Pathfinder library in zig
1,9,6,8,4,6,4,9,1,6,1,1,2,1,9,1,3,9,1,6,1,1,2,8,1,1,5,1,9,1,9,8,4,5,3,6,1,2,9,9,1,5,3,4,1,5,8,9,1,1,9,8,1,5,4,2,6,8,9,5,9,1,3,2,6,4,1,1,1,4,6,9,4,8,1,7,6,1,2,2,6,7,2,1,8,8,3,8,4,6,2,5,8,3,4,9,1,8,7,9
1,5,2,5,7,1,1,2,1,6,1,3,3,1,4,2,1,9,5,6,1,9,4,1,5,7,3,6,5,1,1,8,4,4,8,1,1,1,9,6,7,1,2,7,8,2,5,5,6,1,1,1,3,7,8,1,7,2,2,2,2,2,1,2,1,1,2,8,4,6,9,3,2,2,7,2,4,1,1,8,9,6,1,1,9,1,5,5,8,1,6,6,2,4,8,1,9,2,1,2
2,1,4,3,6,3,1,1,6,2,3,6,1,9,1,2,2,2,1,9,2,2,2,3,7,3,6,1,3,9,1,3,9,3,3,3,9,3,2,8,2,3,1,9,1,2,1,1,8,3,1,3,1,7,9,3,6,3,1,8,7,1,9,7,5,1,1,9,7,1,8,8,7,9,6,1,7,7,1,6,1,7,3,3,1,7,3,2,1,9,4,2,3,9,5,8,6,2,2,7
2,5,2,1,6,2,5,3,1,4,1,2,1,4,4,1,8,9,9,4,1,3,9,4,8,9,5,1,2,2,4,9,3,5,6,5,4,6,1,1,2,6,1,1,6,8,6,4,4,2,5,2,1,7,3,4,3,3,1,1,1,3,7,9,1,1,8,1,4,4,9,1,8,5,9,1,2,6,1,3,5,2,8,4,5,1,3,3,9,3,1,1,1,1,3,6,3,2,1,1
3,4,1,9,1,1,6,3,9,5,1,7,1,3,1,6,7,5,4,2,6,3,1,4,4,6,1,9,3,1,6,1,2,1,1,1,9,1,4,1,7,8,9,7,9,1,1,5,6,1,7,6,1,3,3,4,9,1,1,1,9,1,7,2,4,1,3,8,3,5,7,3,1,8,1,2,1,4,3,1,2,8,3,3,9,4,6,2,1,5,7,2,1,1,7,1,4,8,3,2
4,5,2,4,9,6,4,1,5,3,2,4,7,4,2,8,3,1,9,3,1,4,1,2,9,9,1,2,9,1,1,2,9,9,5,3,7,3,2,1,1,4,9,1,3,3,3,7,6,5,2,3,1,3,1,7,1,2,3,9,5,2,3,9,2,9,7,6,1,1,3,8,5,5,5,1,5,2,1,2,3,2,1,8,7,2,4,8,8,6,6,7,3,2,2,6,2,3,1,4
3,7,1,1,5,6,9,9,2,2,5,7,2,1,1,2,3,1,1,1,1,1,2,3,1,3,8,1,6,2,1,5,6,9,8,1,9,6,1,3,1,1,5,8,2,4,1,5,2,6,2,3,2,1,1,1,4,9,1,5,3,8,9,2,1,1,4,3,5,1,9,3,8,5,2,6,4,8,3,5,1,3,9,9,4,1,3,1,8,9,9,2,2,1,2,4,6,1,8,4
9,3,7,2,2,1,8,2,1,1,2,2,7,9,2,3,2,9,1,1,1,6,5,1,4,1,6,3,6,4,7,1,3,1,2,8,1,5,4,2,6,5,1,4,5,8,9,2,8,5,4,4,3,1,9,2,7,2,1,1,5,3,3,3,8,2,9,6,5,3,2,1,2,2,8,3,2,1,8,2,1,3,5,7,2,3,4,6,1,5,1,2,7,1,1,4,8,3,1,4
7,2,5,2,4,3,9,6,1,2,4,3,6,9,2,8,7,2,1,1,9,7,3,2,4,1,4,2,7,6,1,1,6,5,1,3,3,3,4,5,6,1,4,5,1,8,7,2,5,4,2,7,6,4,3,2,2,7,2,1,1,2,9,1,2,6,1,8,4,8,3,1,1,8,2,2,3,6,4,9,1,1,6,6,9,2,1,9,4,4,7,1,2,3,9,2,2,1,3,4
3,1,2,4,2,2,2,2,8,5,3,3,8,3,2,7,5,1,4,9,1,1,6,2,2,1,2,1,5,5,7,6,3,9,1,9,2,2,3,1,7,7,5,7,2,1,6,1,9,2,4,1,4,5,5,8,1,1,9,1,2,4,1,9,7,1,4,1,8,6,2,9,6,1,1,1,7,5,4,8,9,2,1,4,4,1,1,6,2,6,9,5,1,8,3,1,6,1,7,4
5,1,1,3,4,3,1,5,1,2,4,1,6,8,1,1,1,8,6,1,6,2,1,1,9,5,8,6,1,8,4,2,1,9,5,1,3,1,5,4,1,1,5,6,5,4,7,3,2,5,1,2,8,3,4,8,3,2,9,4,4,6,2,2,3,3,1,2,7,2,2,1,2,6,7,3,4,2,2,2,1,1,4,1,3,2,1,5,4,7,3,1,6,8,5,4,1,1,1,4
8,9,1,8,7,6,1,2,6,3,1,1,5,1,1,1,4,3,2,5,7,3,1,3,1,4,1,7,3,4,4,9,1,4,4,5,6,8,1,5,1,2,1,3,1,2,1,5,1,1,4,3,6,2,6,7,5,1,5,7,2,9,9,7,9,6,4,9,3,1,3,6,7,1,4,4,9,3,1,1,1,1,3,2,2,2,2,1,9,1,9,4,3,1,1,8,4,5,3,9
2,3,1,5,1,1,2,8,6,8,2,1,1,2,1,5,1,1,9,1,2,3,3,9,1,4,3,6,2,1,4,8,5,1,8,9,2,1,3,2,4,3,8,1,1,7,1,9,8,4,1,1,3,6,1,7,3,2,9,3,5,2,1,3,3,8,9,2,1,9,3,2,1,9,1,3,1,1,1,2,8,6,3,5,6,9,9,1,5,8,1,6,1,7,1,1,2,3,1,1
8,2,1,3,4,3,9,2,7,8,4,2,6,5,1,8,9,1,6,8,4,1,3,2,1,1,5,8,9,1,5,3,3,8,8,7,1,7,5,1,1,5,7,5,1,1,5,1,1,5,1,2,4,1,1,5,2,6,3,6,2,5,7,2,1,8,6,5,8,1,3,5,3,2,5,2,4,9,3,2,5,1,1,6,1,6,4,2,3,2,1,3,3,1,3,1,9,2,3,8
3,8,1,4,6,4,8,2,1,2,3,1,2,2,1,7,7,3,2,2,2,4,2,1,5,3,6,5,1,1,6,4,2,2,2,9,2,4,1,3,3,1,5,9,3,1,2,5,1,1,8,2,6,6,7,6,9,1,2,1,2,1,4,1,2,5,1,1,9,2,2,6,1,1,2,9,3,1,4,1,3,3,6,1,1,3,4,1,1,1,1,1,2,1,1,8,3,6,2,5
1,6,3,2,1,5,3,2,8,2,1,1,5,8,2,7,1,9,9,4,9,4,2,1,9,4,7,8,5,1,6,8,4,8,8,1,9,4,2,9,4,3,9,4,2,1,1,4,6,1,6,2,4,6,4,3,8,1,5,7,2,1,1,6,2,7,1,2,5,1,1,2,7,1,9,1,3,2,3,1,1,1,9,2,1,2,2,1,7,8,1,8,2,1,5,6,1,2,2,9
2,9,6,4,9,9,3,9,8,2,2,7,5,4,1,1,1,2,3,5,1,1,3,2,1,1,1,4,1,9,4,4,2,2,1,1,3,8,1,5,9,2,2,4,4,9,4,5,8,3,1,2,2,6,1,1,9,5,9,3,9,4,2,4,1,1,5,8,9,9,9,9,1,8,4,6,1,3,9,3,1,8,4,3,3,1,4,1,6,2,3,1,7,5,6,9,9,4,2,2
3,1,8,5,9,1,1,1,3,2,2,2,2,2,2,5,8,8,2,1,2,8,9,1,1,4,2,5,2,3,1,7,1,1,1,9,3,1,2,1,1,6,2,1,1,4,9,9,3,2,4,5,1,5,8,8,1,3,3,9,6,4,3,3,4,9,3,1,3,2,1,4,2,1,5,6,1,1,2,3,5,3,2,1,2,1,9,1,8,8,1,3,1,1,2,2,2,2,4,3
2,5,9,7,4,1,9,1,7,6,1,1,7,8,7,2,6,2,3,3,7,2,2,5,7,5,4,7,9,6,3,2,8,8,1,1,4,3,5,9,1,9,8,2,7,4,1,2,3,1,1,1,2,1,7,1,1,1,5,1,5,1,1,7,1,3,4,5,8,2,4,7,1,2,1,3,8,3,5,3,7,9,4,4,3,4,8,2,1,8,7,2,3,1,7,1,6,9,2,1
1,1,5,6,1,2,8,4,5,2,7,2,3,1,1,7,1,4,8,1,7,8,5,2,2,6,2,1,6,1,1,1,9,1,1,3,6,1,1,6,5,1,4,1,1,1,1,3,5,5,2,7,6,1,3,6,1,3,5,1,8,7,3,8,5,7,2,9,5,2,2,1,3,9,1,5,1,6,9,8,3,7,1,1,1,3,1,2,1,1,9,8,7,6,1,2,5,7,2,1
8,2,3,2,3,3,2,3,3,1,3,1,1,5,9,1,3,1,8,4,3,9,8,2,4,1,1,1,2,1,6,9,6,8,8,3,4,1,4,3,2,1,1,8,9,2,3,1,8,7,7,8,9,7,6,1,6,1,3,3,2,1,2,1,4,2,9,2,4,4,1,5,1,1,7,8,3,8,9,9,5,3,2,2,1,2,8,1,1,2,3,4,4,1,1,1,1,1,1,3
2,3,2,1,9,6,6,8,8,2,4,2,3,1,9,1,1,6,1,1,3,9,3,1,4,5,9,8,3,1,1,4,5,7,1,7,9,9,8,9,1,6,5,1,9,1,2,1,4,7,5,1,1,1,7,4,1,1,8,1,1,4,1,2,9,7,1,7,5,7,5,1,8,1,1,6,9,1,3,2,4,2,3,1,4,2,9,2,9,5,7,5,3,2,4,1,2,9,8,3
5,1,7,6,1,1,8,3,6,5,2,3,1,1,1,3,2,2,8,2,5,3,1,1,2,1,8,9,9,5,7,1,5,9,3,5,1,1,5,8,5,1,3,4,7,3,4,2,8,8,2,4,3,5,9,1,9,9,4,5,7,9,3,2,1,3,7,4,6,9,3,2,9,9,1,5,8,1,2,1,6,9,5,3,1,1,3,3,1,7,6,1,3,1,7,1,5,2,1,1
7,6,5,1,1,3,1,4,5,7,2,2,8,4,9,1,9,8,5,1,2,3,3,3,4,1,2,1,7,9,1,1,4,2,3,1,6,2,2,4,3,4,5,1,4,1,4,1,2,3,8,8,1,3,7,9,2,1,7,4,5,3,6,3,8,1,9,2,1,4,4,2,1,8,1,2,1,2,3,1,2,2,1,1,1,4,1,5,1,7,1,2,1,8,4,2,3,2,1,1
3,4,6,2,3,9,1,9,1,7,2,9,7,9,9,7,8,1,2,1,1,1,3,9,4,3,5,6,2,3,2,3,9,1,7,7,1,4,3,7,3,9,1,4,1,9,1,4,9,4,4,1,4,3,1,3,4,2,3,1,2,8,2,1,3,7,1,5,1,1,3,6,8,7,5,1,4,7,1,1,6,7,1,5,2,8,2,4,4,2,6,2,3,6,1,1,9,2,2,9
4,6,7,3,1,8,5,1,5,2,1,1,2,5,9,2,8,1,9,1,8,1,8,6,5,5,9,1,6,1,3,2,4,9,1,1,9,1,5,4,1,1,2,2,8,2,3,3,7,3,9,1,3,4,2,1,9,2,9,7,9,2,1,1,2,9,2,1,1,2,1,1,4,2,2,1,1,2,1,7,9,5,1,6,5,3,3,9,2,5,3,2,1,2,1,4,6,5,3,4
4,2,3,4,9,5,7,2,1,5,1,1,9,1,1,8,6,2,2,8,5,1,1,2,2,1,2,1,2,8,8,1,8,4,2,1,4,1,1,9,1,2,3,1,5,9,6,7,5,3,8,1,7,8,1,9,2,4,9,2,1,3,9,2,1,3,9,6,5,1,7,3,8,8,6,1,6,4,1,3,2,4,1,3,5,4,4,9,3,1,1,3,8,7,5,2,8,3,4,1
5,2,1,9,6,2,3,9,2,2,5,9,4,3,9,1,3,7,2,9,1,9,2,3,6,7,1,8,3,3,2,1,8,6,1,3,3,2,8,4,1,8,7,9,6,1,8,5,2,8,6,5,7,7,4,3,1,8,2,6,9,2,4,3,6,5,1,8,1,8,1,4,4,1,9,1,5,2,4,9,9,6,1,5,9,1,1,1,3,1,3,2,4,2,9,1,8,4,2,1
7,1,6,3,4,7,3,1,9,2,1,4,9,7,2,5,2,2,1,2,1,2,2,6,1,1,6,1,2,1,1,4,5,1,2,1,2,2,1,3,3,1,2,9,8,9,1,1,1,2,3,3,5,1,4,9,3,3,3,3,1,9,9,1,2,4,3,9,1,3,2,9,1,4,1,1,7,2,6,8,2,8,4,4,2,2,9,5,1,9,2,9,1,8,3,3,6,1,4,1
9,1,2,2,1,2,1,5,2,2,3,4,2,1,5,8,3,5,5,1,1,4,5,9,1,2,2,9,4,1,8,9,5,4,4,1,1,9,2,9,5,8,2,1,3,3,4,6,6,6,7,1,8,1,1,4,2,5,7,2,5,9,8,5,3,1,3,5,1,9,7,9,6,5,4,3,5,1,3,4,5,9,1,8,8,2,2,9,9,9,1,4,1,1,9,1,9,2,1,9
1,7,9,2,3,2,1,4,8,1,1,6,8,1,7,5,5,1,5,5,8,3,2,1,1,9,1,4,3,5,5,1,1,9,4,2,5,2,3,6,1,1,3,4,3,8,2,1,7,2,5,5,8,1,1,3,2,7,5,4,8,8,1,8,5,3,3,4,3,9,1,1,8,1,1,2,2,2,5,6,4,7,9,9,2,4,1,1,8,9,4,3,1,1,2,2,1,9,4,2
6,2,3,5,9,6,1,5,2,1,3,6,2,3,6,2,3,3,1,1,4,6,9,5,7,1,1,8,4,1,7,1,3,4,1,9,5,2,2,1,3,7,2,1,1,5,1,7,4,3,3,3,5,6,2,1,1,4,5,7,7,9,2,1,4,5,3,1,2,5,9,1,5,9,7,6,3,1,7,1,2,9,2,4,8,1,2,6,3,3,1,1,7,6,5,1,4,5,2,2
1,3,1,5,3,2,2,1,7,4,6,5,1,1,1,9,9,2,7,4,1,1,8,5,3,8,6,1,3,1,3,1,1,8,3,1,8,5,2,1,8,5,1,6,3,7,5,1,2,4,1,7,7,7,9,1,7,1,1,4,1,5,4,9,4,6,8,4,9,1,2,1,6,9,1,8,1,5,1,4,7,7,1,9,6,1,2,1,5,8,3,9,8,1,6,3,1,7,5,5
3,9,4,1,5,1,2,4,4,2,3,3,3,1,3,1,7,3,3,9,6,4,9,3,8,1,4,1,1,3,1,3,3,2,1,8,1,1,8,7,1,7,2,1,2,1,9,1,1,1,3,5,9,1,9,7,5,2,6,3,7,3,3,9,8,1,2,9,9,1,5,1,3,2,3,1,4,1,1,2,1,2,5,9,6,2,5,5,6,2,3,6,1,1,1,1,3,5,3,9
4,2,2,1,4,1,1,7,8,3,2,2,1,1,8,1,6,2,2,9,4,8,6,9,2,3,5,1,1,6,4,3,1,2,6,3,9,5,1,1,9,1,1,5,9,2,5,2,1,1,2,8,1,1,9,2,1,1,7,3,9,9,4,1,2,4,4,4,2,7,4,7,1,1,1,1,8,9,2,9,2,5,5,7,1,1,3,1,1,9,2,5,7,3,4,3,9,9,1,9
1,1,7,9,1,9,6,1,1,5,2,1,2,2,5,1,2,6,1,6,2,9,5,1,3,3,1,2,9,9,1,6,1,4,7,9,4,1,6,1,9,8,3,4,4,1,1,1,2,2,5,9,2,6,1,1,3,7,2,5,6,5,1,1,9,1,5,7,2,3,1,1,8,3,1,9,3,3,2,7,3,9,1,4,2,1,5,3,9,2,2,1,2,3,1,4,3,1,1,7
4,2,3,1,7,1,1,3,9,5,2,1,6,2,1,2,8,1,9,8,7,5,4,2,3,8,2,3,2,1,2,7,1,1,1,6,1,1,9,6,1,1,1,8,2,7,5,3,3,2,2,4,9,3,2,1,9,7,9,4,1,8,5,9,7,3,1,1,1,1,4,4,2,8,9,9,6,1,4,5,2,4,4,8,3,2,2,8,5,2,7,6,1,7,3,8,6,3,7,8
3,9,1,8,2,4,6,3,1,7,2,8,3,5,1,5,3,2,9,1,5,8,1,2,9,1,9,7,3,7,4,3,1,1,3,2,1,2,1,1,7,1,4,1,1,1,8,3,2,1,1,7,9,6,7,2,5,4,2,7,2,1,2,2,1,1,6,5,1,8,7,3,1,2,1,3,3,4,1,1,1,7,9,4,8,1,8,2,1,1,4,2,1,1,2,2,4,8,4,7
2,9,2,3,8,1,8,1,4,7,3,5,9,8,1,7,2,6,4,9,2,6,7,1,1,2,1,9,2,3,4,4,8,2,5,9,1,4,9,3,1,3,8,1,5,5,1,4,7,2,5,1,1,1,9,9,1,4,1,2,9,5,6,5,3,9,2,3,9,1,2,7,1,1,7,6,1,1,1,1,3,7,4,7,6,6,8,3,6,2,1,5,4,7,2,1,4,2,1,7
1,9,6,1,3,8,1,3,6,1,7,3,4,2,3,2,1,2,3,8,4,3,9,1,1,2,6,1,2,4,7,1,1,3,6,1,9,3,5,3,5,1,3,9,9,3,3,2,3,2,6,2,5,9,8,1,1,8,1,8,1,1,7,9,5,1,4,3,7,1,4,2,2,8,8,3,5,4,9,9,2,9,2,3,1,3,9,4,5,8,4,1,6,5,2,1,1,8,3,2
8,5,1,4,1,1,1,7,2,2,9,5,1,3,2,6,1,6,2,6,1,3,1,9,1,8,1,3,3,4,6,2,3,1,1,7,2,2,1,4,4,4,1,6,1,8,7,8,1,8,1,8,3,6,2,2,1,3,5,9,7,2,3,5,8,8,4,1,1,4,8,4,1,3,1,6,1,6,9,2,1,9,1,8,2,9,9,5,6,1,2,5,6,3,2,3,3,8,2,1
1,3,6,5,7,3,2,5,4,2,8,3,1,9,6,4,7,3,1,2,1,6,3,1,3,2,7,2,6,1,9,2,8,3,7,2,1,2,4,2,1,7,1,4,5,1,8,1,5,3,5,6,1,2,1,3,3,1,1,1,3,3,1,1,6,2,3,9,8,4,4,3,2,3,5,3,1,1,8,7,2,1,9,3,8,9,1,9,5,6,2,1,9,1,4,5,1,1,1,1
2,8,2,2,9,3,9,3,6,1,3,1,9,1,9,8,1,5,5,1,9,1,3,1,2,1,9,3,2,1,7,3,4,1,7,2,6,1,4,2,2,6,3,4,1,7,9,4,2,3,3,2,1,2,2,2,7,1,8,6,6,6,5,4,3,3,4,5,3,1,1,1,7,1,9,9,7,3,1,4,1,2,1,8,6,2,1,5,3,1,5,1,4,6,8,7,7,9,2,7
1,1,1,1,4,5,4,3,5,9,8,1,3,5,2,4,1,2,3,7,6,1,9,6,9,5,1,5,7,2,9,9,2,2,4,3,7,7,1,1,1,4,7,2,3,5,2,6,5,4,5,1,4,9,2,1,8,3,3,5,2,7,2,3,9,9,2,1,5,6,2,1,4,6,4,3,5,8,4,1,8,2,7,1,1,6,8,2,7,5,4,2,2,6,1,5,1,2,6,3
2,9,7,7,2,3,4,3,3,6,5,5,2,2,5,5,4,6,1,7,9,2,6,3,6,5,5,1,9,1,6,6,7,3,2,1,3,9,2,1,5,6,4,4,3,4,1,2,1,8,4,7,7,3,1,3,5,2,8,1,5,4,7,4,1,5,3,1,5,2,2,1,1,8,5,8,9,2,3,4,9,9,4,3,6,9,8,1,6,2,2,8,2,3,1,4,2,3,4,8
1,2,9,2,1,1,6,1,3,1,5,4,8,4,8,5,8,2,3,1,8,1,1,1,8,5,1,9,8,3,4,2,1,9,2,6,7,1,1,2,9,9,4,5,1,8,1,9,4,9,3,1,1,3,9,2,5,2,1,9,4,5,2,9,1,3,3,1,8,7,3,8,9,4,2,2,5,3,1,7,1,1,1,9,5,2,7,4,9,2,6,6,8,3,5,1,6,3,7,1
4,9,1,1,1,9,1,3,6,1,1,8,8,7,6,6,1,1,3,5,5,2,1,1,5,1,7,2,2,6,5,1,3,8,2,9,3,7,9,1,3,2,1,8,8,9,2,1,2,1,6,9,6,4,5,4,5,1,8,6,9,6,7,1,9,9,1,4,1,2,1,6,1,7,4,8,4,1,6,4,1,2,3,1,2,6,1,2,8,5,6,4,1,1,2,4,3,1,8,6
1,3,1,7,1,7,1,1,7,8,1,8,6,6,4,6,3,2,9,4,4,1,1,5,2,4,2,6,2,2,8,8,1,3,2,6,3,6,6,1,1,9,8,7,2,1,3,2,3,1,2,8,3,4,1,1,1,1,3,2,6,6,1,7,2,1,1,7,2,6,4,9,1,9,3,2,4,7,3,9,2,1,1,2,5,9,1,5,1,1,1,3,8,2,1,6,2,1,9,8
1,1,8,5,1,1,2,1,9,4,7,7,2,9,2,1,8,9,9,8,1,9,1,6,4,2,2,7,5,9,9,2,1,6,3,1,2,8,1,1,9,2,1,6,8,8,1,2,1,2,9,3,7,5,8,4,3,2,6,4,8,2,2,1,1,1,8,3,1,1,6,8,2,1,4,2,2,1,1,8,2,2,2,1,1,4,3,8,8,6,4,2,2,1,1,5,8,1,1,3
4,5,4,2,9,1,3,9,1,4,2,8,1,2,9,1,3,5,1,2,8,3,3,1,3,2,4,9,3,9,1,8,1,6,2,6,7,7,9,8,7,6,1,3,1,1,6,2,2,9,1,4,8,8,4,3,6,9,1,1,3,2,1,8,5,5,3,1,6,5,2,5,6,6,9,7,9,5,7,1,3,2,9,3,3,6,1,1,9,4,2,9,2,5,1,5,5,2,6,1
4,4,9,4,4,3,1,1,4,6,1,2,9,2,1,3,3,5,1,5,3,4,9,2,9,6,1,5,4,1,8,6,1,2,5,2,4,8,1,3,6,8,8,4,2,3,4,3,1,9,3,1,3,9,8,9,1,4,9,7,2,3,1,1,1,5,2,1,4,1,5,1,3,1,5,4,9,8,8,1,1,9,4,1,9,6,1,4,6,7,1,2,5,1,4,9,7,1,1,1
9,6,2,3,7,8,1,2,4,7,2,1,6,3,1,1,6,8,4,1,1,4,8,1,4,2,1,6,2,9,1,2,7,9,4,2,1,1,2,1,1,1,1,1,3,3,3,2,2,1,1,3,4,4,3,3,3,3,2,6,1,5,5,3,6,5,5,1,4,5,2,1,2,1,2,8,3,9,5,7,5,7,1,4,7,1,2,3,4,1,4,3,1,5,5,2,3,2,8,9
5,3,2,1,1,5,8,3,2,1,1,6,9,2,8,8,2,1,1,4,3,2,6,1,1,6,1,7,3,3,9,9,8,9,1,1,5,9,1,5,6,9,9,5,2,2,2,4,8,1,2,3,1,2,4,4,6,8,1,2,3,7,4,1,1,1,2,9,1,6,9,8,1,1,1,3,2,5,1,2,7,9,2,1,2,3,4,2,2,2,6,7,1,8,1,1,9,5,7,2
3,4,7,4,5,6,1,2,1,1,3,7,2,2,2,7,2,1,2,2,4,1,1,3,3,6,9,5,8,1,2,9,3,2,2,3,6,2,3,9,3,5,6,4,3,4,4,9,4,8,4,5,6,1,1,6,1,1,7,1,7,3,1,3,5,9,8,8,1,1,3,5,1,5,7,1,4,5,1,4,5,3,5,1,3,9,9,5,7,1,1,2,1,1,4,3,1,8,3,3
8,1,1,2,8,6,1,2,1,9,1,2,7,1,1,5,3,1,1,3,2,1,9,9,1,2,2,1,1,7,6,2,7,7,5,4,8,7,3,8,4,1,3,7,8,1,7,4,7,4,7,9,9,4,2,7,7,6,1,2,5,1,8,3,3,2,1,2,1,5,5,9,4,8,6,2,1,1,6,1,1,1,7,7,5,1,2,4,6,1,4,1,5,6,1,8,1,1,3,2
4,9,6,2,7,6,1,7,8,6,2,4,2,3,3,6,1,1,4,1,2,5,1,5,1,1,3,2,2,6,6,3,9,1,3,1,6,1,2,5,1,3,4,3,9,5,3,3,6,1,2,1,1,1,1,2,1,6,1,7,4,6,2,5,1,1,1,1,2,3,8,2,1,1,2,2,7,5,5,6,4,3,6,4,1,2,6,1,5,8,8,2,2,3,8,3,3,9,4,1
4,1,9,8,7,9,1,5,3,9,4,1,5,1,3,1,9,3,9,2,1,4,7,1,9,3,5,6,1,4,4,1,1,1,4,6,2,2,9,2,3,8,6,5,1,4,1,2,1,4,2,4,2,1,2,1,9,6,6,3,9,1,3,2,1,5,1,8,6,2,1,2,3,6,3,5,1,3,4,1,8,7,8,1,2,2,7,2,9,9,4,5,3,2,5,5,4,7,1,8
4,5,9,8,2,3,1,1,2,1,3,1,1,6,1,5,6,1,1,9,1,7,1,6,1,8,1,5,2,2,6,9,9,1,2,2,1,4,6,1,1,1,2,1,6,5,2,6,2,1,1,8,2,1,6,4,2,1,2,5,2,5,3,1,1,5,2,3,1,2,2,2,3,2,9,2,4,4,2,1,8,4,4,9,1,3,1,6,8,4,2,3,9,4,2,6,4,4,2,2
6,2,3,9,9,2,2,3,2,1,1,7,7,6,2,7,2,9,3,4,8,9,3,2,2,1,1,5,3,9,5,6,9,6,2,9,7,8,1,7,3,9,3,9,9,1,2,1,8,9,1,3,4,7,1,1,9,7,2,2,1,1,2,1,2,7,1,1,6,5,8,4,1,5,1,4,3,1,2,4,7,9,8,5,5,3,6,2,1,1,9,5,2,1,8,8,4,9,6,9
1,1,2,9,1,1,4,4,2,9,4,4,2,5,4,2,2,5,1,1,4,9,1,3,2,1,6,5,1,1,9,4,2,4,3,8,3,1,1,3,4,1,1,9,2,1,4,7,1,7,5,4,1,2,1,1,2,1,2,1,4,3,1,9,2,3,7,5,2,7,5,8,3,1,9,1,7,3,5,1,4,3,2,1,2,4,6,4,2,1,9,7,3,2,3,9,2,1,1,2
1,6,5,1,2,3,1,7,3,1,8,5,6,5,5,4,1,9,1,8,8,1,1,4,1,1,1,2,4,1,3,4,5,1,2,5,1,1,7,2,2,1,8,3,2,3,2,4,1,2,4,1,6,6,2,9,2,8,1,1,1,7,3,1,2,7,1,5,1,2,8,2,2,1,4,2,1,6,1,7,1,7,2,1,3,1,2,3,1,1,8,6,1,3,6,1,3,9,5,8
4,2,9,8,1,1,2,9,4,7,1,4,5,1,1,8,9,9,9,2,4,1,6,5,8,6,2,4,2,2,2,9,1,1,2,1,2,3,4,8,4,3,2,9,7,2,4,2,4,6,4,2,4,5,1,3,1,2,2,5,5,9,9,1,2,1,1,3,2,5,3,3,3,5,7,1,2,8,6,3,2,4,4,8,1,1,9,9,9,4,4,6,2,8,3,7,4,3,9,2
2,7,6,1,2,1,6,2,2,1,1,1,1,1,9,9,2,9,5,2,1,6,8,3,8,1,2,1,7,3,1,3,3,1,1,6,9,9,9,2,9,1,1,4,2,8,4,8,1,1,9,3,3,1,7,3,1,6,4,5,7,2,1,3,2,2,5,1,2,2,9,9,5,6,1,8,9,1,1,8,6,1,6,1,4,1,8,1,3,3,1,8,1,1,1,5,1,2,4,2
4,1,2,9,3,7,8,1,1,3,4,7,2,8,1,6,1,2,7,4,8,2,4,3,3,6,6,2,8,2,3,5,2,9,8,1,4,7,1,2,1,3,3,4,2,1,6,9,8,1,9,1,2,4,8,1,8,2,3,9,1,9,5,3,1,5,1,3,9,5,2,2,9,1,1,1,9,3,2,9,8,2,4,3,6,8,2,7,8,7,3,3,1,4,5,2,1,1,1,9
1,5,9,1,5,6,1,8,2,2,1,1,2,6,1,9,6,2,3,2,3,1,5,1,9,7,4,2,5,4,2,1,4,9,1,4,1,6,8,9,3,7,6,4,1,4,2,1,6,7,3,8,2,3,3,4,7,3,2,3,1,1,1,1,3,3,2,1,3,9,3,1,6,4,5,1,9,1,3,2,1,9,3,4,1,5,6,1,4,3,8,2,2,1,3,9,7,8,7,4
3,9,2,7,2,5,1,3,7,9,3,1,1,5,8,6,6,7,6,5,3,9,1,2,3,4,4,4,1,4,6,1,9,9,3,1,9,1,3,6,2,7,4,3,5,1,2,9,1,2,1,8,1,4,6,4,2,8,1,3,8,1,1,2,8,1,6,8,1,1,1,1,2,9,9,2,4,5,2,1,5,9,5,4,8,4,8,1,6,1,6,1,1,2,1,5,8,8,1,4
9,4,1,2,1,1,4,2,1,6,6,6,1,1,1,3,7,5,1,1,8,1,2,2,1,2,8,2,1,8,2,4,2,3,1,3,3,3,1,3,6,1,2,4,1,5,1,6,1,1,9,1,2,1,1,3,3,1,5,8,9,2,1,6,1,7,2,4,7,2,3,5,9,9,8,9,4,7,1,9,1,1,1,3,8,1,1,2,6,9,2,4,4,1,9,3,4,1,3,4
2,2,2,3,2,2,5,3,1,3,9,2,5,9,1,2,1,9,1,3,7,1,1,1,9,9,6,2,3,7,1,2,2,9,1,2,2,1,4,3,9,5,3,3,5,9,5,2,3,1,1,9,7,4,6,4,5,2,5,1,6,4,1,2,2,5,2,4,6,5,9,2,6,2,1,1,8,1,7,1,9,1,2,9,9,1,1,2,6,1,9,1,7,6,1,9,6,2,1,7
1,3,4,6,1,5,8,4,1,2,3,8,9,5,1,6,1,3,1,9,1,6,9,9,1,1,5,9,3,2,1,1,7,1,7,2,7,8,9,2,9,6,7,1,3,4,9,3,1,6,8,8,6,6,1,1,3,1,5,1,1,8,3,5,3,9,1,3,2,9,2,8,9,9,2,1,2,8,3,6,9,6,2,3,4,6,7,3,8,1,9,2,6,5,5,8,2,1,7,5
1,5,2,2,4,6,1,8,4,1,1,9,2,5,6,7,4,4,6,6,1,2,3,4,2,1,3,1,2,1,7,4,1,7,1,5,1,6,1,6,6,4,9,9,1,6,3,9,4,6,7,6,9,3,1,4,2,4,3,3,4,1,3,1,6,4,5,2,7,9,3,1,6,1,1,5,8,3,1,1,3,4,2,5,7,1,6,1,4,1,1,1,1,4,3,3,9,3,1,6
2,9,1,8,2,7,1,2,1,2,1,4,3,9,7,5,1,2,3,1,9,1,4,9,2,5,8,9,1,1,1,4,1,5,8,1,6,1,2,2,6,5,8,2,4,7,9,1,1,5,2,2,1,1,4,9,1,1,7,5,1,8,8,9,7,1,3,8,3,6,9,2,3,1,1,9,7,5,2,1,2,1,5,8,3,4,9,2,3,1,6,9,3,4,2,2,2,7,8,3
2,3,3,5,8,2,2,5,6,7,9,1,7,1,2,4,9,8,1,4,6,7,8,9,3,5,6,4,1,9,2,2,1,5,1,5,1,3,5,3,2,9,7,1,2,2,1,2,3,1,2,9,2,1,2,2,6,1,1,2,2,3,1,9,9,6,7,9,1,4,1,1,2,5,8,6,9,2,4,6,1,1,5,1,4,5,8,1,6,2,2,6,7,2,1,2,5,1,7,1
5,2,6,2,4,1,3,5,4,1,8,8,9,8,9,1,1,8,1,9,2,9,9,1,1,3,1,4,1,5,3,2,1,2,7,2,8,7,2,4,2,9,1,8,1,1,8,1,5,6,2,9,4,1,1,3,2,2,2,2,8,1,3,7,3,3,5,5,3,4,2,1,4,3,1,2,9,5,8,1,6,7,3,9,9,3,1,8,1,9,9,3,5,4,5,7,9,9,2,1
9,1,4,9,2,1,9,5,1,1,8,8,5,7,7,6,1,1,9,1,6,3,1,5,2,4,9,2,4,2,7,7,4,4,9,1,1,1,4,1,6,1,3,2,1,1,1,2,1,1,1,4,7,1,5,2,1,2,2,5,1,2,2,9,2,9,1,2,4,1,1,3,7,5,6,6,4,8,8,6,2,5,1,1,4,2,1,3,2,2,3,2,1,2,1,5,1,1,4,8
1,1,8,1,1,5,7,1,1,8,7,2,4,3,1,7,9,1,1,2,1,3,7,1,1,3,5,8,7,1,9,1,8,8,2,6,3,5,7,4,7,6,2,4,9,9,5,6,4,9,2,2,1,4,1,2,1,3,4,6,2,7,4,8,6,1,1,1,7,8,3,7,9,2,2,8,5,2,1,1,7,3,9,5,1,6,9,1,9,2,8,1,5,4,1,5,4,4,1,2
3,2,1,3,2,1,1,5,1,3,6,2,7,2,9,3,8,1,9,4,2,9,1,6,4,2,2,4,2,3,7,1,2,2,9,3,2,2,1,4,8,9,5,4,5,1,4,5,4,6,1,4,2,4,2,6,2,1,3,1,7,5,2,2,4,7,1,1,6,5,1,3,6,3,8,2,2,9,7,2,3,2,6,5,4,7,2,5,1,5,9,1,2,8,3,1,1,1,1,4
4,4,8,4,7,3,2,9,1,2,1,1,4,2,1,1,5,5,3,1,4,9,8,1,1,9,2,1,4,2,1,3,5,1,3,1,3,1,1,9,1,4,1,2,1,9,4,1,4,1,5,7,1,4,3,6,1,9,5,3,2,5,2,2,8,1,1,6,3,9,9,1,1,3,7,6,1,9,1,3,1,1,1,1,1,1,3,7,3,3,1,9,9,1,1,5,2,9,1,3
1,2,6,2,2,7,7,7,3,1,1,6,5,5,4,2,1,1,6,1,1,1,2,8,2,4,7,7,4,1,7,4,2,7,4,6,6,6,1,7,2,6,5,7,1,1,3,2,2,6,7,2,1,1,9,1,7,7,4,5,6,9,3,6,3,2,2,5,3,1,7,1,1,2,4,1,9,3,5,3,1,4,2,8,3,1,1,9,1,1,2,9,3,1,2,7,1,9,3,2
8,2,1,4,4,8,7,1,2,3,4,1,1,4,1,9,9,6,4,1,2,9,1,1,8,1,2,9,2,5,4,2,4,7,9,1,8,4,4,2,8,3,2,1,9,6,3,7,4,1,3,1,8,4,8,2,6,1,3,7,9,8,4,9,4,1,2,8,5,4,1,1,2,6,2,6,2,7,1,5,1,9,9,2,8,5,3,6,3,1,2,3,5,5,1,1,7,3,1,3
1,8,3,2,1,2,3,9,4,9,3,3,8,9,3,1,1,4,5,3,1,3,4,1,1,2,1,1,9,3,1,5,3,7,4,9,6,1,8,1,4,3,1,5,1,1,2,1,9,1,8,2,2,7,9,2,8,4,2,1,1,8,5,9,1,3,1,6,7,6,5,2,3,2,1,1,6,7,1,2,9,5,2,6,4,6,7,7,2,9,4,3,1,1,1,5,1,2,2,8
1,1,1,3,3,3,1,9,5,2,8,1,1,7,4,2,1,1,9,8,7,5,1,9,5,3,1,6,4,4,9,5,9,1,3,1,1,2,6,1,6,1,8,9,1,6,8,2,5,1,1,1,5,1,7,6,3,2,7,1,9,3,9,8,3,1,1,9,1,9,1,4,1,2,9,2,2,1,3,7,2,5,1,4,9,8,1,1,2,1,9,9,1,3,8,1,4,3,1,1
2,1,8,3,4,3,2,2,3,1,2,9,1,1,8,1,1,2,1,6,7,1,9,6,1,9,4,5,2,2,1,6,3,7,2,5,1,3,7,9,1,9,2,2,9,9,9,3,5,3,7,1,3,9,1,1,3,2,6,1,8,7,4,7,1,1,3,1,4,7,5,9,9,9,8,3,1,2,2,7,1,3,3,6,1,3,3,9,1,1,2,8,2,1,3,6,4,3,1,8
1,2,4,1,5,4,9,6,4,2,1,2,9,9,2,3,3,1,8,1,6,2,1,1,2,1,1,3,9,1,5,3,3,7,8,6,1,4,3,2,3,4,1,8,9,9,7,2,1,9,6,8,1,1,6,3,3,2,3,2,1,2,3,2,3,3,7,3,7,1,3,1,1,1,7,2,2,8,5,4,4,4,6,9,3,9,1,2,3,1,1,1,7,5,8,5,2,3,4,6
6,9,4,3,4,2,5,1,4,9,1,2,6,5,6,2,1,6,5,7,3,8,7,4,2,5,3,9,6,2,2,6,6,6,2,2,1,4,2,9,5,7,4,2,2,2,5,2,8,2,9,7,9,9,6,5,1,1,5,6,2,2,1,1,9,1,7,1,2,1,6,9,8,4,9,5,1,8,4,5,2,1,1,9,2,2,1,1,1,2,1,3,9,2,8,9,1,9,2,5
3,9,5,3,9,1,1,9,6,3,2,1,5,8,1,4,1,6,1,2,6,4,1,1,3,9,9,5,5,1,1,6,8,5,5,4,4,2,1,1,7,9,7,1,8,4,3,1,9,2,9,5,1,3,1,4,7,6,8,2,3,1,1,8,1,2,9,1,2,2,1,9,2,8,2,6,6,6,2,4,6,8,1,1,4,5,2,1,1,1,6,3,2,2,4,4,1,1,3,6
6,1,1,6,3,4,6,3,4,5,6,5,1,1,2,1,6,6,4,9,4,1,9,9,1,1,2,1,1,2,1,3,1,1,4,1,3,3,2,8,9,5,1,5,5,2,3,1,4,2,5,6,1,1,3,4,5,7,8,8,9,1,1,6,1,9,4,3,2,7,1,1,8,6,1,9,5,3,3,4,9,1,3,4,8,8,9,8,1,5,2,2,3,1,2,3,5,1,9,4
1,9,5,3,4,4,1,1,9,1,2,4,9,1,6,2,1,8,6,9,5,2,3,2,1,5,9,1,3,6,1,4,1,7,1,6,2,8,5,9,2,2,5,3,1,1,1,2,3,7,2,2,6,3,3,8,5,4,5,3,5,1,5,6,1,2,1,3,2,7,2,1,1,1,2,1,9,1,4,5,1,1,7,3,1,2,4,1,2,4,6,2,7,2,3,4,2,1,1,3
7,1,1,6,5,4,1,2,9,3,1,1,4,6,1,2,1,9,1,1,3,4,5,4,4,2,1,4,8,4,6,9,1,8,5,1,1,1,2,2,3,2,9,1,2,6,1,3,1,8,4,9,2,7,1,2,5,9,3,1,3,5,6,9,4,1,5,5,7,1,1,1,5,1,3,4,1,4,1,8,1,5,2,1,5,3,1,2,1,1,3,8,9,4,8,8,8,1,7,2
2,1,2,9,2,1,2,4,1,4,4,8,8,7,2,2,1,8,2,3,7,2,3,9,8,7,1,1,8,4,7,4,7,5,1,9,4,1,8,8,4,4,4,2,2,2,5,3,1,9,1,8,3,1,6,1,1,1,3,3,8,5,1,1,9,6,7,9,2,1,1,4,2,3,1,7,4,9,2,1,2,2,1,4,1,5,1,1,8,3,1,5,2,9,1,1,2,8,7,8
7,2,9,9,9,7,1,1,4,8,1,1,1,1,3,3,5,2,1,1,3,7,4,7,7,2,1,1,2,9,1,3,9,3,5,3,9,9,8,3,1,4,6,4,7,8,5,1,2,3,5,4,4,5,1,4,3,5,4,1,8,1,1,8,5,9,9,9,3,7,3,5,4,1,9,7,1,1,8,8,1,1,3,5,1,8,2,5,1,2,6,5,6,2,4,7,1,8,3,8
3,2,2,1,7,5,3,1,2,9,2,2,2,9,4,2,9,2,4,1,6,1,1,4,3,5,1,2,6,5,9,4,2,6,8,1,9,1,8,4,8,1,2,4,5,5,2,7,2,9,1,6,7,1,4,6,8,3,1,3,3,4,2,3,1,3,2,1,2,1,1,2,8,5,1,3,1,6,1,6,8,1,6,1,8,5,2,1,2,5,1,8,8,2,3,6,7,1,2,6
7,5,1,4,3,9,5,6,1,3,9,3,3,6,3,4,1,4,1,3,1,2,2,1,1,1,4,5,2,4,3,3,5,5,5,5,3,2,7,1,1,1,7,3,2,2,4,1,7,2,3,2,9,7,2,8,6,2,4,1,1,2,1,1,8,8,1,3,1,2,3,1,1,6,8,4,7,1,4,7,1,8,1,2,7,5,3,9,3,1,4,1,3,1,6,1,3,7,8,1
3,7,5,5,1,6,4,1,8,1,8,8,4,7,3,7,3,4,4,1,5,7,2,4,1,1,9,1,4,4,1,9,1,7,2,8,2,4,3,5,9,8,5,8,7,2,2,6,8,3,6,9,1,2,8,9,1,4,8,7,1,2,1,1,2,4,6,7,8,1,4,8,9,1,6,1,6,1,4,8,2,7,2,7,2,7,3,1,2,1,4,5,5,3,1,4,1,9,1,2
1,2,1,3,1,5,1,3,4,6,8,5,1,1,9,1,5,2,7,1,4,3,9,8,7,9,2,9,9,4,4,8,1,9,1,8,5,1,2,2,1,7,1,1,1,9,4,3,1,9,2,8,5,1,2,7,1,8,3,4,1,1,2,6,5,1,4,3,8,5,3,1,1,2,6,4,4,7,1,6,2,9,2,1,1,1,1,6,1,2,5,4,6,1,4,7,2,1,7,7
7,9,4,5,1,1,9,1,1,1,9,1,9,5,3,5,2,3,4,6,6,2,1,3,2,6,2,1,9,4,4,6,4,1,6,7,3,2,2,1,4,7,1,9,4,4,1,1,8,2,1,2,2,1,6,7,1,2,8,9,1,2,9,7,1,8,2,7,8,3,9,4,4,7,4,4,7,1,1,8,5,9,2,7,1,9,1,9,3,9,5,4,1,1,2,5,8,1,4,2
2,8,3,3,1,2,3,3,1,3,2,9,3,1,9,9,8,4,4,7,1,1,3,1,4,5,2,1,1,9,9,7,1,9,3,6,1,1,9,1,9,3,1,4,3,8,6,6,1,2,2,2,2,1,2,2,2,8,9,9,3,1,1,1,1,1,1,4,9,7,1,1,1,3,9,5,1,2,2,6,2,1,7,1,2,9,7,2,3,7,1,1,3,9,9,3,9,6,1,9
4,3,2,1,2,9,3,4,8,9,6,5,6,6,9,8,5,2,1,6,5,3,2,8,2,4,1,4,2,9,5,1,1,3,1,9,1,9,8,6,2,5,2,7,6,4,5,1,3,9,9,1,5,5,4,3,3,1,5,6,2,2,1,2,6,2,9,4,1,2,6,2,1,4,5,4,1,1,1,1,1,4,2,7,1,5,6,9,2,9,9,3,1,7,7,2,6,1,8,1
3,1,3,1,2,4,1,1,8,9,7,3,1,3,3,5,2,3,1,2,1,4,3,1,9,8,7,2,3,1,1,1,1,9,7,8,9,9,2,1,5,1,2,3,9,2,8,1,6,1,2,3,5,9,7,3,8,7,1,2,8,4,1,2,6,6,7,1,1,9,9,1,5,3,8,6,4,1,4,2,1,7,1,9,5,1,2,9,4,9,2,2,2,1,9,1,3,4,8,2
7,1,3,6,1,3,2,5,1,3,1,3,2,2,8,1,6,3,9,7,1,2,3,1,1,6,1,8,2,3,1,2,1,1,2,6,8,2,9,1,8,3,1,3,1,3,4,2,5,1,2,5,1,8,9,3,2,8,1,6,1,6,8,1,9,9,3,3,5,3,1,1,9,7,1,1,5,1,1,1,9,6,6,3,9,1,1,1,6,2,2,9,6,3,4,4,1,1,8,1
4,5,1,6,3,1,1,1,8,1,5,6,5,1,2,3,2,9,6,1,9,4,7,7,9,6,7,1,4,5,6,3,2,1,6,1,1,3,2,9,6,1,5,3,2,4,4,1,1,3,8,2,7,4,3,4,1,9,1,1,1,2,1,9,9,5,1,2,2,4,1,3,5,4,1,1,3,3,4,6,1,3,1,5,4,1,4,2,1,6,8,7,1,2,9,4,2,5,6,1