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.*;
import java.math.BigInteger;
import java.util.*;
import java.util.concurrent.atomic.AtomicIntegerArray;

public class Solution {

    public static void main(String[] args) throws Exception {
        MyReader reader = new MyReader(System.in);
//        MyReader reader = new MyReader(new FileInputStream("input.txt"));
        MyWriter writer = new MyWriter(System.out);
        new Solution().run(reader, writer);
        writer.close();
    }

    private void run(MyReader reader, MyWriter writer) throws Exception {
        int n = reader.nextInt();
        int m = reader.nextInt();
        List<Integer>[] edges = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            edges[i] = new ArrayList<>();
        }
        for (int i = 0; i < m; i++) {
            int a = reader.nextInt() - 1;
            int b = reader.nextInt() - 1;
            edges[a].add(b);
        }
        vis = new int[n];
        for (int i = 0; i < n; i++) {
            if (vis[i] == 0) {
                if (dfs(i, edges) == 1) {
                    break;
                }
            }
        }
        if (cy.size() == 0) {
            System.out.println("YES");
            return;
        }
        for (int i = cy.size() - 1; i > 0; i--) {
            edges[cy.get(i)].remove(cy.get(i - 1));
            Arrays.fill(vis, 0);
            int r = 0;
            for (int j = 0; j < n; j++) {
                if (vis[j] == 0) {
                    r += dfs(j, edges);
                }
            }
            if (r == 0) {
                System.out.println("YES");
                return;
            }
            edges[cy.get(i)].add(cy.get(i - 1));
        }
        System.out.println("NO");
    }

    private int dfs(int n, List<Integer>[] edges) {
        vis[n] = 1;
        for (int w : edges[n]) {
            if (vis[w] == 1) {
                if (!q) {
                    cy.add(w);
                    cy.add(n);
                }
                return 1;
            } else if (vis[w] == 0) {
                if (dfs(w, edges) == 1) {
                    if (!q) {
                        cy.add(n);
                    }
                    if (n == cy.get(0)) {
                        q = true;
                    }
                    return 1;
                }
            }
        }
        vis[n] = 2;
        return 0;
    }

    private boolean q;
    private int[] vis;
    List<Integer> cy = new ArrayList<>();

    static class MyReader {

        final BufferedInputStream in;
        final int bufSize = 1 << 16;
        final byte buf[] = new byte[bufSize];
        int i = bufSize;
        int k = bufSize;
        boolean end = false;
        final StringBuilder str = new StringBuilder();

        MyReader(InputStream in) {
            this.in = new BufferedInputStream(in, bufSize);
        }

        int nextInt() throws IOException {
            return (int) nextLong();
        }

        int[] nextIntArray(int n) throws IOException {
            int[] m = new int[n];
            for (int i = 0; i < n; i++) {
                m[i] = nextInt();
            }
            return m;
        }

        int[][] nextIntMatrix(int n, int m) throws IOException {
            int[][] a = new int[n][0];
            for (int j = 0; j < n; j++) {
                a[j] = nextIntArray(m);
            }
            return a;
        }

        long nextLong() throws IOException {
            int c;
            long x = 0;
            boolean sign = true;
            while ((c = nextChar()) <= 32) ;
            if (c == '-') {
                sign = false;
                c = nextChar();
            }
            if (c == '+') {
                c = nextChar();
            }
            while (c >= '0') {
                x = x * 10 + (c - '0');
                c = nextChar();
            }
            return sign ? x : -x;
        }

        long[] nextLongArray(int n) throws IOException {
            long[] m = new long[n];
            for (int i = 0; i < n; i++) {
                m[i] = nextLong();
            }
            return m;
        }

        int nextChar() throws IOException {
            if (i == k) {
                k = in.read(buf, 0, bufSize);
                i = 0;
            }
            return i >= k ? -1 : buf[i++];
        }

        String nextString() throws IOException {
            if (end) {
                return null;
            }
            str.setLength(0);
            int c;
            while ((c = nextChar()) <= 32 && c != -1) ;
            if (c == -1) {
                end = true;
                return null;
            }
            while (c > 32) {
                str.append((char) c);
                c = nextChar();
            }
            return str.toString();
        }

        String nextLine() throws IOException {
            if (end) {
                return null;
            }
            str.setLength(0);
            int c = nextChar();
            while (c != '\n' && c != '\r' && c != -1) {
                str.append((char) c);
                c = nextChar();
            }
            if (c == -1) {
                end = true;
                if (str.length() == 0) {
                    return null;
                }
            }
            if (c == '\r') {
                nextChar();
            }
            return str.toString();
        }

        char[] nextCharArray() throws IOException {
            return nextString().toCharArray();
        }

        char[][] nextCharMatrix(int n) throws IOException {
            char[][] a = new char[n][0];
            for (int i = 0; i < n; i++) {
                a[i] = nextCharArray();
            }
            return a;
        }
    }

    static class MyWriter {

        final BufferedOutputStream out;
        final int bufSize = 1 << 16;
        final byte buf[] = new byte[bufSize];
        int i = 0;
        final byte c[] = new byte[30];
        static final String newLine = System.getProperty("line.separator");

        MyWriter(OutputStream out) {
            this.out = new BufferedOutputStream(out, bufSize);
        }

        void print(long x) throws IOException {
            int j = 0;
            if (i + 30 >= bufSize) {
                flush();
            }
            if (x < 0) {
                buf[i++] = (byte) ('-');
                x = -x;
            }
            while (j == 0 || x != 0) {
                c[j++] = (byte) (x % 10 + '0');
                x /= 10;
            }
            while (j-- > 0)
                buf[i++] = c[j];
        }

        void print(int[] m) throws IOException {
            for (int a : m) {
                print(a);
                print(' ');
            }
        }

        void print(long[] m) throws IOException {
            for (long a : m) {
                print(a);
                print(' ');
            }
        }

        void print(String s) throws IOException {
            for (int i = 0; i < s.length(); i++) {
                print(s.charAt(i));
            }
        }

        void print(char x) throws IOException {
            if (i == bufSize) {
                flush();
            }
            buf[i++] = (byte) x;
        }

        void print(char[] m) throws IOException {
            for (char c : m) {
                print(c);
            }
        }

        void println(String s) throws IOException {
            print(s);
            println();
        }

        void println() throws IOException {
            print(newLine);
        }

        void flush() throws IOException {
            out.write(buf, 0, i);
            out.flush();
            i = 0;
        }

        void close() throws IOException {
            flush();
            out.close();
        }
    }
}