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 long long INF = 10000000000000;
vector<vector<long long>> g;
vector<long long> cycle;
long long n, m, cnt = 0;
void ans(long long f, long long s, vector<long long>& pred) {
  long long p = f;
  while (p != s) {
    cycle.push_back(p);
    p = pred[p];
  }
  cycle.push_back(p);
}
void dfs1(long long v, vector<long long>& cols, vector<long long>& pred) {
  cols[v] = 1;
  for (long long u = 0; u < n; u++) {
    if (cols[u] == 0 && g[v][u] == 1) {
      pred[u] = v;
      dfs1(u, cols, pred);
    } else if (cols[u] == 1 && cycle.size() == 0 && g[v][u] == 1)
      ans(v, u, pred);
  }
  cols[v] = 2;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  g.resize(n);
  for (long long i = 0; i < n; i++) {
    g[i].assign(n, 0);
  }
  for (long long i = 0; i < m; i++) {
    long long u, v;
    cin >> u >> v;
    u--;
    v--;
    g[u][v] = 1;
  }
  vector<long long> cols(n, 0), pred(n, 0);
  for (long long i = 0; i < n; i++) {
    if (cols[i] == 0) dfs1(i, cols, pred);
  }
  if (cycle.size() == 0) {
    cout << "YES";
    return 0;
  }
  vector<long long> dop = cycle;
  reverse(dop.begin(), dop.end());
  for (long long i = 0; i < dop.size(); i++) {
    cycle.resize(0);
    g[dop[i]][dop[(i + 1) % dop.size()]] = 0;
    vector<long long> cols(n, 0), pred(n, 0);
    for (long long i = 0; i < n; i++) {
      if (cols[i] == 0) dfs1(i, cols, pred);
    }
    if (cycle.size() == 0) {
      cout << "YES";
      return 0;
    }
    g[dop[i]][dop[(i + 1) % dop.size()]] = 1;
  }
  cout << "NO";
  return 0;
}
