Question5_output.txt

0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
2
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
1
1
1
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
0
1
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
2
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
1
0
0
0
0
1
2
1
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
2
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
1
1
0
0
0
1
1
1
2
0
2
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
2
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
4
5