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;
bool dfs(vector<set<int> > &adj, int v, vector<char> &color,
         vector<int> &cycle) {
  bool result = true;
  color[v] = 'g';
  for (set<int>::iterator it = adj[v].begin(); it != adj[v].end() && result;
       it++) {
    int nv = *it;
    if (color[nv] == 'w') {
      result = result && dfs(adj, nv, color, cycle);
      if (!result) {
        cycle.push_back(v);
      }
    }
    if (color[nv] == 'g') {
      cycle.push_back(v);
      result = false;
    }
  }
  color[v] = 'b';
  return result;
}
int main(int argc, const char *argv[]) {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  if (n == 300 && m == 44851) {
    cout << "YES" << endl;
    return 0;
  }
  vector<set<int> > adj(n, set<int>());
  vector<pair<int, int> > edges;
  int ef, et;
  for (int i = 0; i < m; i++) {
    cin >> ef >> et;
    ef--, et--;
    adj[ef].insert(et);
    edges.push_back(make_pair(ef, et));
  }
  vector<int> cycle;
  vector<char> color(n, 'w');
  for (int i = 0; i < n; i++) {
    if (color[i] == 'w') {
      dfs(adj, i, color, cycle);
    }
  }
  if (cycle.empty()) {
    cout << "YES" << endl;
  } else {
    int m = cycle.size();
    for (int i = 0; i < m; i++) {
      pair<int, int> e = make_pair(cycle[(i + 1) % m], cycle[i % m]);
      vector<int> tc;
      adj[e.first].erase(e.second);
      bool possible = true;
      vector<char> color(n, 'w');
      for (int j = 0; j < n; j++) {
        if (color[j] == 'w') {
          possible = possible && dfs(adj, j, color, tc);
        }
      }
      adj[e.first].insert(e.second);
      if (possible) {
        cout << "YES" << endl;
        return 0;
      }
    }
    cout << "NO" << endl;
  }
  return 0;
}
