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 MAXN = 500;
const int MAXM = (int)1e5;
vector<int> g[MAXN + 1];
int x[MAXM + 1], y[MAXM + 1];
int ok[MAXN + 1];
bool flag;
vector<int> edge;
void dfs(int nod) {
  ok[nod] = 1;
  edge.push_back(nod);
  for (auto it : g[nod]) {
    if (flag == 0) {
      if (ok[it] == 0) {
        dfs(it);
      } else if (ok[it] == 1) {
        flag = 1;
        edge.push_back(it);
      }
    }
  }
  ok[nod] = 2;
  if (flag == 0) edge.pop_back();
}
int a, b;
void dfs1(int nod) {
  ok[nod] = 1;
  for (auto it : g[nod]) {
    if (flag == 0 && !(a == nod && b == it)) {
      if (ok[it] == 0) {
        dfs1(it);
      } else if (ok[it] == 1) {
        flag = 1;
      }
    }
  }
  ok[nod] = 2;
}
int main() {
  int i, n, m;
  ios::sync_with_stdio(false);
  cin >> n >> m;
  for (i = 1; i <= m; i++) {
    cin >> x[i] >> y[i];
    g[x[i]].push_back(y[i]);
  }
  for (i = 1; i <= n && flag == 0; i++) {
    if (ok[i] == 0) {
      dfs(i);
    }
  }
  if (flag == 0) {
    cout << "YES";
    return 0;
  }
  int sz = edge.size();
  for (i = sz - 2; i >= 0; i--) {
    a = edge[i], b = edge[i + 1];
    if (i == sz - 2 || b != edge.back()) {
      memset(ok, 0, sizeof(ok));
      flag = 0;
      for (int j = 1; j <= n && flag == 0; j++) {
        if (ok[j] == 0) dfs1(j);
      }
      if (flag == 0) {
        cout << "YES";
        return 0;
      }
    } else
      break;
  }
  cout << "NO";
  return 0;
}
