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 inf = 1e9 + 7;
template <class T>
void dbs(string str, T t) {
  cout << str << " : " << t << endl;
}
template <class T, class... second>
void dbs(string str, T t, second... s) {
  int idx = str.find(',');
  cout << str.substr(0, idx) << " : " << t << ",";
  dbs(str.substr(idx + 1), s...);
}
template <class second, class T>
ostream& operator<<(ostream& os, const pair<second, T>& p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class second, class T>
ostream& operator<<(ostream& os, const map<second, T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class T>
void prc(T a, T b) {
  cout << "[";
  for (T i = a; i != b; ++i) {
    if (i != a) cout << ", ";
    cout << *i;
  }
  cout << "]";
  cout << endl;
}
vector<vector<int> > v;
int dfs(int node, vector<int>& visited, vector<int>& active) {
  visited[node] = active[node] = 1;
  int g = 0;
  for (int i = 0; i < v[node].size(); i++) {
    if (active[v[node][i]])
      g++;
    else if (!visited[v[node][i]])
      g += dfs(v[node][i], visited, active);
  }
  active[node] = 0;
  return g;
}
int main() {
  int n, m;
  cin >> n >> m;
  v.resize(n);
  for (int i = 0; i < m; i++) {
    int x, y;
    cin >> x >> y;
    v[x - 1].push_back(y - 1);
  }
  for (int i = 0; i < n; i++) {
    vector<int> visited(n, 0), active(n, 0);
    int g = 0;
    g += dfs(i, visited, active);
    for (int j = 0; j < n; j++) {
      if (!visited[j]) g += dfs(j, visited, active);
    }
    if (g <= 1) {
      cout << "YES\n";
      return 0;
    }
  }
  cout << "NO\n";
}
