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;
vector<int> path[510];
int in[510], in2[510];
int n, m;
bool isAcyclic() {
  queue<int> trop;
  int cnt = 0;
  for (int i = 1; i <= n; i++)
    if (in[i] <= 0) {
      trop.push(i);
      cnt++;
    }
  while (!trop.empty()) {
    int cur = trop.front();
    trop.pop();
    for (int i = 0; i < path[cur].size(); i++) {
      int cur1 = path[cur][i];
      in[cur1]--;
      if (in[cur1] == 0) {
        trop.push(cur1);
        cnt++;
      }
    }
  }
  return (cnt == n);
}
int main() {
  cin >> n >> m;
  int temp, temp1;
  for (int i = 0; i < m; i++) {
    scanf("%d%d", &temp, &temp1);
    path[temp].push_back(temp1);
    in2[temp1]++;
  }
  for (int i = 1; i <= n; i++) {
    memcpy(in, in2, sizeof(in));
    in[i]--;
    if (isAcyclic()) {
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
  return 0;
}
