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;
#pragma GCC optimize("Ofast")
#pragma GCC optimize("fast-math")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,tune=native")
mt19937 rnd(51);
const long long N = 510;
vector<long long> par(N);
set<long long> g[N];
vector<long long> used(N);
long long c_e = 0, c_b = 0;
bool dfs(long long v) {
  used[v] = 1;
  for (auto to : g[v]) {
    if (!used[to]) {
      par[to] = v;
      if (dfs(to)) return 1;
    }
    if (used[to] == 1) {
      c_e = v, c_b = to;
      return 1;
    }
  }
  used[v] = 2;
  return 0;
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, m;
  cin >> n >> m;
  for (long long i = 0; i < m; i++) {
    long long a, b;
    cin >> a >> b;
    g[a].insert(b);
  }
  for (long long i = 1; i <= n; i++) {
    if (used[i] == 0) {
      if (dfs(i)) {
        vector<long long> v;
        v.push_back(c_b);
        for (long long u = c_e; u != c_b; u = par[u]) {
          v.push_back(u);
        }
        v.push_back(c_b);
        reverse(v.begin(), v.end());
        for (long long j = 0; j < v.size() - 1; j++) {
          g[v[j]].erase(v[j + 1]);
          fill(used.begin(), used.end(), 0);
          bool x = 0;
          for (long long k = 1; k <= n; k++) {
            if (!used[k]) {
              if (dfs(k)) {
                x = 1;
              }
            }
          }
          if (!x) {
            cout << "YES";
            return 0;
          }
          g[v[j]].insert(v[j + 1]);
        }
        cout << "NO";
        return 0;
      }
    }
  }
  cout << "YES\n";
  return 0;
}
