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;
int n, m;
vector<int> v[600], masir;
bool mark[600];
bool seen[600];
int ans;
int i1 = -1;
void dfs(int x) {
  mark[x] = 1;
  if (i1 == -1) masir.push_back(x);
  if (ans == 1) return;
  for (int i = 0; i < v[x].size(); i++) {
    if (ans == 1) return;
    int k = v[x][i];
    if (i1 != -1 && masir[i1] == x && k == masir[i1 + 1]) continue;
    if (mark[k]) {
      if (i1 == -1) masir.push_back(k);
      ans = 1;
      return;
    }
    if (seen[k]) continue;
    dfs(k);
  }
  if (ans == 1) return;
  if (i1 == -1) masir.pop_back();
  mark[x] = 0;
  seen[x] = 1;
}
void clean() {
  for (int i = 0; i <= n; i++) {
    mark[i] = 0;
    seen[i] = 0;
  }
}
int main() {
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    int x, y;
    cin >> x >> y;
    v[x].push_back(y);
  }
  ans = 0;
  clean();
  for (int i = 1; i <= n; i++) {
    if (ans == 1) break;
    if (seen[i]) continue;
    dfs(i);
  }
  if (ans == 0) {
    cout << "YES" << endl;
    return 0;
  }
  for (i1 = 0; i1 + 1 < masir.size(); i1++) {
    clean();
    ans = 0;
    for (int i = 1; i <= n; i++) {
      if (ans == 1) break;
      if (seen[i]) continue;
      dfs(i);
    }
    if (ans == 0) {
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
}
