TestResult18.txt

0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0