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 MAXN = 505;
vector<int> graf[MAXN];
int n, m, bio[MAXN], flag;
vector<pair<int, int> > edges;
pair<int, int> forbid;
bool dfs(int node) {
  bio[node] = flag + 2;
  for (int nex : graf[node]) {
    assert(true);
    if (bio[nex] == flag + 1 || forbid == make_pair(node, nex)) continue;
    if (bio[nex] == flag + 2) {
      edges.push_back(make_pair(node, nex));
      return true;
    }
    edges.push_back(make_pair(node, nex));
    if (dfs(nex)) return true;
    edges.pop_back();
  }
  bio[node] = flag + 1;
  return false;
}
bool check() {
  flag += 3;
  for (int i = 0; i < n; i++) {
    if (bio[i] <= flag && dfs(i)) return true;
  }
  return false;
}
void fin(bool a) {
  if (a) {
    cout << "YES" << endl;
    exit(0);
  }
  cout << "NO" << endl;
  exit(0);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> m;
  int a, b;
  for (int i = 0; i < m; i++) {
    cin >> a >> b;
    graf[a - 1].push_back(b - 1);
  }
  if (!check()) fin(true);
  vector<pair<int, int> > myedges = edges;
  for (pair<int, int> &nex : myedges) {
    edges.clear();
    forbid = nex;
    if (!check()) fin(true);
  }
  fin(false);
  return 0;
}
