You are given a [directed graph](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/Directed_acyclic_graph) 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).

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.

Examples

Input

3 4
1 2
2 3
3 2
3 1


Output

YES


Input

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


Output

NO

Note

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

In the second example you have to remove at least two edges (for example, <image> and <image>) in order to make the graph acyclic.
#include <bits/stdc++.h>
using namespace std;
const int N = 505;
int n, m;
vector<int> g[N], in(N, 0), deg(N, 0);
vector<bool> vis(N, 0);
void dfs(int u) {
  vis[u] = true;
  for (int v : g[u])
    if (!vis[v] && --deg[v] <= 0) dfs(v);
}
int main() {
  scanf("%d %d ", &n, &m);
  for (int i = 1; i <= m; i++) {
    int u, v;
    scanf("%d %d ", &u, &v);
    g[u].push_back(v);
    in[v]++;
  }
  for (int i = 1; i <= n; i++) {
    deg = in;
    fill(vis.begin(), vis.end(), false);
    deg[i]--;
    for (int j = 1; j <= n; j++)
      if (deg[j] <= 0 && !vis[j]) dfs(j);
    bool flag = 0;
    for (int j = 1; j <= n; j++)
      if (!vis[j]) flag = 1;
    if (!flag) {
      cout << "YES";
      return 0;
    }
  }
  cout << "NO";
}
