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.util.List;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
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;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        List<Integer>[] adj;
        List<Cycle> cycles;
        int[] v;
        int n;
        int m;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.nextInt();
            m = in.nextInt();
            adj = new List[n];
            for (int i = 0; i < n; ++i) adj[i] = new ArrayList<>();
            for (int i = 0; i < m; ++i) {
                int u = in.nextInt() - 1;
                int v = in.nextInt() - 1;
                adj[u].add(v);
            }
            v = new int[n];
            cycles = new ArrayList<>();
            for (int i = 0; i < n; ++i) {
                if (v[i] == 0) dfs(i);
            }
            if (cycles.isEmpty()) {
                out.println("YES");
            } else {
                for (Cycle cycle : cycles) {
                    if (checkForCycle(cycle)) {
                        out.println("YES");
                        return;
                    }
                }
                out.println("NO");

            }
        }

        private boolean checkForCycle(Cycle cycle) {
            v = new int[n];
            for (int i = 0; i < n; ++i) {
                boolean result = v[i] == 0 && !check(i, cycle);
                if (result) return false;
            }
            return true;
        }

        private boolean dfs(int root) {
            v[root] = 1;
            for (int child : adj[root]) {
                if (v[child] == 1) {
                    cycles.add(new Cycle(root, child));
                    return false;
                } else if (v[child] == 0) {
                    if (!dfs(child)) {
                        cycles.add(new Cycle(root, child));
                        return false;
                    }
                }
            }
            v[root] = 2;
            return true;
        }

        private boolean check(int root, Cycle cycle) {
            v[root] = 1;
            for (int child : adj[root]) {
                if (child == cycle.child && root == cycle.parent) continue;
                if (v[child] == 1) return false;
                if (v[child] == 0) {
                    if (!check(child, cycle)) return false;
                }
            }
            v[root] = 2;
            return true;
        }

        class Cycle {
            int parent;
            int child;

            public Cycle(int parent, int child) {
                this.parent = parent;
                this.child = child;
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

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

    }
}

