1
2
2
2
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
2
43
3
1
2
2
1
1
2
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
2
2
2
1
1
1
2
1
-1
-1
1
2
2
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
-1
1
1
2
2
1
1
3
2
1
1
1
1
2
1
3
1
2
1
1
1
1
1
2
1
2
1
1
-1
1
1
1
1
1
1
1
2
2
1
2
1
1
-1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
2
2
1
1
2
1
2
2
2
2
1
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
3
2
1
1
1
2
2
-1
2
2
1
2
1
1
2
2
1
1
1
2
1
1
2
2
1
1
2
2
1
1
2
1
1
2
2
1
2
2
1
1
2
2
2
2
1
1
1
1
1
1
-1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
-1
1
2
1
1
1
1
2
1
3
2
2
1
2
2
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
-1
1
2
2
1
2
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
-1
2
2
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
3
2
2
1
1
1
2
1
1
2
2
2
1
2
1
1
3
71
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
2
3
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
17
3
1
2
1
1
2
1
1
2
1
2
1
2
1
2
2
1
1
2
2
1
2
2
2
1
1
2
1
2
2
2
1
2
93
2
2
1
2
1
2
1
1
-1
2
1
2
2
1
1
2
2
1
2
1
1
1
2
3
2
2
2
1
1
2
1
2
2
1
2
2
1
2
2
2
1
3
1
2
2
2
1
1
1
1
2
1
1
-1
2
1
2
2
1
2
1
2
-1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
2
1
1
3
2
1
1
1
5
1
2
1
2
2
2
2
2
1
2
2
2
1
1
25
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
2
1
2
1
2
2
1
1
2
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
7
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
-1
1
1
2
1
2
2
1
1
1
2
1
1
7
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
2
2
2
1
2
2
2
1
2
2
2
1
3
2
1
2
2
2
1
1
2
2
2
2
2
1
1
2
1
2
2
1
1
2
1
1
2
2
1
1
-1
1
1
1
3
2
2
3
2
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
3
2
1
2
1
2
1
2
1
1
1
1
1
-1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
2
1
1
3
2
2
2
2
1
1
1
2
1
2
1
2
2
2
1
1
2
1
2
1
2
1
2
2
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
2
2
1
2
1
2
1
2
2
1
2
1
1
1
2
2
1
2
2
2
1
2
1
1
2
2
2
2
1
1
2
2
1
2
1
-1
1
1
2
1
1
2
2
3
2
3
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
3
2
1
2
1
2
1
2
-1
2
1
-1
2
2
43
2
1
2
2
-1
1
3
1
1
1
1
2
-1
9
2
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
2
2
1
1
-1
2
2
2
1
1
2
1
1
2
2
2
1
2
1
1
2
1
1
1
1
-1
1
3
1
1
1
2
1
1
1
1
1
2
1
2
2
-1
1
2
-1
1
2
1
2
2
2
1
2
1
1
1
1
2
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
15
2
1
2
1
5
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
2
2
1
2
1
1
2
1
2
1
1
2
1
2
2
2
2
2
2
1
1
1
2
1
2
2
3
1
1
1
1
2
1
1
2
1
2
2
1
2
1
2
1
1
1
1
2
2
2
1
2
-1
2
2
1
1
1
2
1
1
2
2
1
1
2
2
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
2
2
2
2
1
1
2
2
1
2
1
3
1
2
2
2
2
-1
1
2
2
1
2
2
2
1
1
1
2
2
1
2
3
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
3
1
1
2
1
1
2
2
2
1
1
2
2
1
1
2
2
2
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
2
2
-1
1
2
2
1
1
2
1
1
2
2
2
2
2
2
2
1
1
1
1
1
2
1
3
1
2
1
1
1
1
21
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
2
-1
2
1
1
1
1
1
1
-1
1
-1
1
2
1
1
2
-1
2
1
1
2
1
2
2
2
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
2
1
2
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
1
2
1
2
2
1
1
1
2
1
2
2
2
2
1
2
2
2
2
3
2
1
1
1
1
1
2
1
1
1
2
2
1
2
3
2
2
-1
1
1
2
2
1
1
2
2
1
1
-1
2
2
2
2
1
1
1
5
1
1
2
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
2
2
1
1
1
1
2
2
2
1
2
2
1
2
-1
1
1
1
2
1
2
-1
1
2
2
-1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
2
1
1
1
-1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
-1
1
2
1
2
1
2
1
2
1
2
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
2
2
2
-1
11
1
1
1
2
1
-1
1
2
1
2
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
2
2
2
1
2
1
19
1
2
2
2
2
1
1
2
2
1
1
1
1
2
2
1
2
1
2
2
2
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
9
1
1
2
2
2
2
2
2
1
2
2
1
1
1
2
2
2
2
2
1
2
1
2
1
1
1
1
1
2
2
2
1
3
1
1
1
1
2
2
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
2
2
2
2
2
2
1
1
-1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
2
2
1
2
3
1
1
1
2
1
1
2
3
2
3
2
1
2
2
2
1
2
2
2
1
2
2
1
1
2
1
2
1
1
2
3
2
2
2
2
1
1
2
1
2
2
1
1
1
1
1
-1
2
1
1
2
2
2
1
2
2
2
2
1
1
2
1
1
2
3
1
1
1
2
3
1
2
2
2
2
1
1
2
2
2
2
1
1
1
1
2
1
-1
-1
1
1
1
2
1
1
1
2
2
2
1
2
1
2
2
1
2
2
1
1
-1
1
1
2
2
1
2
2
2
1
2
1
1
2
2
1
2
2
1
1
1
2
2
2
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
2
2
2
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
3
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
2
1
1
1
2
1
2
1
1
2
2
1
2
2
1
1
1
1
-1
1
2
1
1
2
2
2
2
1
2
3
1
2
1
2
1
2
1
-1
1
2
2
2
1
2
1
2
2
1
3
1
1
2
2
1
1
2
2
2
1
1
2
2
1
2
1
1
2
2
2
1
2
1
1
1
1
2
1
2
1
-1
1
1
2
-1
1
2
1
1
1
1
2
1
-1
2
1
1
3
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
2
1
2
2
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
2
2
2
1
1
1
1
-1
2
2
2
2
2
2
1
1
1
2
2
1
2
1
2
1
2
2
2
1
1
2
2
1
2
1
1
2
2
1
2
1
1
-1
2
1
2
1
1
1
2
1
1
1
1
2
2
-1
1
2
2
1
1
2
1
2
2
1
1
1
1
2
1
7
1
2
2
2
2
1
1
1
1
2
1
-1
1
1
1
1
1
1
2
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
2
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
2
2
2
1
1
2
2
2
2
1
2
2
2
1
2
2
2
1
2
1
3
2
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
2
2
1
9
1
1
2
1
1
3
1
1
1
1
1
2
3
2
1
2
2
2
1
2
1
1
2
2
2
1
1
34
1
1
2
1
1
2
2
2
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
-1
2
1
2
1
2
1
2
2
1
1
2
2
2
2
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
3
2
2
1
2
1
2
1
1
1
1
2
1
1
25
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
2
2
2
2
1
2
1
1
2
2
1
1
2
1
1
-1
2
1
2
1
1
1
2
1
1
1
2
1
2
2
2
1
2
1
2
1
2
1
1
2
1
1
2
2
2
1
2
1
2
1
2
2
2
1
1
1
1
1
2
2
1
2
2
1
1
-1
-1
2
2
2
-1
2
2
1
1
2
2
2
1
2
1
2
1
2
1
1
2
2
1
1
2
1
1
2
1
2
2
2
-1
1
2
1
1
1
1
2
2
1
1
2
1
-1
1
1
2
1
1
1
2
7
2
1
1
1
1
2
2
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
3
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
3
2
1
2
2
2
1
-1
1
1
2
2
2
1
2
1
2
1
1
3
1
2
1
1
2
2
2
2
2
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
2
2
-1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
-1
2
2
1
2
2
1
1
1
1
1
2
2
2
1
2
2
2
2
1
2
1
2
1
1
2
2
2
1
1
2
1
1
2
2
1
2
1
2
2
2
2
2
1
1
2
2
1
2
2
1
1
1
2
2
2
2
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
2
2
2
1
2
3
3
1
3
1
1
2
1
2
2
2
1
1
1
1
1
2
1
2
2
2
1
1
3
1
1
1
1
1
1
1
1
1
1
3
2
1
2
2
1
1
1
2
2
1
2
2
2
1
2
1
1
1
1
2
2
2
2
3
1
2
1
2
2
2
1
1
2
1
1
2
2
3
2
1
1
2
2
-1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
3
-1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
-1
1
1
1
2
1
2
1
1
2
1
1
2
2
2
2
1
2
1
1
2
1
3
1
2
1
1
1
1
1
2
-1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
1
2
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
-1
2
1
1
2
2
1
1
1
3
1
1
2
2
2
1
1
3
1
2
2
1
2
1
1
2
2
2
2
2
1
1
2
2
2
1
2
2
2
1
2
2
2
1
1
2
2
1
2
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
-1
1
1
2
2
1
1
1
2
1
-1
2
3
1
2
2
2
1
1
1
2
1
2
2
1
2
1
2
2
2
2
1
1
1
2
1
-1
2
1
2
2
2
2
1
2
2
1
1
1
1
2
1
2
2
2
1
-1
3
2
1
1
1
2
1
1
1
3
1
1
2
2
1
2
2
1
2
1
1
2
2
1
2
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
-1
1
1
1
2
2
2
3
-1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
2
2
1
2
2
1
2
2
2
1
1
2
2
1
1
2
1
1
2
2
2
2
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
2
2
2
2
1
1
2
1
1
1
2
1
1
1
2
2
2
1
2
1
-1
2
1
2
2
1
2
1
3
2
1
1
1
2
1
11
1
2
1
2
2
3
2
1
2
2
1
1
1
2
1
2
1
1
1
1
2
2
1
3
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
2
2
2
2
1
2
1
2
2
1
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
3
2
1
2
1
2
1
2
2
2
2
3
1
2
1
1
2
1
-1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
3
2
1
1
3
2
1
1
1
2
1
1
1
2
1
-1
1
2
2
2
2
2
1
1
1
2
1
1
2
2
1
2
1
9
1
2
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
2
1
2
1
2
2
2
1
5
1
1
1
2
1
1
1
1
1
2
1
1
1
-1
1
2
2
-1
2
2
1
2
1
2
2
1
2
1
1
1
1
1
2
2
2
1
2
1
1
2
2
1
2
1
1
3
2
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
2
2
2
1
2
2
1
2
1
1
2
1
1
2
2
1
1
2
2
2
2
1
2
2
2
2
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
2
2
1
2
2
1
1
1
1
2
2
1
2
2
1
2
1
1
1
2
2
1
2
2
2
2
1
2
2
1
2
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
3
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
7
1
1
2
1
1
2
2
2
1
2
1
1
2
2
2
-1
2
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
2
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
1
2
2
1
1
2
2
2
1
5
2
1
2
1
1
2
6
2
3
1
1
2
2
1
1
2
1
2
2
2
2
2
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
2
2
2
2
2
2
1
2
2
2
1
1
1
1
2
2
2
2
1
1
2
2
2
3
2
1
2
1
1
2
2
2
2
2
1
1
1
1
2
2
1
1
-1
1
1
1
2
1
1
3
2
2
1
2
1
2
3
2
1
2
1
1
1
1
1
2
2
1
2
2
2
2
1
2
1
1
2
1
1
2
2
3
2
2
1
1
2
2
2
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
2
3
1
2
1
2
2
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
2
1
2
2
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
2
2
3
-1
1
1
2
-1
1
1
1
1
2
-1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
-1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
2
2
1
1
1
1
2
2
2
1
2
2
1
1
1
1
2
2
2
1
2
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
-1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
2
2
1
1
1
2
2
1
2
2
3
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
-1
1
1
1
2
1
2
2
1
1
2
2
1
-1
1
3
1
2
2
2
1
2
2
2
-1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
3
2
1
2
3
2
1
1
1
2
1
1
1
2
2
2
2
1
2
2
1
1
1
1
1
2
2
-1
1
11
1
1
2
1
2
2
2
1
2
1
1
2
2
2
2
1
2
2
1
2
1
1
1
2
1
2
2
2
-1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
3
1
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
2
2
2
1
1
2
2
1
3
1
1
1
2
1
2
1
1
1
2
1
2
2
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
2
2
1
1
1
2
1
1
2
1
1
2
2
1
2
1
2
2
-1
2
2
-1
2
1
3
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
3
2
-1
1
2
1
2
1
2
2
2
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
2
1
17
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
2
2
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
2
1
2
2
2
8
2
2
1
2
1
2
2
2
1
1
1
1
2
2
2
2
2
1
1
1
2
1
2
-1
1
1
2
1
1
2
2
2
1
2
2
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
2
11
1
2
1
2
2
1
1
2
2
1
2
37
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
2
2
1
2
1
2
2
2
2
1
2
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
7
1
1
1
3
1
2
1
1
1
1
1
2
1
1
2
2
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
-1
2
2
1
1
2
2
3
1
1
1
1
1
1
1
2
1
2
1
2
5
2
1
2
1
1
2
2
1
1
1
2
2
2
1
2
2
2
1
2
1
1
1
2
1
2
1
2
2
1
1
1
2
2
2
2
2
1
1
2
2
1
1
1
-1
1
1
2
2
2
1
1
1
3
2
2
2
2
2
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
2
2
2
1
1
-1
1
1
1
1
2
2
2
1
2
2
1
2
2
1
1
1
2
2
1
2
1
2
2
2
2
1
2
1
2
1
2
1
1
2
2
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
-1
1
1
2
1
1
1