Problem: You are given a directed graph with n vertices and m directed edges without self-loops or multiple edges.

Let's denote the k-coloring of a digraph as following: you color each edge in one of k colors. The k-coloring is good if and only if there no cycle formed by edges of same color.

Find a good k-coloring of given digraph with minimum possible k.

Input

The first line contains two integers n and m (2 ≤ n ≤ 5000, 1 ≤ m ≤ 5000) — the number of vertices and edges in the digraph, respectively.

Next m lines contain description of edges — one per line. Each edge is a pair of integers u and v (1 ≤ u, v ≤ n, u ≠ v) — there is directed edge from u to v in the graph.

It is guaranteed that each ordered pair (u, v) appears in the list of edges at most once.

Output

In the first line print single integer k — the number of used colors in a good k-coloring of given graph.

In the second line print m integers c_1, c_2, ..., c_m (1 ≤ c_i ≤ k), where c_i is a color of the i-th edge (in order as they are given in the input).

If there are multiple answers print any of them (you still have to minimize k).

Examples

Input


4 5
1 2
1 3
3 4
2 4
1 4


Output


1
1 1 1 1 1 


Input


3 3
1 2
2 3
3 1


Output


2
1 1 2 

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.List;
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;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DColoringEdges solver = new DColoringEdges();
        solver.solve(1, in, out);
        out.close();
    }

    static class DColoringEdges {
        static List<int[]>[] g;
        static int n;
        static int m;
        static boolean cycle = false;
        static int[] col;
        static int[] res;

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            n = in.nextInt();
            m = in.nextInt();
            g = new List[n];
            for (int i = 0; i < n; ++i) {
                g[i] = new ArrayList<>();
            }
            col = new int[n];
            res = new int[m];

            for (int i = 0; i < m; ++i) {
                int u = in.nextInt() - 1;
                int v = in.nextInt() - 1;
                g[u].add(new int[]{v, i});
            }

            for (int i = 0; i < n; ++i) {
                if (col[i] == 0)
                    dfs(i);
            }

            out.println(cycle ? 2 : 1);
            boolean first = true;
            for (int r : res) {
                if (!first) out.print(" ");
                first = false;
                out.print(r);
            }
            out.println();
        }

        private static void dfs(int cur) {
            col[cur] = 1;
            for (int[] p : g[cur]) {
                int next = p[0];
                int id = p[1];
                if (col[next] == 0) {
                    dfs(next);
                    res[id] = 1;
                } else if (col[next] == 2) {
                    res[id] = 1;
                } else {
                    res[id] = 2;
                    cycle = true;
                }
            }
            col[cur] = 2;
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;

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

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

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

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}