Almost Acyclic Graph
Description
You are given a directed graph consisting of n vertices and m edges (each edge is directed, so it can be traversed in only one direction). You are allowed to remove at most one edge from it.
Can you make this graph acyclic by removing at most one edge from it? A directed graph is called acyclic iff it doesn't contain any cycle (a non-empty path that starts and ends in the same vertex).
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).
If it is possible to make this graph acyclic by removing at most one edge, print YES. Otherwise, print NO.
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.
Samples
3 4
1 2
2 3
3 2
3 1
YES
5 6
1 2
2 3
3 2
3 1
2 1
4 5
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.