paranormal-or-skeptic/train/expected.tsv
Jakub Pokrywka 756ef4277a first commit
2021-04-19 12:49:39 +02:00

566 KiB

1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1