petite-difference-challenge2/dev-0/out.tsv

1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
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
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
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
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
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
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
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
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
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
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
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
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
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
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
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
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
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
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
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
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
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
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
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
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
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
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
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
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
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
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
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
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
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
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
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
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
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
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
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
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
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
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
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
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
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
1
0
1
0
1
1
0
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
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
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
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
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
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
1
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
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
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
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
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
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
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
1
1
1
1
1
1
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
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
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
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
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
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
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
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
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
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
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
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
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
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
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
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
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
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
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
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
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
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
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
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
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
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
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
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
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
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
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
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
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
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
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
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
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
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
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
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
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
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
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
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
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
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
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
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
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
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
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
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
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
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
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
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
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
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
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
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
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
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
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
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
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
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
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
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
0
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
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
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
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
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
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
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
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
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
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
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
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
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
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
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
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
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
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
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
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
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
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
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
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
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
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
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
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
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
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
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
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
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
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
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
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
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
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
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
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
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
0
1
0
0
1
0
1
0
0
0
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
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
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
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
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
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
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
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
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
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
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
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
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
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
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
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
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
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
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
0
0
1
1
1
1
1
0
0
1
1
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
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
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
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
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
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
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
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
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
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
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
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
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
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
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
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
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
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
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
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
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
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
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
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
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
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
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
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
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
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
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
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
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
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
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
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
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
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
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
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
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
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
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
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
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
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
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
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
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
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
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
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
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
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
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
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
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
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
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
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
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
0
1
1
0
1
0
1
1
0
1
0
1
0
0
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
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
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
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
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
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
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
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
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
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
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
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
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
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
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
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
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
0
1
0
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
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
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
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
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
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
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
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
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
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
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
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
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
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
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
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
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
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
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
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
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
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
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
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
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
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
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
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
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
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
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
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
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
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
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
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
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
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
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
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
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
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
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
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
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
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
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
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
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
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
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
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
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
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
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
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
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
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
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
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
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
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
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
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
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
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
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
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
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
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
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
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
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
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
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
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
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
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
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
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
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
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
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
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
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
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
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
1
1
1
1
1
1
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
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
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
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
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
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
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
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
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
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
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
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
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
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
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
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
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
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
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
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
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
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
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
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
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
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
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
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
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
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
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
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
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
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
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
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
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
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
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
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
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
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
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
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
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
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
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
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
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
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
1
1
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
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
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
0
0
1
1
0
0
1
0
0
0
0
1
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
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
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
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
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
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
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
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
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
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
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
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
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
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
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
1
1
0
0
0
0
1
0
1
1
1
1
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
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
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
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
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
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
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
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
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
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
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
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
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
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
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
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
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
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
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
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
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
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
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
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
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
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
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
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
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
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
0
1
0
1
0
0
1
0
1
0
1
1
0
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
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
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
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
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
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
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
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
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
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
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
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
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
0
1
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
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
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
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
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
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
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
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
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
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
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
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
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
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
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
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
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
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
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
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
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
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
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
1
1
1
1
0
1
0
0
0
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
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
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
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
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
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
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
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
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
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
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
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
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
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
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
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
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
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
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
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
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
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
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
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
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
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
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
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
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
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
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
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
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
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
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
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
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
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
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
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
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
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
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
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
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
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
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
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
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
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
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
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
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
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
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
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
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
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
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
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
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
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
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
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
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
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
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
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
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
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
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
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
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
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
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
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
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
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
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
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
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
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
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
1
0
0
1
0
1
0
1
1
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
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
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
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
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
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
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
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
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
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
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
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
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
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
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
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
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
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
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
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
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
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
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
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
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
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
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
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
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
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
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
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
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
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
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
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
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
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
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
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
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
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
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
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
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
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
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
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
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
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
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
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
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
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
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
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
1
1
1
1
1
0
1
1
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
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
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
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
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
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
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
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
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
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
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
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
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
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
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
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
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
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
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
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
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
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
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
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
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
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
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
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
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
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
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
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
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
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
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
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
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
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
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
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
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
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
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
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
0
1
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
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
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
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
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
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
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
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
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
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
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
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
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
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
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
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
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
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
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
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
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
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
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
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
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
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
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
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
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
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
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
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
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
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
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
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
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
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
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
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
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
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
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
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
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
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
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
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
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
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
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
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
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
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
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
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
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
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
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
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
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
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
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
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
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
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
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
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
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
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
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
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
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
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
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
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
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
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
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
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
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
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
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
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
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
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
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
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
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
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
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
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
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
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
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
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
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
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
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
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
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
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
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
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
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
1
1
0
0
0
1
1
1
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
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
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
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
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
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
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
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
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
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
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
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
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
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
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
1
0
1
1
1
0
0
0
1
0
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
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
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
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
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
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
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
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
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
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
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
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
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
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
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
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
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
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
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
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
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
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
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
1
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
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
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
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
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
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
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
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
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
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
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
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
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
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
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
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
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
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
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
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
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
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
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
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
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
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
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
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
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
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
0
1
0
0
0
0
1
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
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
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
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
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
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
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
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
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
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
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
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
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
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
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
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
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
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
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
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
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
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
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
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
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
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1