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;
const int maxm = 100;
const int inf = 2147483647;
const double eps = 1e-9;
const long long INF = 9223372036854775807ll;
long long qpow(long long a, long long b, long long c) {
  long long ans = 1;
  while (b) {
    if (b & 1) ans = ans * a % c;
    a = a * a % c;
    b >>= 1;
  }
  return ans;
}
vector<int> g[maxn];
int n;
int deg[maxn], dgg[maxn];
queue<int> q, f;
bool check(int k) {
  q = f;
  deg[k]--;
  if (!deg[k]) q.push(k);
  int cnt = 0;
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    cnt++;
    for (register int i = (0); i < (g[u].size()); ++i) {
      int v = g[u][i];
      deg[v]--;
      if (!deg[v]) q.push(v);
    }
  }
  memcpy(deg, dgg, sizeof(int) * (n + 1));
  if (cnt == n) return true;
  return false;
}
int main() {
  int m;
  scanf("%d%d", &n, &m);
  for (register int i = (0); i < (m); ++i) {
    int u, v;
    scanf("%d%d", &u, &v);
    deg[v]++;
    g[u].push_back(v);
  }
  memcpy(dgg, deg, sizeof(int) * (n + 1));
  for (register int i = (1); i < (n + 1); ++i)
    if (!deg[i]) q.push(i);
  f = q;
  for (register int i = (1); i < (n + 1); ++i) {
    if (deg[i] && check(i)) return printf("YES\n"), 0;
  }
  printf("NO\n");
}
