),(23,16)],24)
[5,5,4,1] => 110100010 => ([(0,4),(0,5),(1,17),(2,3),(2,29),(2,30),(3,22),(3,27),(4,1),(4,31),(4,33),(5,2),(5,31),(5,33),(7,14),(8,11),(9,15),(10,16),(11,12),(12,9),(13,10),(14,13),(15,6),(16,6),(17,7),(18,19),(18,20),(19,9),(19,21),(20,10),(20,21),(21,15),(21,16),(22,18),(22,25),(23,18),(23,26),(24,7),(24,28),(25,12),(25,19),(26,13),(26,20),(27,11),(27,25),(28,14),(28,26),(29,22),(29,23),(30,8),(30,27),(31,24),(31,30),(31,32),(32,8),(32,23),(32,28),(33,17),(33,24),(33,29),(33,32)],34)
[5,5,3,2] => 110010100 => ([(0,3),(0,4),(1,16),(2,22),(2,29),(3,2),(3,30),(3,32),(4,1),(4,30),(4,32),(6,13),(7,10),(8,14),(9,15),(10,11),(11,8),(12,9),(13,12),(14,5),(15,5),(16,6),(17,18),(17,19),(18,8),(18,20),(19,9),(19,20),(20,14),(20,15),(21,23),(21,27),(22,24),(22,28),(23,17),(23,25),(24,17),(24,26),(25,11),(25,18),(26,12),(26,19),(27,10),(27,25),(28,13),(28,26),(29,6),(29,7),(29,28),(30,21),(30,22),(30,31),(31,7),(31,23),(31,24),(31,27),(32,16),(32,21),(32,29),(32,31)],33)
[5,4,4,2] => 101100100 => ([(0,3),(0,4),(1,28),(1,30),(2,29),(2,31),(3,1),(3,32),(3,33),(4,2),(4,32),(4,33),(6,14),(7,11),(8,15),(9,16),(10,12),(11,13),(12,8),(13,9),(14,10),(15,5),(16,5),(17,18),(17,19),(18,8),(18,20),(19,9),(19,20),(20,15),(20,16),(21,7),(21,25),(22,17),(22,26),(23,17),(23,24),(24,12),(24,18),(25,11),(25,26),(26,13),(26,19),(27,10),(27,24),(28,23),(28,27),(29,22),(29,25),(30,14),(30,27),(31,7),(31,22),(31,23),(32,6),(32,21),(32,29),(32,30),(33,6),(33,21),(33,28),(33,31)],34)
[5,4,3,3] => 101011000 => ([(0,4),(0,5),(1,16),(2,1),(2,25),(3,23),(3,26),(4,2),(4,32),(4,33),(5,3),(5,32),(5,33),(7,13),(8,11),(9,14),(10,15),(11,12),(12,9),(13,10),(14,6),(15,6),(16,7),(17,19),(17,20),(18,17),(18,28),(19,10),(19,22),(20,9),(20,22),(21,7),(21,28),(22,14),(22,15),(23,18),(23,27),(24,8),(24,30),(25,16),(25,21),(26,18),(26,21),(27,17),(27,29),(28,13),(28,19),(29,12),(29,20),(30,11),(30,29),(31,8),(31,27),(31,30),(32,23),(32,24),(32,31),(33,24),(33,25),(33,26),(33,31)],34)
[5,4,3,2,1] => 1010101010 => ([(0,1),(0,2),(1,18),(1,19),(2,18),(2,19),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,12),(8,13),(9,12),(9,13),(10,6),(10,7),(11,6),(11,7),(12,16),(12,17),(13,16),(13,17),(14,10),(14,11),(15,10),(15,11),(16,4),(16,5),(17,4),(17,5),(18,14),(18,15),(19,14),(19,15)],20)
[4,4,4,3] => 11101000 => ([(0,5),(0,6),(1,4),(1,26),(2,3),(2,25),(3,8),(4,9),(5,2),(5,24),(5,27),(6,1),(6,24),(6,27),(8,12),(9,13),(10,14),(11,15),(12,10),(13,11),(14,7),(15,7),(16,22),(16,23),(17,14),(17,15),(18,12),(18,22),(19,13),(19,23),(20,16),(20,18),(21,16),(21,19),(22,10),(22,17),(23,11),(23,17),(24,20),(24,21),(25,8),(25,18),(26,9),(26,19),(27,20),(27,21),(27,25),(27,26)],28)
[4,4,4,2,1] => 111001010 => ([(0,4),(0,5),(1,16),(2,1),(2,25),(3,23),(3,26),(4,2),(4,32),(4,33),(5,3),(5,32),(5,33),(7,13),(8,11),(9,14),(10,15),(11,12),(12,9),(13,10),(14,6),(15,6),(16,7),(17,19),(17,20),(18,17),(18,28),(19,10),(19,22),(20,9),(20,22),(21,7),(21,28),(22,14),(22,15),(23,18),(23,27),(24,8),(24,30),(25,16),(25,21),(26,18),(26,21),(27,17),(27,29),(28,13),(28,19),(29,12),(29,20),(30,11),(30,29),(31,8),(31,27),(31,30),(32,23),(32,24),(32,31),(33,24),(33,25),(33,26),(33,31)],34)
[4,4,3,3,1] => 110110010 => ([(0,3),(0,4),(1,28),(1,30),(2,29),(2,31),(3,1),(3,32),(3,33),(4,2),(4,32),(4,33),(6,14),(7,11),(8,15),(9,16),(10,12),(11,13),(12,8),(13,9),(14,10),(15,5),(16,5),(17,18),(17,19),(18,8),(18,20),(19,9),(19,20),(20,15),(20,16),(21,7),(21,25),(22,17),(22,26),(23,17),(23,24),(24,12),(24,18),(25,11),(25,26),(26,13),(26,19),(27,10),(27,24),(28,23),(28,27),(29,22),(29,25),(30,14),(30,27),(31,7),(31,22),(31,23),(32,6),(32,21),(32,29),(32,30),(33,6),(33,21),(33,28),(33,31)],34)
[4,4,3,2,2] => 110101100 => ([(0,3),(0,4),(1,16),(2,22),(2,29),(3,2),(3,30),(3,32),(4,1),(4,30),(4,32),(6,13),(7,10),(8,14),(9,15),(10,11),(11,8),(12,9),(13,12),(14,5),(15,5),(16,6),(17,18),(17,19),(18,8),(18,20),(19,9),(19,20),(20,14),(20,15),(21,23),(21,27),(22,24),(22,28),(23,17),(23,25),(24,17),(24,26),(25,11),(25,18),(26,12),(26,19),(27,10),(27,25),(28,13),(28,26),(29,6),(29,7),(29,28),(30,21),(30,22),(30,31),(31,7),(31,23),(31,24),(31,27),(32,16),(32,21),(32,29),(32,31)],33)
[4,3,3,3,2] => 101110100 => ([(0,4),(0,5),(1,17),(2,3),(2,29),(2,30),(3,22),(3,27),(4,1),(4,31),(4,33),(5,2),(5,31),(5,33),(7,14),(8,11),(9,15),(10,16),(11,12),(12,9),(13,10),(14,13),(15,6),(16,6),(17,7),(18,19),(18,20),(19,9),(19,21),(20,10),(20,21),(21,15),(21,16),(22,18),(22,25),(23,18),(23,26),(24,7),(24,28),(25,12),(25,19),(26,13),(26,20),(27,11),(27,25),(28,14),(28,26),(29,22),(29,23),(30,8),(30,27),(31,24),(31,30),(31,32),(32,8),(32,23),(32,28),(33,17),(33,24),(33,29),(33,32)],34)
[3,3,3,3,3] => 11111000 => ([(0,7),(0,8),(1,6),(1,19),(2,4),(2,18),(3,14),(4,15),(5,3),(5,23),(6,5),(6,22),(7,1),(7,20),(8,2),(8,20),(10,11),(11,12),(12,9),(13,9),(14,13),(15,10),(16,12),(16,13),(17,11),(17,16),(18,15),(18,21),(19,21),(19,22),(20,18),(20,19),(21,10),(21,17),(22,17),(22,23),(23,14),(23,16)],24)
[3,3,3,3,2,1] => 111101010 => ([(0,4),(0,5),(1,3),(1,18),(2,14),(3,2),(3,26),(4,25),(4,29),(5,1),(5,25),(5,29),(7,10),(8,11),(9,12),(10,13),(11,9),(12,6),(13,6),(14,7),(15,12),(15,13),(16,20),(16,28),(17,7),(17,24),(18,19),(18,26),(19,17),(19,21),(20,8),(20,22),(21,23),(21,24),(22,11),(22,23),(23,9),(23,15),(24,10),(24,15),(25,16),(25,27),(26,14),(26,17),(27,19),(27,20),(27,28),(28,8),(28,21),(28,22),(29,16),(29,18),(29,27)],30)
[3,3,3,2,2,2] => 111011100 => ([(0,4),(0,5),(1,16),(2,3),(2,28),(2,31),(3,23),(3,30),(4,1),(4,24),(4,29),(5,2),(5,24),(5,29),(7,13),(8,11),(9,14),(10,15),(11,12),(12,9),(13,10),(14,6),(15,6),(16,8),(17,18),(17,19),(18,10),(18,20),(19,9),(19,20),(20,14),(20,15),(21,7),(21,26),(22,17),(22,26),(23,17),(23,27),(24,25),(24,28),(25,21),(25,22),(26,13),(26,18),(27,12),(27,19),(28,22),(28,23),(29,16),(29,25),(29,31),(30,7),(30,11),(30,27),(31,8),(31,21),(31,30)],32)
[6,6,4] => 110010000 => ([(0,5),(0,6),(1,17),(2,3),(2,30),(3,8),(4,2),(4,23),(4,32),(5,4),(5,29),(5,31),(6,1),(6,29),(6,31),(8,14),(9,12),(10,15),(11,16),(12,13),(13,10),(14,11),(15,7),(16,7),(17,9),(18,20),(18,21),(19,18),(19,26),(20,11),(20,22),(21,10),(21,22),(22,15),(22,16),(23,19),(23,28),(24,18),(24,27),(25,19),(25,24),(26,13),(26,21),(27,14),(27,20),(28,12),(28,26),(29,23),(29,25),(30,8),(30,27),(31,17),(31,25),(31,32),(32,9),(32,24),(32,28),(32,30)],33)
[6,5,5] => 101100000 => ([(0,6),(0,7),(1,4),(1,23),(2,17),(3,2),(3,30),(4,3),(4,29),(5,24),(5,27),(6,1),(6,28),(6,31),(7,5),(7,28),(7,31),(9,15),(10,14),(11,16),(12,13),(13,11),(14,12),(15,8),(16,8),(17,9),(18,22),(18,26),(19,11),(19,21),(20,9),(20,21),(21,15),(21,16),(22,19),(22,20),(23,18),(23,29),(24,18),(24,25),(25,12),(25,26),(26,13),(26,19),(27,14),(27,25),(28,10),(28,27),(29,22),(29,30),(30,17),(30,20),(31,10),(31,23),(31,24)],32)
[5,5,5,1] => 111000010 => ([(0,6),(0,7),(1,2),(1,28),(2,9),(3,5),(3,24),(3,27),(4,30),(4,31),(5,4),(5,29),(5,32),(6,3),(6,23),(6,33),(7,1),(7,23),(7,33),(9,17),(10,14),(11,18),(12,19),(13,16),(14,13),(15,12),(16,11),(17,15),(18,8),(19,8),(20,18),(20,19),(21,12),(21,20),(22,11),(22,20),(23,10),(23,27),(24,25),(24,29),(25,17),(25,26),(26,15),(26,21),(27,14),(27,32),(28,9),(28,25),(29,26),(29,30),(30,21),(30,22),(31,16),(31,22),(32,13),(32,31),(33,10),(33,24),(33,28)],34)
[5,5,4,2] => 110100100 => ([(0,3),(0,4),(1,15),(2,20),(2,22),(3,2),(3,30),(3,31),(4,1),(4,30),(4,31),(6,12),(7,10),(8,13),(9,14),(10,8),(11,9),(12,11),(13,5),(14,5),(15,6),(16,23),(16,25),(17,8),(17,19),(18,9),(18,19),(19,13),(19,14),(20,16),(20,24),(21,6),(21,26),(22,16),(22,29),(23,17),(23,18),(24,7),(24,25),(25,10),(25,17),(26,12),(26,27),(27,11),(27,18),(28,24),(28,26),(28,29),(29,7),(29,23),(29,27),(30,20),(30,21),(30,28),(31,15),(31,21),(31,22),(31,28)],32)
[5,5,3,3] => 110011000 => ([(0,4),(0,5),(1,15),(2,27),(2,29),(3,1),(3,28),(3,31),(4,2),(4,22),(4,23),(5,3),(5,22),(5,23),(7,12),(8,11),(9,13),(10,14),(11,10),(12,9),(13,6),(14,6),(15,8),(16,12),(16,25),(17,25),(17,26),(18,13),(18,14),(19,17),(19,24),(20,7),(20,16),(21,16),(21,17),(22,29),(22,31),(23,27),(23,28),(24,11),(24,26),(25,9),(25,18),(26,10),(26,18),(27,19),(27,21),(28,20),(28,21),(29,19),(29,30),(30,7),(30,8),(30,24),(31,15),(31,20),(31,30)],32)
[5,5,3,2,1] => 1100101010 => ([(0,3),(0,4),(1,16),(2,20),(2,21),(3,2),(3,35),(3,36),(4,1),(4,35),(4,36),(6,13),(7,11),(8,14),(9,15),(10,12),(11,8),(12,9),(13,10),(14,5),(15,5),(16,6),(17,8),(17,19),(18,9),(18,19),(19,14),(19,15),(20,25),(20,28),(21,6),(21,28),(22,27),(22,34),(23,17),(23,18),(24,7),(24,31),(25,26),(25,30),(26,23),(26,29),(27,24),(27,33),(28,13),(28,30),(29,12),(29,18),(30,10),(30,29),(31,11),(31,17),(32,25),(32,27),(32,34),(33,7),(33,23),(33,31),(34,24),(34,26),(34,33),(35,20),(35,22),(35,32),(36,16),(36,21),(36,22),(36,32)],37)
[5,4,4,3] => 101101000 => ([(0,4),(0,5),(1,16),(2,1),(2,24),(3,22),(3,25),(4,2),(4,32),(4,33),(5,3),(5,32),(5,33),(7,13),(8,11),(9,14),(10,15),(11,12),(12,9),(13,10),(14,6),(15,6),(16,7),(17,18),(17,19),(18,10),(18,21),(19,9),(19,21),(20,7),(20,28),(21,14),(21,15),(22,8),(22,29),(23,20),(23,27),(24,16),(24,20),(25,26),(25,29),(26,17),(26,30),(27,17),(27,28),(28,13),(28,18),(29,11),(29,30),(30,12),(30,19),(31,8),(31,26),(31,27),(32,22),(32,23),(32,31),(33,23),(33,24),(33,25),(33,31)],34)
[5,4,4,2,1] => 1011001010 => ([(0,3),(0,4),(1,34),(1,35),(2,33),(2,36),(3,1),(3,39),(3,40),(4,2),(4,39),(4,40),(6,15),(7,10),(8,16),(9,17),(10,11),(11,13),(12,14),(13,8),(14,9),(15,12),(16,5),(17,5),(18,21),(18,22),(19,18),(19,29),(20,18),(20,30),(21,9),(21,23),(22,8),(22,23),(23,16),(23,17),(24,19),(24,20),(25,19),(25,27),(26,20),(26,28),(27,12),(27,29),(28,11),(28,30),(29,14),(29,21),(30,13),(30,22),(31,15),(31,27),(32,10),(32,28),(33,25),(33,31),(34,24),(34,25),(35,24),(35,26),(36,6),(36,31),(37,7),(37,26),(37,32),(38,6),(38,7),(38,32),(39,33),(39,34),(39,37),(39,38),(40,35),(40,36),(40,37),(40,38)],41)
[5,4,3,3,1] => 1010110010 => ([(0,3),(0,4),(1,34),(1,35),(2,33),(2,36),(3,1),(3,39),(3,40),(4,2),(4,39),(4,40),(6,15),(7,10),(8,16),(9,17),(10,11),(11,13),(12,14),(13,8),(14,9),(15,12),(16,5),(17,5),(18,21),(18,22),(19,18),(19,29),(20,18),(20,30),(21,9),(21,23),(22,8),(22,23),(23,16),(23,17),(24,19),(24,20),(25,19),(25,27),(26,20),(26,28),(27,12),(27,29),(28,11),(28,30),(29,14),(29,21),(30,13),(30,22),(31,15),(31,27),(32,10),(32,28),(33,25),(33,31),(34,24),(34,25),(35,24),(35,26),(36,6),(36,31),(37,7),(37,26),(37,32),(38,6),(38,7),(38,32),(39,33),(39,34),(39,37),(39,38),(40,35),(40,36),(40,37),(40,38)],41)
[5,4,3,2,2] => 1010101100 => ([(0,3),(0,4),(1,16),(2,20),(2,21),(3,2),(3,35),(3,36),(4,1),(4,35),(4,36),(6,13),(7,11),(8,14),(9,15),(10,12),(11,8),(12,9),(13,10),(14,5),(15,5),(16,6),(17,8),(17,19),(18,9),(18,19),(19,14),(19,15),(20,25),(20,28),(21,6),(21,28),(22,27),(22,34),(23,17),(23,18),(24,7),(24,31),(25,26),(25,30),(26,23),(26,29),(27,24),(27,33),(28,13),(28,30),(29,12),(29,18),(30,10),(30,29),(31,11),(31,17),(32,25),(32,27),(32,34),(33,7),(33,23),(33,31),(34,24),(34,26),(34,33),(35,20),(35,22),(35,32),(36,16),(36,21),(36,22),(36,32)],37)
[4,4,4,4] => 11110000 => ([(0,7),(0,8),(1,6),(1,19),(2,5),(2,18),(3,14),(4,15),(5,3),(5,23),(6,4),(6,24),(7,2),(7,20),(8,1),(8,20),(10,12),(11,13),(12,9),(13,9),(14,10),(15,11),(16,21),(16,22),(17,12),(17,13),(18,16),(18,23),(19,16),(19,24),(20,18),(20,19),(21,10),(21,17),(22,11),(22,17),(23,14),(23,21),(24,15),(24,22)],25)
[4,4,4,3,1] => 111010010 => ([(0,4),(0,5),(1,16),(2,1),(2,24),(3,22),(3,25),(4,2),(4,32),(4,33),(5,3),(5,32),(5,33),(7,13),(8,11),(9,14),(10,15),(11,12),(12,9),(13,10),(14,6),(15,6),(16,7),(17,18),(17,19),(18,10),(18,21),(19,9),(19,21),(20,7),(20,28),(21,14),(21,15),(22,8),(22,29),(23,20),(23,27),(24,16),(24,20),(25,26),(25,29),(26,17),(26,30),(27,17),(27,28),(28,13),(28,18),(29,11),(29,30),(30,12),(30,19),(31,8),(31,26),(31,27),(32,22),(32,23),(32,31),(33,23),(33,24),(33,25),(33,31)],34)
[4,4,4,2,2] => 111001100 => ([(0,4),(0,5),(1,15),(2,27),(2,29),(3,1),(3,28),(3,31),(4,2),(4,22),(4,23),(5,3),(5,22),(5,23),(7,12),(8,11),(9,13),(10,14),(11,10),(12,9),(13,6),(14,6),(15,8),(16,12),(16,25),(17,25),(17,26),(18,13),(18,14),(19,17),(19,24),(20,7),(20,16),(21,16),(21,17),(22,29),(22,31),(23,27),(23,28),(24,11),(24,26),(25,9),(25,18),(26,10),(26,18),(27,19),(27,21),(28,20),(28,21),(29,19),(29,30),(30,7),(30,8),(30,24),(31,15),(31,20),(31,30)],32)
[4,4,3,3,2] => 110110100 => ([(0,3),(0,4),(1,15),(2,20),(2,22),(3,2),(3,30),(3,31),(4,1),(4,30),(4,31),(6,12),(7,10),(8,13),(9,14),(10,8),(11,9),(12,11),(13,5),(14,5),(15,6),(16,23),(16,25),(17,8),(17,19),(18,9),(18,19),(19,13),(19,14),(20,16),(20,24),(21,6),(21,26),(22,16),(22,29),(23,17),(23,18),(24,7),(24,25),(25,10),(25,17),(26,12),(26,27),(27,11),(27,18),(28,24),(28,26),(28,29),(29,7),(29,23),(29,27),(30,20),(30,21),(30,28),(31,15),(31,21),(31,22),(31,28)],32)
[4,3,3,3,3] => 101111000 => ([(0,6),(0,7),(1,2),(1,28),(2,9),(3,5),(3,24),(3,27),(4,30),(4,31),(5,4),(5,29),(5,32),(6,3),(6,23),(6,33),(7,1),(7,23),(7,33),(9,17),(10,14),(11,18),(12,19),(13,16),(14,13),(15,12),(16,11),(17,15),(18,8),(19,8),(20,18),(20,19),(21,12),(21,20),(22,11),(22,20),(23,10),(23,27),(24,25),(24,29),(25,17),(25,26),(26,15),(26,21),(27,14),(27,32),(28,9),(28,25),(29,26),(29,30),(30,21),(30,22),(31,16),(31,22),(32,13),(32,31),(33,10),(33,24),(33,28)],34)
[3,3,3,3,3,1] => 111110010 => ([(0,6),(0,7),(1,4),(1,23),(2,17),(3,2),(3,30),(4,3),(4,29),(5,24),(5,27),(6,1),(6,28),(6,31),(7,5),(7,28),(7,31),(9,15),(10,14),(11,16),(12,13),(13,11),(14,12),(15,8),(16,8),(17,9),(18,22),(18,26),(19,11),(19,21),(20,9),(20,21),(21,15),(21,16),(22,19),(22,20),(23,18),(23,29),(24,18),(24,25),(25,12),(25,26),(26,13),(26,19),(27,14),(27,25),(28,10),(28,27),(29,22),(29,30),(30,17),(30,20),(31,10),(31,23),(31,24)],32)
[3,3,3,3,2,2] => 111101100 => ([(0,5),(0,6),(1,17),(2,3),(2,30),(3,8),(4,2),(4,23),(4,32),(5,4),(5,29),(5,31),(6,1),(6,29),(6,31),(8,14),(9,12),(10,15),(11,16),(12,13),(13,10),(14,11),(15,7),(16,7),(17,9),(18,20),(18,21),(19,18),(19,26),(20,11),(20,22),(21,10),(21,22),(22,15),(22,16),(23,19),(23,28),(24,18),(24,27),(25,19),(25,24),(26,13),(26,21),(27,14),(27,20),(28,12),(28,26),(29,23),(29,25),(30,8),(30,27),(31,17),(31,25),(31,32),(32,9),(32,24),(32,28),(32,30)],33)
[6,6,5] => 110100000 => ([(0,6),(0,7),(1,10),(2,5),(2,24),(3,17),(4,3),(4,30),(5,4),(5,29),(6,2),(6,28),(6,31),(7,1),(7,28),(7,31),(9,15),(10,14),(11,16),(12,13),(13,11),(14,12),(15,8),(16,8),(17,9),(18,22),(18,26),(19,11),(19,21),(20,9),(20,21),(21,15),(21,16),(22,19),(22,20),(23,18),(23,25),(24,18),(24,29),(25,12),(25,26),(26,13),(26,19),(27,14),(27,25),(28,23),(28,27),(29,22),(29,30),(30,17),(30,20),(31,10),(31,23),(31,24),(31,27)],32)
[5,5,5,2] => 111000100 => ([(0,5),(0,6),(1,2),(1,30),(2,8),(3,4),(3,31),(3,33),(4,22),(4,23),(5,1),(5,24),(5,32),(6,3),(6,24),(6,32),(8,15),(9,12),(10,16),(11,17),(12,13),(13,10),(14,11),(15,14),(16,7),(17,7),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,16),(21,17),(22,18),(22,27),(23,18),(23,26),(24,25),(24,31),(25,9),(25,29),(26,13),(26,19),(27,14),(27,20),(28,15),(28,27),(29,12),(29,26),(30,8),(30,28),(31,23),(31,29),(32,25),(32,30),(32,33),(33,9),(33,22),(33,28)],34)
[5,5,4,3] => 110101000 => ([(0,4),(0,5),(1,17),(2,3),(2,27),(3,7),(4,1),(4,26),(4,31),(5,2),(5,26),(5,31),(7,12),(8,11),(9,8),(10,13),(11,14),(12,10),(13,15),(14,16),(15,6),(16,6),(17,9),(18,12),(18,22),(19,20),(19,21),(20,11),(20,23),(21,23),(21,24),(22,10),(22,24),(23,14),(23,25),(24,13),(24,25),(25,15),(25,16),(26,28),(26,29),(27,7),(27,18),(28,9),(28,19),(28,30),(29,18),(29,19),(29,30),(30,8),(30,20),(30,21),(30,22),(31,17),(31,27),(31,28),(31,29)],32)
[5,5,4,2,1] => 1101001010 => ([(0,3),(0,4),(1,17),(2,25),(2,26),(3,2),(3,36),(3,38),(4,1),(4,36),(4,38),(6,14),(7,10),(8,15),(9,16),(10,11),(11,12),(12,9),(13,8),(14,13),(15,5),(16,5),(17,7),(18,22),(18,23),(19,20),(19,21),(20,18),(20,33),(21,18),(21,32),(22,9),(22,24),(23,8),(23,24),(24,15),(24,16),(25,19),(25,28),(26,19),(26,27),(27,21),(27,30),(28,20),(28,31),(29,6),(29,30),(30,14),(30,32),(31,11),(31,33),(32,13),(32,23),(33,12),(33,22),(34,7),(34,29),(34,35),(35,6),(35,10),(35,31),(36,26),(36,34),(36,37),(37,27),(37,28),(37,29),(37,35),(38,17),(38,25),(38,34),(38,37)],39)
[5,5,3,3,1] => 1100110010 => ([(0,3),(0,4),(1,29),(1,36),(2,30),(2,31),(3,1),(3,32),(3,33),(4,2),(4,32),(4,33),(6,13),(7,14),(8,15),(9,16),(10,11),(11,12),(12,8),(13,9),(14,10),(15,5),(16,5),(17,20),(17,21),(18,17),(18,28),(19,17),(19,27),(20,9),(20,23),(21,8),(21,23),(22,6),(22,27),(23,15),(23,16),(24,19),(24,22),(25,18),(25,19),(26,18),(26,34),(27,13),(27,20),(28,12),(28,21),(29,26),(29,35),(30,25),(30,26),(31,24),(31,25),(32,7),(32,31),(32,36),(33,7),(33,29),(33,30),(34,6),(34,11),(34,28),(35,10),(35,22),(35,34),(36,14),(36,24),(36,35)],37)
[5,5,3,2,2] => 1100101100 => ([(0,3),(0,4),(1,35),(1,37),(2,34),(2,36),(3,2),(3,38),(3,39),(4,1),(4,38),(4,39),(6,12),(7,13),(8,14),(9,15),(10,8),(11,9),(12,10),(13,11),(14,5),(15,5),(16,20),(16,21),(17,16),(17,32),(18,16),(18,33),(19,17),(19,18),(20,8),(20,22),(21,9),(21,22),(22,14),(22,15),(23,17),(23,30),(24,18),(24,31),(25,6),(25,30),(26,7),(26,31),(27,6),(27,7),(28,19),(28,23),(29,19),(29,24),(30,12),(30,32),(31,13),(31,33),(32,10),(32,20),(33,11),(33,21),(34,25),(34,27),(35,26),(35,27),(36,23),(36,25),(37,24),(37,26),(38,28),(38,29),(38,34),(38,35),(39,28),(39,29),(39,36),(39,37)],40)
[5,4,4,4] => 101110000 => ([(0,6),(0,7),(1,3),(1,27),(2,18),(3,2),(3,30),(4,5),(4,31),(4,32),(5,25),(5,29),(6,1),(6,26),(6,33),(7,4),(7,26),(7,33),(9,12),(10,14),(11,17),(12,16),(13,15),(14,13),(15,11),(16,8),(17,8),(18,9),(19,12),(19,22),(20,19),(20,21),(21,11),(21,22),(22,16),(22,17),(23,9),(23,19),(24,20),(24,23),(25,20),(25,28),(26,10),(26,32),(27,24),(27,30),(28,15),(28,21),(29,13),(29,28),(30,18),(30,23),(31,24),(31,25),(32,14),(32,29),(33,10),(33,27),(33,31)],34)
[5,4,4,3,1] => 1011010010 => ([(0,3),(0,4),(1,34),(1,36),(2,33),(2,35),(3,2),(3,39),(3,40),(4,1),(4,39),(4,40),(6,14),(7,15),(8,16),(9,17),(10,12),(11,13),(12,8),(13,9),(14,10),(15,11),(16,5),(17,5),(18,21),(18,22),(19,18),(19,29),(20,18),(20,30),(21,8),(21,23),(22,9),(22,23),(23,16),(23,17),(24,19),(24,27),(25,20),(25,28),(26,19),(26,20),(27,10),(27,29),(28,11),(28,30),(29,12),(29,21),(30,13),(30,22),(31,14),(31,27),(32,15),(32,28),(33,24),(33,31),(34,25),(34,32),(35,6),(35,31),(36,7),(36,32),(37,6),(37,24),(37,26),(38,7),(38,25),(38,26),(39,33),(39,34),(39,37),(39,38),(40,35),(40,36),(40,37),(40,38)],41)
[5,4,4,2,2] => 1011001100 => ([(0,3),(0,4),(1,29),(1,36),(2,30),(2,31),(3,1),(3,32),(3,33),(4,2),(4,32),(4,33),(6,13),(7,14),(8,15),(9,16),(10,11),(11,12),(12,8),(13,9),(14,10),(15,5),(16,5),(17,20),(17,21),(18,17),(18,28),(19,17),(19,27),(20,9),(20,23),(21,8),(21,23),(22,6),(22,27),(23,15),(23,16),(24,19),(24,22),(25,18),(25,19),(26,18),(26,34),(27,13),(27,20),(28,12),(28,21),(29,26),(29,35),(30,25),(30,26),(31,24),(31,25),(32,7),(32,31),(32,36),(33,7),(33,29),(33,30),(34,6),(34,11),(34,28),(35,10),(35,22),(35,34),(36,14),(36,24),(36,35)],37)
[5,4,3,3,2] => 1010110100 => ([(0,3),(0,4),(1,17),(2,25),(2,26),(3,2),(3,36),(3,38),(4,1),(4,36),(4,38),(6,14),(7,10),(8,15),(9,16),(10,11),(11,12),(12,9),(13,8),(14,13),(15,5),(16,5),(17,7),(18,22),(18,23),(19,20),(19,21),(20,18),(20,33),(21,18),(21,32),(22,9),(22,24),(23,8),(23,24),(24,15),(24,16),(25,19),(25,28),(26,19),(26,27),(27,21),(27,30),(28,20),(28,31),(29,6),(29,30),(30,14),(30,32),(31,11),(31,33),(32,13),(32,23),(33,12),(33,22),(34,7),(34,29),(34,35),(35,6),(35,10),(35,31),(36,26),(36,34),(36,37),(37,27),(37,28),(37,29),(37,35),(38,17),(38,25),(38,34),(38,37)],39)
[4,4,4,4,1] => 111100010 => ([(0,6),(0,7),(1,3),(1,27),(2,18),(3,2),(3,30),(4,5),(4,31),(4,32),(5,25),(5,29),(6,1),(6,26),(6,33),(7,4),(7,26),(7,33),(9,12),(10,14),(11,17),(12,16),(13,15),(14,13),(15,11),(16,8),(17,8),(18,9),(19,12),(19,22),(20,19),(20,21),(21,11),(21,22),(22,16),(22,17),(23,9),(23,19),(24,20),(24,23),(25,20),(25,28),(26,10),(26,32),(27,24),(27,30),(28,15),(28,21),(29,13),(29,28),(30,18),(30,23),(31,24),(31,25),(32,14),(32,29),(33,10),(33,27),(33,31)],34)
[4,4,4,3,2] => 111010100 => ([(0,4),(0,5),(1,17),(2,3),(2,27),(3,7),(4,1),(4,26),(4,31),(5,2),(5,26),(5,31),(7,12),(8,11),(9,8),(10,13),(11,14),(12,10),(13,15),(14,16),(15,6),(16,6),(17,9),(18,12),(18,22),(19,20),(19,21),(20,11),(20,23),(21,23),(21,24),(22,10),(22,24),(23,14),(23,25),(24,13),(24,25),(25,15),(25,16),(26,28),(26,29),(27,7),(27,18),(28,9),(28,19),(28,30),(29,18),(29,19),(29,30),(30,8),(30,20),(30,21),(30,22),(31,17),(31,27),(31,28),(31,29)],32)
[4,4,3,3,3] => 110111000 => ([(0,5),(0,6),(1,2),(1,30),(2,8),(3,4),(3,31),(3,33),(4,22),(4,23),(5,1),(5,24),(5,32),(6,3),(6,24),(6,32),(8,15),(9,12),(10,16),(11,17),(12,13),(13,10),(14,11),(15,14),(16,7),(17,7),(18,19),(18,20),(19,10),(19,21),(20,11),(20,21),(21,16),(21,17),(22,18),(22,27),(23,18),(23,26),(24,25),(24,31),(25,9),(25,29),(26,13),(26,19),(27,14),(27,20),(28,15),(28,27),(29,12),(29,26),(30,8),(30,28),(31,23),(31,29),(32,25),(32,30),(32,33),(33,9),(33,22),(33,28)],34)
[3,3,3,3,3,2] => 111110100 => ([(0,6),(0,7),(1,10),(2,5),(2,24),(3,17),(4,3),(4,30),(5,4),(5,29),(6,2),(6,28),(6,31),(7,1),(7,28),(7,31),(9,15),(10,14),(11,16),(12,13),(13,11),(14,12),(15,8),(16,8),(17,9),(18,22),(18,26),(19,11),(19,21),(20,9),(20,21),(21,15),(21,16),(22,19),(22,20),(23,18),(23,25),(24,18),(24,29),(25,12),(25,26),(26,13),(26,19),(27,14),(27,25),(28,23),(28,27),(29,22),(29,30),(30,17),(30,20),(31,10),(31,23),(31,24),(31,27)],32)
[6,5,4,3,2,1] => 101010101010 => ([(0,1),(0,2),(1,22),(1,23),(2,22),(2,23),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,12),(8,13),(9,12),(9,13),(10,6),(10,7),(11,6),(11,7),(12,16),(12,17),(13,16),(13,17),(14,10),(14,11),(15,10),(15,11),(16,20),(16,21),(17,20),(17,21),(18,14),(18,15),(19,14),(19,15),(20,4),(20,5),(21,4),(21,5),(22,18),(22,19),(23,18),(23,19)],24)
[5,5,4,3,2,1] => 11010101010 => ([(0,2),(0,3),(1,14),(2,22),(2,29),(3,1),(3,22),(3,29),(5,8),(6,12),(7,5),(8,10),(9,6),(10,9),(11,13),(12,4),(13,4),(14,7),(15,17),(15,23),(16,12),(16,13),(17,18),(17,26),(18,21),(18,28),(19,20),(19,25),(20,11),(20,16),(21,19),(21,27),(22,15),(22,24),(23,5),(23,18),(23,26),(24,7),(24,17),(24,23),(25,6),(25,11),(25,16),(26,8),(26,21),(26,28),(27,9),(27,20),(27,25),(28,10),(28,19),(28,27),(29,14),(29,15),(29,24)],30)
[6,5,4,3,2] => 10101010100 => ([(0,2),(0,3),(1,14),(2,22),(2,29),(3,1),(3,22),(3,29),(5,8),(6,12),(7,5),(8,10),(9,6),(10,9),(11,13),(12,4),(13,4),(14,7),(15,17),(15,23),(16,12),(16,13),(17,18),(17,26),(18,21),(18,28),(19,20),(19,25),(20,11),(20,16),(21,19),(21,27),(22,15),(22,24),(23,5),(23,18),(23,26),(24,7),(24,17),(24,23),(25,6),(25,11),(25,16),(26,8),(26,21),(26,28),(27,9),(27,20),(27,25),(28,10),(28,19),(28,27),(29,14),(29,15),(29,24)],30)
[5,5,4,3,2] => 1101010100 => ([(0,3),(0,4),(1,19),(2,18),(3,2),(3,25),(3,32),(4,1),(4,25),(4,32),(6,8),(7,9),(8,10),(9,11),(10,14),(11,15),(12,6),(13,7),(14,16),(15,17),(16,5),(17,5),(18,12),(19,13),(20,22),(20,23),(21,28),(21,29),(22,14),(22,24),(23,15),(23,24),(24,16),(24,17),(25,26),(25,27),(26,12),(26,21),(26,31),(27,13),(27,21),(27,31),(28,8),(28,20),(28,30),(29,9),(29,20),(29,30),(30,10),(30,11),(30,22),(30,23),(31,6),(31,7),(31,28),(31,29),(32,18),(32,19),(32,26),(32,27)],33)
[5,4,4,3,2] => 1011010100 => ([(0,3),(0,4),(1,18),(2,25),(2,26),(3,2),(3,35),(3,38),(4,1),(4,35),(4,38),(6,15),(7,10),(8,16),(9,17),(10,11),(11,13),(12,14),(13,8),(14,9),(15,12),(16,5),(17,5),(18,7),(19,22),(19,23),(20,19),(20,32),(21,19),(21,31),(22,8),(22,24),(23,9),(23,24),(24,16),(24,17),(25,27),(25,29),(26,6),(26,29),(27,20),(27,33),(28,21),(28,30),(29,15),(29,33),(30,11),(30,31),(31,13),(31,22),(32,14),(32,23),(33,12),(33,32),(34,7),(34,28),(34,37),(35,26),(35,34),(35,36),(36,6),(36,27),(36,28),(36,37),(37,10),(37,20),(37,21),(37,30),(38,18),(38,25),(38,34),(38,36)],39)
[5,5,3,3,2] => 1100110100 => ([(0,3),(0,4),(1,35),(1,37),(2,36),(2,38),(3,1),(3,39),(3,40),(4,2),(4,39),(4,40),(6,15),(7,10),(8,16),(9,17),(10,11),(11,13),(12,14),(13,8),(14,9),(15,12),(16,5),(17,5),(18,21),(18,22),(19,18),(19,31),(20,18),(20,32),(21,8),(21,23),(22,9),(22,23),(23,16),(23,17),(24,19),(24,30),(25,27),(25,29),(26,6),(26,29),(27,20),(27,33),(28,19),(28,20),(29,15),(29,33),(30,11),(30,31),(31,13),(31,21),(32,14),(32,22),(33,12),(33,32),(34,10),(34,30),(35,24),(35,28),(36,24),(36,34),(37,7),(37,27),(37,28),(38,6),(38,7),(38,34),(39,25),(39,26),(39,35),(39,36),(40,25),(40,26),(40,37),(40,38)],41)
[5,5,4,2,2] => 1101001100 => ([(0,3),(0,4),(1,35),(1,37),(2,36),(2,38),(3,1),(3,39),(3,40),(4,2),(4,39),(4,40),(6,15),(7,10),(8,16),(9,17),(10,11),(11,13),(12,14),(13,8),(14,9),(15,12),(16,5),(17,5),(18,21),(18,22),(19,18),(19,31),(20,18),(20,32),(21,8),(21,23),(22,9),(22,23),(23,16),(23,17),(24,19),(24,30),(25,27),(25,29),(26,6),(26,29),(27,20),(27,33),(28,19),(28,20),(29,15),(29,33),(30,11),(30,31),(31,13),(31,21),(32,14),(32,22),(33,12),(33,32),(34,10),(34,30),(35,24),(35,28),(36,24),(36,34),(37,7),(37,27),(37,28),(38,6),(38,7),(38,34),(39,25),(39,26),(39,35),(39,36),(40,25),(40,26),(40,37),(40,38)],41)
[5,5,4,3,1] => 1101010010 => ([(0,3),(0,4),(1,18),(2,25),(2,26),(3,2),(3,35),(3,38),(4,1),(4,35),(4,38),(6,15),(7,10),(8,16),(9,17),(10,11),(11,13),(12,14),(13,8),(14,9),(15,12),(16,5),(17,5),(18,7),(19,22),(19,23),(20,19),(20,32),(21,19),(21,31),(22,8),(22,24),(23,9),(23,24),(24,16),(24,17),(25,27),(25,29),(26,6),(26,29),(27,20),(27,33),(28,21),(28,30),(29,15),(29,33),(30,11),(30,31),(31,13),(31,22),(32,14),(32,23),(33,12),(33,32),(34,7),(34,28),(34,37),(35,26),(35,34),(35,36),(36,6),(36,27),(36,28),(36,37),(37,10),(37,20),(37,21),(37,30),(38,18),(38,25),(38,34),(38,36)],39)
[6,6,5,4,3,2] => 110101010100 => ([(0,3),(0,4),(1,23),(2,22),(3,2),(3,30),(3,40),(4,1),(4,30),(4,40),(6,14),(7,15),(8,16),(9,17),(10,6),(11,7),(12,18),(13,19),(14,8),(15,9),(16,12),(17,13),(18,20),(19,21),(20,5),(21,5),(22,10),(23,11),(24,33),(24,34),(25,27),(25,28),(26,35),(26,36),(27,18),(27,29),(28,19),(28,29),(29,20),(29,21),(30,31),(30,32),(31,10),(31,24),(31,37),(32,11),(32,24),(32,37),(33,14),(33,26),(33,39),(34,15),(34,26),(34,39),(35,16),(35,25),(35,38),(36,17),(36,25),(36,38),(37,6),(37,7),(37,33),(37,34),(38,12),(38,13),(38,27),(38,28),(39,8),(39,9),(39,35),(39,36),(40,22),(40,23),(40,31),(40,32)],41)
[6,5,5,4,3,2] => 101101010100 => ([(0,3),(0,4),(1,22),(2,29),(2,30),(3,2),(3,46),(3,50),(4,1),(4,46),(4,50),(6,18),(7,11),(8,20),(9,21),(10,17),(11,12),(12,19),(13,14),(14,16),(15,13),(16,8),(17,9),(18,15),(19,10),(20,5),(21,5),(22,7),(23,26),(23,27),(24,34),(24,41),(25,24),(25,39),(26,8),(26,28),(27,9),(27,28),(28,20),(28,21),(29,25),(29,37),(30,6),(30,37),(31,23),(31,36),(32,23),(32,38),(33,31),(33,42),(34,32),(34,40),(35,44),(35,45),(36,17),(36,27),(37,18),(37,39),(38,16),(38,26),(39,15),(39,41),(40,14),(40,38),(41,13),(41,40),(42,10),(42,36),(43,7),(43,35),(43,49),(44,33),(44,34),(44,48),(45,12),(45,33),(45,48),(46,30),(46,43),(46,47),(47,6),(47,25),(47,35),(47,49),(48,19),(48,31),(48,32),(48,42),(49,11),(49,24),(49,44),(49,45),(50,22),(50,29),(50,43),(50,47)],51)
[5,5,5,4,3,2] => 11101010100 => ([(0,4),(0,5),(1,21),(2,3),(2,34),(3,8),(4,1),(4,33),(4,41),(5,2),(5,33),(5,41),(7,16),(8,15),(9,10),(10,7),(11,9),(12,17),(13,12),(14,13),(15,14),(16,18),(17,19),(18,20),(19,6),(20,6),(21,11),(22,37),(22,38),(23,15),(23,28),(24,26),(24,27),(25,12),(25,30),(26,16),(26,31),(27,30),(27,31),(28,14),(28,29),(29,13),(29,25),(30,17),(30,32),(31,18),(31,32),(32,19),(32,20),(33,35),(33,36),(34,8),(34,23),(35,11),(35,22),(35,39),(36,22),(36,23),(36,39),(37,24),(37,29),(37,40),(38,10),(38,24),(38,40),(39,9),(39,28),(39,37),(39,38),(40,7),(40,25),(40,26),(40,27),(41,21),(41,34),(41,35),(41,36)],42)
[6,5,4,4,3,2] => 101011010100 => ([(0,3),(0,4),(1,20),(2,33),(2,34),(3,2),(3,49),(3,52),(4,1),(4,49),(4,52),(6,17),(7,12),(8,18),(9,19),(10,11),(11,13),(12,10),(13,16),(14,15),(15,8),(16,9),(17,14),(18,5),(19,5),(20,7),(21,28),(21,29),(22,30),(22,31),(23,24),(23,25),(24,21),(24,27),(25,27),(25,39),(26,21),(26,37),(27,28),(27,43),(28,22),(28,42),(29,22),(29,41),(30,9),(30,32),(31,8),(31,32),(32,18),(32,19),(33,23),(33,36),(34,23),(34,35),(35,25),(35,38),(36,24),(36,26),(37,29),(37,40),(38,6),(38,39),(39,17),(39,43),(40,13),(40,41),(41,16),(41,30),(42,15),(42,31),(43,14),(43,42),(44,11),(44,40),(45,10),(45,44),(46,7),(46,48),(46,51),(47,6),(47,37),(47,44),(48,38),(48,45),(48,47),(49,34),(49,46),(49,50),(50,35),(50,36),(50,48),(50,51),(51,12),(51,26),(51,45),(51,47),(52,20),(52,33),(52,46),(52,50)],53)
[6,5,4,3,3,2] => 101010110100 => ([(0,3),(0,4),(1,20),(2,32),(2,33),(3,2),(3,49),(3,52),(4,1),(4,49),(4,52),(6,17),(7,10),(8,18),(9,19),(10,12),(11,13),(12,11),(13,15),(14,16),(15,8),(16,9),(17,14),(18,5),(19,5),(20,7),(21,24),(21,25),(22,29),(22,30),(23,21),(23,27),(24,26),(24,28),(25,26),(25,44),(26,22),(26,41),(27,25),(27,43),(28,22),(28,42),(29,8),(29,31),(30,9),(30,31),(31,18),(31,19),(32,23),(32,34),(33,23),(33,35),(34,27),(34,40),(35,21),(35,36),(36,24),(36,37),(37,28),(37,39),(38,6),(38,45),(39,14),(39,42),(40,12),(40,43),(41,15),(41,29),(42,16),(42,30),(43,11),(43,44),(44,13),(44,41),(45,17),(45,39),(46,7),(46,48),(46,51),(47,6),(47,37),(47,45),(48,36),(48,38),(48,47),(49,33),(49,46),(49,50),(50,34),(50,35),(50,48),(50,51),(51,10),(51,38),(51,40),(51,47),(52,20),(52,32),(52,46),(52,50)],53)
[6,5,4,3,2,2] => 101010101100 => ([(0,3),(0,4),(1,18),(2,22),(2,23),(3,2),(3,45),(3,46),(4,1),(4,45),(4,46),(6,15),(7,13),(8,16),(9,17),(10,11),(11,14),(12,10),(13,9),(14,8),(15,12),(16,5),(17,5),(18,6),(19,9),(19,21),(20,8),(20,21),(21,16),(21,17),(22,30),(22,34),(23,6),(23,34),(24,33),(24,44),(25,19),(25,20),(26,7),(26,39),(27,29),(27,37),(28,27),(28,36),(29,25),(29,35),(30,28),(30,38),(31,32),(31,43),(32,26),(32,41),(33,31),(33,42),(34,15),(34,38),(35,14),(35,20),(36,10),(36,37),(37,11),(37,35),(38,12),(38,36),(39,13),(39,19),(40,30),(40,33),(40,44),(41,7),(41,25),(41,39),(42,27),(42,32),(42,43),(43,26),(43,29),(43,41),(44,28),(44,31),(44,42),(45,22),(45,24),(45,40),(46,18),(46,23),(46,24),(46,40)],47)
[6,6,5,4,3,1] => 110101010010 => ([(0,3),(0,4),(1,22),(2,29),(2,30),(3,2),(3,46),(3,50),(4,1),(4,46),(4,50),(6,18),(7,11),(8,20),(9,21),(10,17),(11,12),(12,19),(13,14),(14,16),(15,13),(16,8),(17,9),(18,15),(19,10),(20,5),(21,5),(22,7),(23,26),(23,27),(24,34),(24,41),(25,24),(25,39),(26,8),(26,28),(27,9),(27,28),(28,20),(28,21),(29,25),(29,37),(30,6),(30,37),(31,23),(31,36),(32,23),(32,38),(33,31),(33,42),(34,32),(34,40),(35,44),(35,45),(36,17),(36,27),(37,18),(37,39),(38,16),(38,26),(39,15),(39,41),(40,14),(40,38),(41,13),(41,40),(42,10),(42,36),(43,7),(43,35),(43,49),(44,33),(44,34),(44,48),(45,12),(45,33),(45,48),(46,30),(46,43),(46,47),(47,6),(47,25),(47,35),(47,49),(48,19),(48,31),(48,32),(48,42),(49,11),(49,24),(49,44),(49,45),(50,22),(50,29),(50,43),(50,47)],51)
[6,5,5,4,3,1] => 101101010010 => ([(0,3),(0,4),(1,49),(1,51),(2,48),(2,50),(3,2),(3,52),(3,53),(4,1),(4,52),(4,53),(6,18),(7,19),(8,20),(9,21),(10,12),(11,13),(12,16),(13,17),(14,10),(15,11),(16,8),(17,9),(18,14),(19,15),(20,5),(21,5),(22,28),(22,29),(23,24),(23,25),(24,22),(24,40),(25,22),(25,41),(26,24),(26,42),(27,25),(27,43),(28,8),(28,30),(29,9),(29,30),(30,20),(30,21),(31,23),(31,26),(32,23),(32,27),(33,26),(33,44),(34,27),(34,45),(35,33),(35,38),(36,34),(36,39),(37,31),(37,32),(38,14),(38,44),(39,15),(39,45),(40,16),(40,28),(41,17),(41,29),(42,12),(42,40),(43,13),(43,41),(44,10),(44,42),(45,11),(45,43),(46,18),(46,38),(47,19),(47,39),(48,35),(48,46),(49,36),(49,47),(50,6),(50,46),(51,7),(51,47),(52,48),(52,49),(52,55),(52,56),(53,50),(53,51),(53,55),(53,56),(54,31),(54,32),(54,33),(54,34),(55,6),(55,35),(55,37),(55,54),(56,7),(56,36),(56,37),(56,54)],57)
[6,6,5,3,2,1] => 110100101010 => ([(0,3),(0,4),(1,20),(2,32),(2,33),(3,2),(3,49),(3,52),(4,1),(4,49),(4,52),(6,17),(7,10),(8,18),(9,19),(10,12),(11,13),(12,11),(13,15),(14,16),(15,8),(16,9),(17,14),(18,5),(19,5),(20,7),(21,24),(21,25),(22,29),(22,30),(23,21),(23,27),(24,26),(24,28),(25,26),(25,44),(26,22),(26,41),(27,25),(27,43),(28,22),(28,42),(29,8),(29,31),(30,9),(30,31),(31,18),(31,19),(32,23),(32,34),(33,23),(33,35),(34,27),(34,40),(35,21),(35,36),(36,24),(36,37),(37,28),(37,39),(38,6),(38,45),(39,14),(39,42),(40,12),(40,43),(41,15),(41,29),(42,16),(42,30),(43,11),(43,44),(44,13),(44,41),(45,17),(45,39),(46,7),(46,48),(46,51),(47,6),(47,37),(47,45),(48,36),(48,38),(48,47),(49,33),(49,46),(49,50),(50,34),(50,35),(50,48),(50,51),(51,10),(51,38),(51,40),(51,47),(52,20),(52,32),(52,46),(52,50)],53)
[6,6,4,3,2,1] => 110010101010 => ([(0,3),(0,4),(1,18),(2,22),(2,23),(3,2),(3,45),(3,46),(4,1),(4,45),(4,46),(6,15),(7,13),(8,16),(9,17),(10,11),(11,14),(12,10),(13,9),(14,8),(15,12),(16,5),(17,5),(18,6),(19,9),(19,21),(20,8),(20,21),(21,16),(21,17),(22,30),(22,34),(23,6),(23,34),(24,33),(24,44),(25,19),(25,20),(26,7),(26,39),(27,29),(27,37),(28,27),(28,36),(29,25),(29,35),(30,28),(30,38),(31,32),(31,43),(32,26),(32,41),(33,31),(33,42),(34,15),(34,38),(35,14),(35,20),(36,10),(36,37),(37,11),(37,35),(38,12),(38,36),(39,13),(39,19),(40,30),(40,33),(40,44),(41,7),(41,25),(41,39),(42,27),(42,32),(42,43),(43,26),(43,29),(43,41),(44,28),(44,31),(44,42),(45,22),(45,24),(45,40),(46,18),(46,23),(46,24),(46,40)],47)
[6,6,5,4,3] => 11010101000 => ([(0,4),(0,5),(1,21),(2,3),(2,34),(3,8),(4,1),(4,33),(4,41),(5,2),(5,33),(5,41),(7,16),(8,15),(9,10),(10,7),(11,9),(12,17),(13,12),(14,13),(15,14),(16,18),(17,19),(18,20),(19,6),(20,6),(21,11),(22,37),(22,38),(23,15),(23,28),(24,26),(24,27),(25,12),(25,30),(26,16),(26,31),(27,30),(27,31),(28,14),(28,29),(29,13),(29,25),(30,17),(30,32),(31,18),(31,32),(32,19),(32,20),(33,35),(33,36),(34,8),(34,23),(35,11),(35,22),(35,39),(36,22),(36,23),(36,39),(37,24),(37,29),(37,40),(38,10),(38,24),(38,40),(39,9),(39,28),(39,37),(39,38),(40,7),(40,25),(40,26),(40,27),(41,21),(41,34),(41,35),(41,36)],42)
[5,4,4,4,3] => 1011101000 => ([(0,5),(0,6),(1,2),(1,36),(2,8),(3,4),(3,37),(3,38),(4,26),(4,35),(5,1),(5,39),(5,41),(6,3),(6,39),(6,41),(8,17),(9,12),(10,18),(11,19),(12,13),(13,15),(14,16),(15,10),(16,11),(17,14),(18,7),(19,7),(20,23),(20,24),(21,20),(21,32),(22,20),(22,33),(23,10),(23,25),(24,11),(24,25),(25,18),(25,19),(26,21),(26,30),(27,22),(27,31),(28,21),(28,22),(29,27),(29,34),(30,13),(30,32),(31,14),(31,33),(32,15),(32,23),(33,16),(33,24),(34,17),(34,31),(35,12),(35,30),(36,8),(36,34),(37,26),(37,28),(38,9),(38,35),(39,29),(39,38),(39,40),(40,9),(40,27),(40,28),(41,29),(41,36),(41,37),(41,40)],42)
[5,4,3,3,3] => 1010111000 => ([(0,5),(0,6),(1,2),(1,36),(2,8),(3,4),(3,37),(3,38),(4,26),(4,27),(5,1),(5,39),(5,41),(6,3),(6,39),(6,41),(8,17),(9,12),(10,18),(11,19),(12,13),(13,15),(14,16),(15,10),(16,11),(17,14),(18,7),(19,7),(20,23),(20,24),(21,20),(21,32),(22,20),(22,33),(23,11),(23,25),(24,10),(24,25),(25,18),(25,19),(26,21),(26,22),(27,21),(27,30),(28,22),(28,31),(29,9),(29,35),(30,14),(30,32),(31,13),(31,33),(32,16),(32,23),(33,15),(33,24),(34,17),(34,30),(35,12),(35,31),(36,8),(36,34),(37,27),(37,34),(38,26),(38,28),(39,29),(39,38),(39,40),(40,9),(40,28),(40,35),(41,29),(41,36),(41,37),(41,40)],42)
[4,4,4,4,2] => 111100100 => ([(0,5),(0,6),(1,3),(1,23),(2,16),(3,2),(3,30),(4,24),(4,31),(5,1),(5,29),(5,32),(6,4),(6,29),(6,32),(8,11),(9,12),(10,14),(11,15),(12,13),(13,10),(14,7),(15,7),(16,8),(17,13),(17,27),(18,27),(18,28),(19,12),(19,17),(20,14),(20,15),(21,9),(21,19),(22,8),(22,28),(23,25),(23,30),(24,19),(24,26),(25,18),(25,22),(26,17),(26,18),(27,10),(27,20),(28,11),(28,20),(29,21),(29,24),(30,16),(30,22),(31,9),(31,25),(31,26),(32,21),(32,23),(32,31)],33)
[3,3,3,3,3,3] => 111111000 => ([(0,8),(0,9),(1,7),(1,21),(2,4),(2,22),(3,17),(4,16),(5,6),(5,26),(6,3),(6,27),(7,5),(7,25),(8,1),(8,23),(9,2),(9,23),(11,13),(12,15),(13,12),(14,10),(15,10),(16,11),(17,14),(18,11),(18,20),(19,14),(19,15),(20,13),(20,24),(21,18),(21,25),(22,16),(22,18),(23,21),(23,22),(24,12),(24,19),(25,20),(25,26),(26,24),(26,27),(27,17),(27,19)],28)
[4,4,4,4,4] => 111110000 => ([(0,8),(0,9),(1,7),(1,23),(2,6),(2,22),(3,17),(4,16),(5,4),(5,29),(6,5),(6,27),(7,3),(7,28),(8,1),(8,24),(9,2),(9,24),(11,15),(12,13),(13,14),(14,10),(15,10),(16,11),(17,12),(18,20),(18,26),(19,18),(19,25),(20,13),(20,21),(21,14),(21,15),(22,19),(22,27),(23,19),(23,28),(24,22),(24,23),(25,12),(25,20),(26,11),(26,21),(27,18),(27,29),(28,17),(28,25),(29,16),(29,26)],30)
[5,5,5,5] => 111100000 => ([(0,8),(0,9),(1,7),(1,23),(2,6),(2,22),(3,17),(4,16),(5,4),(5,29),(6,5),(6,27),(7,3),(7,28),(8,1),(8,24),(9,2),(9,24),(11,15),(12,13),(13,14),(14,10),(15,10),(16,11),(17,12),(18,20),(18,26),(19,18),(19,25),(20,13),(20,21),(21,14),(21,15),(22,19),(22,27),(23,19),(23,28),(24,22),(24,23),(25,12),(25,20),(26,11),(26,21),(27,18),(27,29),(28,17),(28,25),(29,16),(29,26)],30)
[6,6,6] => 111000000 => ([(0,8),(0,9),(1,7),(1,21),(2,4),(2,22),(3,17),(4,16),(5,6),(5,26),(6,3),(6,27),(7,5),(7,25),(8,1),(8,23),(9,2),(9,23),(11,13),(12,15),(13,12),(14,10),(15,10),(16,11),(17,14),(18,11),(18,20),(19,14),(19,15),(20,13),(20,24),(21,18),(21,25),(22,16),(22,18),(23,21),(23,22),(24,12),(24,19),(25,20),(25,26),(26,24),(26,27),(27,17),(27,19)],28)
[5,5,5,5,5] => 1111100000 => ([(0,9),(0,10),(1,8),(1,28),(2,7),(2,27),(3,18),(4,19),(5,3),(5,34),(6,4),(6,35),(7,5),(7,32),(8,6),(8,33),(9,2),(9,29),(10,1),(10,29),(12,14),(13,15),(14,16),(15,17),(16,11),(17,11),(18,12),(19,13),(20,22),(20,23),(21,25),(21,26),(22,14),(22,24),(23,15),(23,24),(24,16),(24,17),(25,20),(25,30),(26,20),(26,31),(27,21),(27,32),(28,21),(28,33),(29,27),(29,28),(30,12),(30,22),(31,13),(31,23),(32,25),(32,34),(33,26),(33,35),(34,18),(34,30),(35,19),(35,31)],36)
[5,4,4,4,4] => 1011110000 => ([(0,7),(0,8),(1,3),(1,30),(2,21),(3,2),(3,35),(4,6),(4,31),(4,34),(5,37),(5,38),(6,5),(6,36),(6,39),(7,1),(7,29),(7,40),(8,4),(8,29),(8,40),(10,18),(11,15),(12,19),(13,20),(14,16),(15,14),(16,17),(17,12),(18,13),(19,9),(20,9),(21,10),(22,26),(22,28),(23,12),(23,25),(24,13),(24,25),(25,19),(25,20),(26,10),(26,32),(27,23),(27,24),(28,27),(28,32),(29,11),(29,34),(30,22),(30,35),(31,22),(31,36),(32,18),(32,24),(33,17),(33,23),(34,15),(34,39),(35,21),(35,26),(36,28),(36,37),(37,27),(37,33),(38,16),(38,33),(39,14),(39,38),(40,11),(40,30),(40,31)],41)
[5,5,5,5,1] => 1111000010 => ([(0,7),(0,8),(1,3),(1,30),(2,21),(3,2),(3,35),(4,6),(4,31),(4,34),(5,37),(5,38),(6,5),(6,36),(6,39),(7,1),(7,29),(7,40),(8,4),(8,29),(8,40),(10,18),(11,15),(12,19),(13,20),(14,16),(15,14),(16,17),(17,12),(18,13),(19,9),(20,9),(21,10),(22,26),(22,28),(23,12),(23,25),(24,13),(24,25),(25,19),(25,20),(26,10),(26,32),(27,23),(27,24),(28,27),(28,32),(29,11),(29,34),(30,22),(30,35),(31,22),(31,36),(32,18),(32,24),(33,17),(33,23),(34,15),(34,39),(35,21),(35,26),(36,28),(36,37),(37,27),(37,33),(38,16),(38,33),(39,14),(39,38),(40,11),(40,30),(40,31)],41)
Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
Map
poset of factors
Description
The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that $u < v$ if and only if $u$ is a factor of $v$.