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 = 510;
const int MAXM = 100100;
int n, m;
vector<int> graf[MAXN];
void load() {
  scanf("%d%d", &n, &m);
  for (int i = 0; i < m; i++) {
    int u, v;
    scanf("%d%d", &u, &v);
    --u;
    --v;
    graf[u].push_back(v);
  }
}
int bio[MAXN];
int badChild[MAXN];
int Badx = -1, Bady = -1;
int start = -1;
bool IsCycle(int x) {
  if (bio[x]) return false;
  bio[x] = 2;
  for (int i = 0; i < graf[x].size(); ++i) {
    int sus = graf[x][i];
    if (x == Badx && sus == Bady) continue;
    if (bio[sus] == 2) {
      start = sus;
      badChild[x] = sus;
      return true;
    }
    if (!bio[sus] && IsCycle(sus)) {
      badChild[x] = sus;
      return true;
    }
  }
  bio[x] = 1;
  return false;
}
int badChild_[MAXN];
bool solve() {
  for (int i = 0; i < n; i++)
    if (IsCycle(i)) break;
  if (start == -1) return true;
  int sus = start;
  int start_ = start;
  for (int i = 0; i < n; i++) badChild_[i] = badChild[i];
  do {
    Badx = sus;
    Bady = badChild_[sus];
    start = -1;
    for (int i = 0; i < n; i++) bio[i] = 0;
    for (int i = 0; i < n; i++)
      if (IsCycle(i)) break;
    if (start == -1) return true;
    sus = badChild_[sus];
  } while (sus != start_);
  return false;
}
int main() {
  load();
  if (solve())
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}
