1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
2
2
1
2
2
1
2
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
2
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
1
1
2
2
2
1
2
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
2
2
2
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
2
2
2
1
2
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
2
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
2
2
1
2
2
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
2
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
2
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
2
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
2
2
2
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
2
1
2
2
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
2
1
1
2
1
1
2
1
2
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
2
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
2
1
2
2
1
2
2
2
1
1
2
2
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
2
1
2
1
2
2
2
2
2
1
1
2
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
2
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
8
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
2
1
2
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
2
2
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
2
2
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
2
1
2
2
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
2
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
2
2
1
2
2
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
2
2
2
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
2
2
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
2
2
2
2
2
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
2
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
2
2
2
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
2
2
2
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
2
1
2
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
2
1
1
2
2
1
1
2
2
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
7
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
2
2
1
2
2
1
2
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
2
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
2
2
1
2
1
2
2
2
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
2
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
2
1
2
2
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
2
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
2
2
2
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
2
2
1
2
1
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
2
1
2
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
2
2
1
1
2
1
1
2
1
1
1
2
2
1
2
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
2
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
1
2
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
2
2
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
2
1
1
1
2
1
2
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
2
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
2
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
2
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
2
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
2
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
2
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
2
2
2
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
2
2
2
2
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
2
2
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
2
2
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
2
2
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
2
2
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
2
1
1
2
2
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
2
1
2
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
2
2
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
2
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
2
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
2
1
2
2
2
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
2
1
2
2
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
2
2
2
2
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
2
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
2
2
1
2
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
2
1
2
2
2
2
2
1
2
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
2
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
2
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
2
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
2
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
2
2
2
2
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
2
1
2
1
2
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
2
1
2
2
1
1
2
2
2
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
2
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
2
2
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
2
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
7
1
1
1
2
1
1
1
2
1
1
2
2
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
1
1
2
1
1
2
2
1
2
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
2
2
2
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
2
2
2
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
2
2
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
2
1
2
2
2
2
1
2
2
2
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
7
2
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
5
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
2
1
2
2
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
1
1
1
2
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
2
2
2
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
2
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
2
2
2
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
2
2
2
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
2
2
1
1
1
2
2
1
1
2
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
2
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
2
2
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
2
2
2
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
5
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
2
1
2
2
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
2
2
1
1
1
2
1
2
2
1
2
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
2
2
2
2
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
1
2
2
2
2
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
2
2
2
2
1
1
2
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
2
2
2
1
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
2
2
2
2
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
2
1
2
2
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
2
1
2
1
2
2
2
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
2
2
2
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
1
1
2
1
2
1
2
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
2
2
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
2
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
2
2
1
2
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
2
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
2
2
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
2
2
2
1
2
2
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
1
2
2
1
2
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
2
1
2
1
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
2
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
2
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
2
2
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
2
2
1
1
1
2
2
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
2
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
2
2
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
2
2
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
7
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
2
2
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
2
1
2
2
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
2
2
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
2
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
2
2
1
2
1
2
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
2
2
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
2
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
2
2
2
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
2
2
1
2
2
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
2
2
1
1
2
1
2
2
1
1
2
2
1
2
2
1
2
2
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
2
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
2
2
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
2
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
2
1
2
1
2
1
2
2
1
1
1
2
1
2
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
2
2
8
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
2
2
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
2
1
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
2
2
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
2
1
2
2
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
2
2
2
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
2
1
2
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
2
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
2
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
2
1
2
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
2
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
2
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
2
1
2
2
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
2
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
2
2
1
2
1
1
2
2
1
1
1
1
1
2
2
2
1
1
2
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
6
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
2
2
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
2
2
1
1
1
2
2
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
2
1
2
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
2
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
2
1
1
2
2
2
2
1
2
2
2
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
2
2
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
2
1
1
2
2
1
2
1
2
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
2
2
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
2
1
2
1
1
1
1
2
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
2
2
1
1
2
1
2
1
2
2
2
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
2
1
2
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
2
2
2
1
2
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
2
2
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
2
2
2
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
2
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
1
2
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
2
2
2
1
2
1
1
2
2
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
2
2
2
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
2
1
2
2
2
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
2
2
2
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
2
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
2
2
2
1
1
2
2
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
2
2
1
2
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
2
1
2
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
2
1
2
1
2
1
2
1
2
1
1
2
2
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
2
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
2
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
2
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
2
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
2
2
1
2
1
2
2
2
1
2
1
2
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
2
1
2
2
2
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
2
2
2
2
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
2
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
2
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
7
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
2
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
2
1
1
1
2
2
2
1
2
1
1
1
1
2
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
2
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
2
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
2
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
2
1
2
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
2
4
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
2
2
2
2
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
2
2
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
2
2
2
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
1
2
1
1
2
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
2
1
1
1
2
1
1
1
2
1
2
2
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
2
2
1
1
2
1
2
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
2
2
2
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
2
2
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
2
2
1
1
2
2
1
2
2
1
1
2
2
2
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
2
2
2
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
2
2
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
2
1
1
2
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
1
2
2
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
2
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
2
2
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
2
2
1
1
2
1
2
1
2
1
1
1
2
2
2
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
2
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
2
1
1
2
1
2
1
2
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
2
1
2
2
1
2
2
1
2
1
2
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
2
1
2
2
2
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
2
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
2
2
1
2
1
1
2
2
2
1
1
1
2
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
2
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
2
2
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
2
2
2
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
2
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
2
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
2
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
2
2
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
2
2
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
2
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
1
2
2
2
1
2
2
2
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
2
2
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
2
2
2
2
1
2
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
2
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
2
2
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
2
2
1
1
1
1
2
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
2
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
2
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
2
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
2
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
2
2
2
1
2
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
2
1
2
1
1
2
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
2
1
2
1
1
1
2
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
2
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
2
2
1
1
2
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
2
2
1
2
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
2
2
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
2
2
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
2
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
2
2
2
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
2
2
1
1
2
1
2
1
1
1
1
1
8
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
2
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
2
1
1
2
2
2
1
1
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
2
2
1
2
1
1
1
1
2
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
2
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
2
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
1
2
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
2
2
2
1
2
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
2
1
2
2
1
1
1
1
2
2
1
2
2
2
1
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
2
1
1
2
1
2
2
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
2
2
2
2
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
2
1
1
2
2
1
1
1
2
2
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
6
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
2
2
1
1
2
2
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
2
1
2
1
2
2
1
1
2
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
2
2
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
2
2
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
2
2
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
2
1
2
2
1
2
1
1
1
2
2
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
2
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
2
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
2
1
2
2
1
1
2
1
1
2
2
1
2
1
2
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
2
1
1
2
2
2
1
2
2
1
1
1
2
2
1
1
1
1
2
2
2
1
2
2
2
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
2
2
2
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
2
2
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
2
1
1
2
2
2
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
2
2
2
1
1
1
2
1
1
2
2
1
1
1
1
2
2
2
1
2
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
7
1
2
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
2
2
1
2
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
2
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
2
2
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
2
1
2
2
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
2
2
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
2
2
1
2
2
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
2
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
2
2
2
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
2
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
2
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
2
1
2
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
2
1
2
2
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
2
2
2
2
1
2
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
2
2
1
2
1
2
1
2
1
2
2
1
2
2
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
1
2
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
2
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
2
2
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
2
2
2
1
2
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
2
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
2
1
1
2
2
1
2
1
1
6
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
2
2
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
6
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
2
2
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
2
2
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
1
1
1
2
2
1
2
2
2
2
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
2
2
1
1
1
2
2
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
2
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
2
1
1
2
2
1
1
1
7
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
3
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
2
1
2
1
2
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
2
2
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
2
1
2
2
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
2
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
2
2
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
2
2
2
2
1
1
1
2
2
2
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
2
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
7
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
2
2
1
1
2
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
2
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
2
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
2
2
1
1
1
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
2
2
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
2
2
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
2
2
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
2
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
2
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
2
2
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
2
2
1
1
1
1
2
2
1
2
2
1
2
1
2
2
1
1
2
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
2
2
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
2
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
2
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
2
1
2
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
2
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
2
2
1
2
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
2
2
2
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
2
2
1
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
7
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
2
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
2
2
2
1
1
2
2
1
1
2
1
2
1
1
2
1
1
2
2
1
2
2
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
2
2
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
2
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
2
2
2
2
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
2
2
1
2
1
2
2
1
1
1
1
2
2
2
1
2
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
2
2
2
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
2
2
1
2
1
1
2
1
2
2
1
1
2
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
2
2
2
1
2
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
2
2
1
1
2
2
1
1
1
2
1
2
1
2
1
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
2
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
2
1
2
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
2
1
1
1
1
2
1
2
1
1
2
2
2
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
2
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
2
2
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
2
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
1
2
2
1
2
1
2
2
2
1
1
2
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
2
1
1
2
2
1
2
1
2
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
2
2
1
2
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
2
1
2
2
2
2
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
2
1
1
1
2
2
2
2
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
2
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
2
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
2
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
2
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
2
2
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1