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 = 1e5 + 7;
int n, m;
int inDeg[maxn], ruDeg[maxn];
std::vector<int> v[maxn];
bool topsort() {
  int sum = 0;
  queue<int> q;
  while (!q.empty()) q.pop();
  for (int i = 1; i <= n; i++) {
    if (!inDeg[i]) q.push(i);
  }
  while (!q.empty()) {
    int now = q.front();
    q.pop();
    sum++;
    for (int i = 0; i < v[now].size(); i++) {
      int to = v[now][i];
      if (--inDeg[to] == 0) {
        q.push(to);
      }
    }
  }
  if (sum == n)
    return 1;
  else
    return 0;
}
int main() {
  cin >> n >> m;
  for (int i = 1; i <= m; i++) {
    int u, w;
    cin >> u >> w;
    v[u].push_back(w);
    inDeg[w]++;
    ruDeg[w]++;
  }
  if (topsort() == 1) {
    cout << "YES"
         << "\n";
  } else {
    bool flag = 0;
    for (int i = 1; i <= n; i++) {
      memcpy(inDeg, ruDeg, sizeof ruDeg);
      if (inDeg[i] >= 1) {
        inDeg[i]--;
        if (topsort() == 1) {
          flag = 1;
          cout << "YES"
               << "\n";
          break;
        }
      }
    }
    if (!flag) puts("NO");
  }
  return 0;
}
