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.
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main {
    static int N = 12345;

    static boolean visited[] = new boolean[N];
    static boolean visiting[] = new boolean[N];

    private static class pair {
        int first;
        int second;
    }

    static ArrayList<Integer> graph[] = new ArrayList[N];
    static ArrayList<pair> ce = new ArrayList<>();

    static int n, m;

    static boolean cycle(int node, int a, int b) {
        // System.out.println(node);
        visiting[node] = true;
        for (int v : graph[node]) {
            if (node == a && v == b) continue;
            if (visited[v]) continue;
            if (visiting[v] || cycle(v, a, b)) {
                if(a != -1) return true;
                pair aa = new pair();
                aa.first = node;
                aa.second = v;
                ce.add(aa);
                return true;
            }

        }
        visiting[node] = false;
        visited[node] = true;
        return false;
    }

    static boolean hasCycle(int a, int b) {
        for (int i = 1; i <= n; i++) visited[i] = false;
        for (int i = 1; i <= n; i++) visiting[i] = false;

        for (int i = 1; i <= n; i++) {
            if (visited[i]) continue;
            if (cycle(i, a, b)) {
                return true;
            }
        }
        return false;
    }

    static boolean del() {
        for (int i = 0; i < ce.size(); i++) {
            pair p = ce.get(i);
            if (!hasCycle(p.first, p.second)) {
                // cout << p.first << " "  << p.second << endl;
                return true;
            }
        }
        return false;
    }


    public static void main(String[] args) throws java.lang.Exception {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        m = sc.nextInt();
        for (int i = 1; i <= n; i++) graph[i] = new ArrayList<>();
        for (int i = 0; i < m; i++) {
            int u = sc.nextInt(), v = sc.nextInt();

            graph[u].add(v);
        }
        if (!hasCycle(-1, -1)) {
            System.out.println("YES");
            return;
        }

        if (del()) {
            System.out.println("YES");
        } else {
            System.out.println("NO");
        }
    }
}