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>
#pragma optimize("O3")
using namespace std;
const int N = 505;
vector<int> T[N];
int vis[N];
int p[N];
vector<int> cycle;
bool ok;
void dfs1(int u, int ls) {
  if (!ok or vis[u] == 2) return;
  if (vis[u] == 1) {
    cycle.push_back(u);
    int lp = ls;
    while (lp != u) {
      cycle.push_back(lp);
      lp = p[lp];
    }
    cycle.push_back(u);
    ok = false;
    return;
  }
  vis[u] = 1;
  p[u] = ls;
  for (auto x : T[u]) {
    dfs1(x, u);
  }
  vis[u] = 2;
}
int bu, bv;
bool dfs2(int u) {
  if (vis[u] == 2) return false;
  if (vis[u] == 1) return true;
  vis[u] = 1;
  for (auto x : T[u]) {
    if (u != bu or x != bv) {
      if (dfs2(x)) return true;
    }
  }
  vis[u] = 2;
  return false;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  int n, m;
  cin >> n >> m;
  ok = true;
  int u, v;
  for (int i = 0; i < m; i++) {
    cin >> u >> v;
    T[u].push_back(v);
  }
  for (int i = 1; i <= n; i++) {
    dfs1(i, -1);
  }
  if (ok) {
    cout << "YES\n";
    return 0;
  }
  bool good;
  for (int i = 1; i < cycle.size(); i++) {
    bu = cycle[i];
    bv = cycle[i - 1];
    for (int j = 1; j <= n; j++) {
      vis[j] = 0;
    }
    good = true;
    for (int j = 1; j <= n; j++) {
      if (dfs2(j)) {
        good = false;
      }
    }
    if (good) {
      cout << "YES\n";
      return 0;
    }
  }
  cout << "NO\n";
  return 0;
}
