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 N = 505, M = 100005;
int n, m, k, u, v;
int head[N], in[N], rein[N];
struct edge {
  int v, next;
} e[M];
inline void add(int u, int v) {
  e[++k] = (edge){v, head[u]};
  head[u] = k;
  ++in[v];
}
inline bool TOPO(void) {
  register int cnt = 0;
  queue<int> q;
  for (register int i = 1; i <= n; ++i) {
    rein[i] = in[i];
    if (!in[i]) q.push(i);
  }
  while (!q.empty()) {
    register int u = q.front();
    q.pop();
    ++cnt;
    for (register int i = head[u]; i; i = e[i].next)
      if (--rein[e[i].v] == 0) q.push(e[i].v);
  }
  if (cnt == n) return true;
  return false;
}
int main(void) {
  scanf("%d%d", &n, &m);
  for (register int i = 1; i <= m; ++i) {
    scanf("%d%d", &u, &v);
    add(u, v);
  }
  for (register int i = 1; i <= n; ++i)
    if (in[i]) {
      --in[i];
      if (TOPO()) {
        puts("YES");
        return 0;
      }
      ++in[i];
    }
  puts("NO");
  return 0;
}
