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 + 10;
const int MAX = 1010;
const long long int mod = 1e9 + 7;
int n, m, anc[MAX];
bool vis[MAX], instack[MAX], block[MAX][MAX], found = 0, ff = 0;
vector<int> adj[MAX];
vector<pair<int, int> > lista;
void monta(int u, int head) {
  lista.push_back({u, head});
  int x = u;
  while (x != head) {
    lista.push_back({anc[x], x});
    x = anc[x];
  }
}
void first(int u) {
  vis[u] = instack[u] = 1;
  if (!found)
    for (auto v : adj[u]) {
      if (block[u][v] or found) continue;
      if (!vis[v]) {
        anc[v] = u;
        first(v);
      } else if (instack[v]) {
        if (!ff and !found) {
          monta(u, v);
        }
        found = 1;
      }
    }
  instack[u] = 0;
}
signed main() {
  ios_base::sync_with_stdio(false), cin.tie(nullptr);
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    adj[a].push_back(b);
  }
  for (int i = 1; i <= n and !found; i++) {
    if (vis[i]) continue;
    first(i);
  }
  ff = 1;
  if (!found) return cout << "YES", 0;
  for (auto x : lista) {
    block[x.first][x.second] = 1;
    found = 0;
    for (int i = 0; i <= n; i++) vis[i] = 0;
    for (int i = 1; i <= n; i++) {
      if (vis[i]) continue;
      first(i);
    }
    if (!found) {
      return cout << "YES\n", 0;
    }
    block[x.first][x.second] = 0;
  }
  cout << "NO\n";
}
