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;
vector<int> G[N];
int n, m, in[N], d[N];
int topuSort(int s) {
  memcpy(in, d, sizeof(d));
  queue<int> p;
  in[s]--;
  int cnt = 0;
  for (int i = 1; i <= n; i++) {
    if (!in[i]) p.push(i);
  }
  while (!p.empty()) {
    cnt++;
    int u = p.front();
    p.pop();
    for (int i = 0; i < G[u].size(); i++) {
      int v = G[u][i];
      in[v]--;
      if (!in[v]) p.push(v);
    }
  }
  return cnt == n;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 0; i < m; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    G[a].push_back(b);
    d[b]++;
  }
  int flag = 0;
  for (int i = 1; i <= n; i++) {
    if (topuSort(i)) {
      flag = 1;
      break;
    }
  }
  if (flag)
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}
