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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Stack;
import java.util.ArrayList;
import java.util.Vector;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DAlmostAcyclicGraph solver = new DAlmostAcyclicGraph();
        solver.solve(1, in, out);
        out.close();
    }

    static class DAlmostAcyclicGraph {
        int n;
        int m;
        ArrayList<Integer>[] adjL;
        Stack<Integer> st;

        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            n = sc.nextInt();
            m = sc.nextInt();
            adjL = new ArrayList[n];
            for (int i = 0; i < n; i++)
                adjL[i] = new ArrayList<>();
            for (int i = 0; i < m; i++) {
                int u = sc.nextInt() - 1, v = sc.nextInt() - 1;
                adjL[u].add(v);
            }
            if (!isCyclic(-1, -1)) {
                pw.println("YES");
            } else {
                Stack<Integer> cycle = (Stack<Integer>) st.clone();
                int prev = cycle.pop();
                while (!cycle.isEmpty()) {
                    if (!isCyclic(cycle.peek(), prev)) {
                        pw.println("YES");
                        return;
                    }
                    prev = cycle.pop();
                }
                pw.println("NO");
            }
        }

        private boolean isCyclic(int x, int y) {
            st = new Stack<>();
            boolean[] vis = new boolean[n];
            for (int i = 0; i < n; i++) {
                if (!vis[i])
                    if (isCyclic(i, vis, new boolean[n], x, y))
                        return true;
            }
            return false;
        }

        private boolean isCyclic(int u, boolean[] vis, boolean[] onStack, int x, int y) {
            if (onStack[u])
                return true;
            vis[u] = true;
            onStack[u] = true;
            st.add(u);
            for (int v : adjL[u]) {
                if (u == x && y == v)
                    continue;
                if ((vis[v] && onStack[v]) || (!vis[v] && isCyclic(v, vis, onStack, x, y))) {
                    st.add(v);
                    return true;
                }
            }
            onStack[u] = false;
            st.pop();
            return false;
        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

