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;
template <class T>
void splitstr(const string &s, vector<T> &out) {
  istringstream in(s);
  out.clear();
  copy(istream_iterator<T>(in), istream_iterator<T>(), back_inserter(out));
}
template <class T>
T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
static void redirect(int argc, const char **argv) {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  if (argc > 1) {
    static filebuf f;
    f.open(argv[1], ios::in);
    cin.rdbuf(&f);
    if (!cin) {
      cerr << "Failed to open '" << argv[1] << "'" << endl;
      exit(1);
    }
  }
  if (argc > 2) {
    static filebuf f;
    f.open(argv[2], ios::out | ios::trunc);
    cout.rdbuf(&f);
    if (!cout) {
      cerr << "Failed to open '" << argv[2] << "'" << endl;
    }
  }
}
static vector<vector<int> > edges;
static int dfs(int cur, vector<bool> &seen, vector<bool> &active) {
  int up = 0;
  seen[cur] = true;
  active[cur] = true;
  for (int y : edges[cur]) {
    if (active[y])
      up++;
    else if (!seen[y])
      up += dfs(y, seen, active);
  }
  active[cur] = false;
  return up;
}
int main(int argc, const char **argv) {
  redirect(argc, argv);
  int N, M;
  cin >> N >> M;
  edges.resize(N);
  for (int i = 0; i < M; i++) {
    int u, v;
    cin >> u >> v;
    u--;
    v--;
    edges[u].push_back(v);
  }
  for (int i = 0; i < N; i++) {
    vector<bool> seen(N), active(N);
    int up = dfs(i, seen, active);
    for (int j = 0; j < N; j++)
      if (!seen[j]) up += dfs(j, seen, active);
    if (up <= 1) {
      cout << "YES\n";
      return 0;
    }
  }
  cout << "NO\n";
  return 0;
}
