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.
import java.text.DecimalFormat;
import java.util.*;

public class Main {

    public static int n,m;
    public static int[] d = new int[505];
    public static int[] a = new int[505];
    public static int map[][] = new int[505][505];

    public static boolean topoSort(int x) {
        Queue<Integer> q = new LinkedList<>();
        for (int i = 0; i < 505; i++) {
            a[i] = d[i];
        }
        a[x]--;
        int num = 0;
        for (int i = 1; i <= n; i++) {
            if (a[i] == 0) {
                q.add(i);
                num++;
            }
        }

        while (!q.isEmpty()) {
            int tmp = q.poll();
            for (int i = 1; i <= n; i++) {
                if (map[tmp][i] == 1) {
                    if (--a[i] == 0){
                        q.add(i);
                        num++;
                    }
                }

            }
        }
        return num == n;
    }

    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        m = sc.nextInt();
        for (int i = 1; i <= m; i++) {
            int x,y;
            x = sc.nextInt();
            y = sc.nextInt();
            map[x][y] = 1;
            d[y]++;
        }
        for (int i = 0; i < n; i++) {
            if (topoSort(i+1)) {
                System.out.println("YES");
                return;
            }
        }
        System.out.println("NO");
    }
}