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.*;
import java.util.*;

/**
 * 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);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);

        out.close();
    }


    static class TaskA {


        public void solve(int x, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            Map<String, Boolean> colMp = new LinkedHashMap<>();
            Map<Integer, List<Integer>> mp = new HashMap<>();
            Map<Integer, Integer> col = new HashMap<>();
            for (int i = 1; i <= n; i++) {
                col.put(i, 0);
                mp.put(i, new ArrayList<>());
            }
            for (int i = 0; i < m; i++) {
                int u = in.nextInt();
                int v = in.nextInt();
                colMp.put(u+"-"+v, Boolean.FALSE);
                mp.get(u).add(v);
            }

            int cyc = 1;
            for (int i : mp.keySet()) {
                if (col.get(i) == 0) {
                    if (dfs(i, mp, col, colMp)) {
                        cyc = 2;
                    }
                }
            }
            out.println(cyc);
            for (String s : colMp.keySet()) {
                out.print((colMp.get(s) ? 2 : 1) + " ");
            }

        }

        private boolean dfs(int i, Map<Integer, List<Integer>> mp, Map<Integer, Integer> col, Map<String, Boolean> kCol) {
            col.put(i, 1);
            boolean isCyc = false;
            for (int j : mp.get(i)) {
                if (col.get(j) == 0) {
                    isCyc = dfs(j, mp, col, kCol) || isCyc;
                } else if (col.get(j) == 1) {
                    isCyc = true;
                    kCol.put(i+"-"+j, Boolean.TRUE);
                }
            }
            col.put(i, 2);
            return isCyc;
        }


    }


    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());
        }

    }
}