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.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.ArrayDeque;
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);
        DColoringEdges solver = new DColoringEdges();
        solver.solve(1, in, out);
        out.close();
    }

    static class DColoringEdges {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();

            ArrayList<Integer> inDegrees = new ArrayList<>();

            List<List<Integer>> adj = new ArrayList<>();

            ArrayList<List<Integer>> edges = new ArrayList<>();

            for (int i = 0; i <= n; i++) {
                adj.add(new ArrayList<>());
                inDegrees.add(0);
            }

            for (int i = 1; i <= m; i++) {
                int u = in.nextInt();
                int v = in.nextInt();

                edges.add(Arrays.asList(u, v));
                adj.get(u).add(v);
                inDegrees.set(v, inDegrees.get(v) + 1);
            }

            ArrayDeque<Integer> queue = new ArrayDeque<>();

            for (int u = 1; u <= n; u++) {
                if (inDegrees.get(u) == 0) {
                    queue.addLast(u);
                }
            }

            ArrayList<Integer> topsort = new ArrayList<>();

            while (!queue.isEmpty()) {
                int u = queue.pollFirst();

                topsort.add(u);
                for (Integer v : adj.get(u)) {
                    inDegrees.set(v, inDegrees.get(v) - 1);
                    if (inDegrees.get(v) == 0) {
                        queue.addLast(v);
                    }
                }
            }

            if (topsort.size() == n) {
                out.println(1);
                for (int i = 0; i < m; i++) {
                    out.printf("1 ");
                }
                out.println();
            }
            else {
                out.println(2);

                for (List<Integer> edge : edges) {
                    if (edge.get(0) < edge.get(1)) {
                        out.printf("1 ");
                    }
                    else {
                        out.printf("2 ");
                    }
                }
                out.println();
            }
        }

    }

    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());
        }

    }
}