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;
int n, m, now[1000000], tot;
int pks[100000];
bool flag;
struct node {
  int r, next;
} side[100005];
bool b[1000000], bo[1000000];
void add(int i, int j) {
  tot++;
  side[tot].r = j;
  side[tot].next = now[i];
  now[i] = tot;
}
void ddfs(int i) {
  b[i] = 1;
  bo[i] = 1;
  for (int p = now[i]; (p); p = side[p].next)
    if ((!b[side[p].r]) || bo[side[p].r]) {
      pks[++tot] = p;
      if (bo[side[p].r]) {
        flag = 1;
        return;
      }
      ddfs(side[p].r);
      if (flag) return;
      tot--;
    }
  bo[i] = 0;
  return;
}
bool dfs(int i, int j) {
  b[i] = 1;
  bo[i] = 1;
  for (int p = now[i]; (p); p = side[p].next)
    if ((p != j) && ((!b[side[p].r]) || bo[side[p].r])) {
      if (bo[side[p].r]) return 1;
      if (dfs(side[p].r, j)) return 1;
    }
  bo[i] = 0;
  return 0;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= m; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    add(x, y);
  }
  tot = 0;
  for (int i = 1; i <= n; i++)
    if ((!b[i]) & (!flag)) ddfs(i);
  for (int j = 1; j <= n; j++) b[j] = 0;
  for (int j = 1; j <= n; j++) bo[j] = 0;
  if (!flag) {
    cout << "YES";
    return 0;
  }
  for (int i = 1; i <= tot; i++) {
    bool flag = 1;
    for (int j = 1; j <= n; j++)
      if (!b[j])
        if (dfs(j, pks[i])) {
          flag = 0;
          break;
        }
    if (flag) {
      cout << "YES";
      return 0;
    }
    for (int j = 1; j <= n; j++) b[j] = 0;
    for (int j = 1; j <= n; j++) bo[j] = 0;
  }
  cout << "NO";
}
