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 = 510, M = 100010;
int n, m, cnt, l, r, ll, rr;
int head[N], in[N], d[N], q[M];
struct edge {
  int to, nxt;
  edge() {}
  edge(int x, int y) { to = x, nxt = y; }
} e[M];
inline void addedge(int x, int y) {
  e[++cnt] = edge(y, head[x]);
  head[x] = cnt;
}
inline bool tp(int x) {
  ll = l;
  rr = r;
  q[++r] = x;
  for (int j = 1; j <= n; j++) d[j] = in[j];
  d[x]--;
  while (l <= r) {
    int u = q[l++];
    for (int i = head[u]; i; i = e[i].nxt) {
      int v = e[i].to;
      d[v]--;
      if (!d[v]) q[++r] = v;
    }
  }
  bool flag = (r == n);
  l = ll, r = rr;
  return flag;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= m; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    addedge(x, y);
    in[y]++;
  }
  l = 1, r = 0;
  for (int i = 1; i <= n; i++)
    if (!in[i]) q[++r] = i;
  while (l <= r) {
    int u = q[l++];
    for (int i = head[u]; i; i = e[i].nxt) {
      int v = e[i].to;
      in[v]--;
      if (!in[v]) q[++r] = v;
    }
  }
  if (r == n) {
    puts("YES");
    return 0;
  }
  for (int i = 1; i <= n; i++)
    if (in[i] == 1) {
      if (tp(i)) {
        puts("YES");
        return 0;
      }
    }
  puts("NO");
  return 0;
}
