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;
vector<pair<int, bool> > adjList[N];
vector<bool> canUse[N];
int n, m;
int ndfn, lowLink[N], dfn[N], comp[N], cnt;
stack<int> stk;
bool inStack[N], vis[N];
void tarjan(int node) {
  lowLink[node] = dfn[node] = ++ndfn;
  stk.push(node), inStack[node] = 1;
  for (int i = 0; i < adjList[node].size(); i++) {
    int ch = adjList[node][i].first;
    if (!canUse[node][i]) continue;
    if (!dfn[ch]) {
      tarjan(ch);
      lowLink[node] = min(lowLink[node], lowLink[ch]);
    } else if (inStack[ch])
      lowLink[node] = min(lowLink[node], dfn[ch]);
  }
  if (lowLink[node] == dfn[node]) {
    cnt++;
    int x = -1;
    while (x != node) x = stk.top(), stk.pop(), inStack[x] = 0;
  }
}
bool hasCycle(int node, int start) {
  if (vis[node]) return node == start;
  vis[node] = true;
  bool onCycle = false;
  for (int i = 0; i < adjList[node].size() && !onCycle; i++) {
    int ch = adjList[node][i].first;
    onCycle |= hasCycle(ch, start);
    adjList[node][i].second = onCycle;
  }
  return onCycle;
}
int main() {
  scanf("%d %d", &n, &m);
  for (int i = 0; i < m; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    adjList[x].push_back(make_pair(y, false));
    canUse[x].push_back(true);
  }
  bool has = false;
  for (int i = 1; i <= n && !has; i++) {
    memset(vis, false, sizeof vis);
    has |= hasCycle(i, i);
  }
  if (!has) return printf("YES"), 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < adjList[i].size(); j++) {
      if (!adjList[i][j].second) continue;
      canUse[i][j] = false;
      memset(dfn, 0, sizeof dfn);
      memset(lowLink, 0, sizeof lowLink);
      ndfn = 0, cnt = 0;
      for (int i = 1; i <= n; i++)
        if (!dfn[i]) tarjan(i);
      if (cnt == n) return printf("YES"), 0;
      canUse[i][j] = true;
    }
  }
  printf("NO");
  return 0;
}
