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.InputMismatchException;
import java.io.IOException;
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 {
        ArrayList<Integer>[] edge;
        ArrayList<Integer>[] used;
        boolean[] visited;
        boolean[] seen;
        int idx = 1;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.readInt();
            int m = in.readInt();

            used = new ArrayList[n + 1];
            visited = new boolean[n + 1];
            seen = new boolean[n + 1];

            edge = new ArrayList[n + 1];
            for (int i = 0; i <= n; i++) {
                edge[i] = new ArrayList<>();
                used[i] = new ArrayList<>();
            }

            for (int i = 0; i < m; i++) {
                int u = in.readInt();
                int v = in.readInt();
                edge[u].add(v);

                used[u].add(0);
            }

            boolean cycle = false;
            for (int i = 1; i <= n; i++) {
                if (seen[i]) continue;
                if (go(i, -1) > 0) {
                    cycle = true;
                    break;
                }
            }
            if (cycle) {
                for (int i = 1; i <= n; i++) {
                    seen = new boolean[n + 1];
                    cycle = false;
                    for (int j = 1; j <= n; j++) {
                        if (seen[j]) continue;
                        if (go(j, i) > 0) {
                            cycle = true;
                            break;
                        }
                    }
                    if (!cycle) break;
                }
            }
            out.print(cycle ? "NO" : "YES");


        }

        int go(int pos, int neg) {
            if (visited[pos]) {
                return pos;
            }
            if (seen[pos]) return -1;
            seen[pos] = true;

            visited[pos] = true;
            for (int i = 0; i < edge[pos].size(); i++) {
                if (used[pos].get(i) == neg) continue;
                int f = go(edge[pos].get(i), neg);
                if (f > 0) {
                    if (neg < 0) used[pos].set(i, idx++);
                    visited[pos] = false;
                    return f;
                }
            }
            visited[pos] = false;
            return -1;
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

