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;
void dfs(int u);
void dfs(int u, int a, int b);
int n, m;
const int N = 100100;
bool fl;
vector<int> v[N];
vector<int> cy, mark, pr;
int main() {
  cin >> n >> m;
  for (; m--;) {
    int a, b;
    cin >> a >> b;
    --a, --b;
    v[a].push_back(b);
  }
  fl = 0;
  mark.resize(n);
  pr.resize(n);
  pr.assign(n, -1);
  mark.assign(n, 0);
  for (int i = 0; i < n; i++) {
    if (fl) break;
    if (!mark[i]) dfs(i);
  }
  if (!fl) {
    cout << "YES";
    return 0;
  }
  for (int i = 1; i < min(int(cy.size()), n + 1); i++) {
    mark.assign(n, 0);
    fl = 0;
    for (int j = 0; j < n; j++)
      if (!mark[j]) dfs(j, cy[i], cy[i - 1]);
    if (!fl) {
      cout << "YES";
      return 0;
    }
  }
  cout << "NO";
  return 0;
}
void dfs(int u) {
  if (fl) return;
  mark[u] = 1;
  for (int i = 0; i < v[u].size(); i++) {
    int t = v[u][i];
    if (mark[t] == 1) {
      fl = 1;
      cy.push_back(t);
      for (int j = u, tc = 0; j != -1 && j != t && tc <= n + 3; tc++, j = pr[j])
        cy.push_back(j);
      cy.push_back(t);
      break;
    } else if (!mark[t]) {
      pr[t] = u;
      dfs(t);
    }
  }
  mark[u] = 2;
}
void dfs(int u, int a, int b) {
  mark[u] = 1;
  for (int i = 0; i < v[u].size(); i++) {
    int t = v[u][i];
    if (a == u && b == t) continue;
    if (mark[t] == 1)
      fl = 1;
    else if (!mark[t])
      dfs(t, a, b);
  }
  mark[u] = 2;
}
