Almost Acyclic Graph

Description:

Input:

The first line contains two integers n and m (2 ≤ n ≤ 500, 1 ≤ m ≤ min(n(n - 1), 100000)) — the number of vertices and the number of edges, respectively.

Then m lines follow. Each line contains two integers u and v denoting a directed edge going from vertex u to vertex v (1 ≤ u, v ≤ n, u ≠ v). Each ordered pair (u, v) is listed at most once (there is at most one directed edge from u to v).

Output:

If it is possible to make this graph acyclic by removing at most one edge, print YES. Otherwise, print NO.

Sample Input:

3 4
1 2
2 3
3 2
3 1

Sample Output:

YES

Sample Input:

5 6
1 2
2 3
3 2
3 1
2 1
4 5

Sample Output:

NO

Note:

In the first example you can remove edge , and the graph becomes acyclic.

In the second example you have to remove at least two edges (for example, and ) in order to make the graph acyclic.