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 = 1e5 + 5;
int n, m;
int tot;
int head[MAXN], cur[MAXN], idec[MAXN];
struct Edge {
  int v, nxt;
  Edge() {}
  Edge(int v, int nxt) : v(v), nxt(nxt) {}
} edge[MAXM];
void init() {
  tot = 0;
  memset(head, -1, sizeof(head));
}
void add_edge(int u, int v) {
  edge[tot] = Edge(v, head[u]);
  head[u] = tot++;
}
int que[MAXN];
int st, ed;
bool topsort(int x) {
  int nst = 1, ned = 0;
  for (int i = 1; i <= n; i++) cur[i] = idec[i];
  cur[x]--;
  que[++ned] = x;
  while (nst <= ned) {
    int u = que[nst++];
    for (int i = head[u]; i != -1; i = edge[i].nxt) {
      int v = edge[i].v;
      if (--cur[v] == 0) que[++ned] = v;
    }
  }
  if (ned + ed == n)
    return true;
  else
    return false;
}
int work() {
  scanf("%d%d", &n, &m);
  init();
  while (m--) {
    int u, v;
    scanf("%d%d", &u, &v);
    add_edge(u, v);
    idec[v]++;
  }
  st = 1, ed = 0;
  for (int i = 1; i <= n; i++) {
    if (idec[i] == 0) que[++ed] = i;
  }
  while (st <= ed) {
    int u = que[st++];
    for (int i = head[u]; i != -1; i = edge[i].nxt) {
      int v = edge[i].v;
      if (--idec[v] == 0) que[++ed] = v;
    }
  }
  if (ed == n) {
    puts("YES");
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    if (idec[i] == 1) {
      if (topsort(i)) {
        puts("YES");
        return 0;
      }
    }
  }
  puts("NO");
  return 0;
}
int main() {
  work();
  return 0;
}
