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.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Washoum
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        inputClass in = new inputClass(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DColoringEdges solver = new DColoringEdges();
        solver.solve(1, in, out);
        out.close();
    }

    static class DColoringEdges {
        static int[] ans;
        static DColoringEdges.Node[] graph;
        static boolean[] visited;
        static boolean[] stack;

        static void dfs(int a) {
            visited[a] = true;
            stack[a] = true;
            for (DColoringEdges.Pair p : graph[a].edges) {
                if (!visited[p.x]) {
                    ans[p.y] = 1;
                    dfs(p.x);
                } else {
                    if (stack[p.x]) {
                        ans[p.y] = 2;
                    } else {
                        ans[p.y] = 1;
                    }
                }
            }
            stack[a] = false;
        }

        public void solve(int testNumber, inputClass sc, PrintWriter out) {
            int n = sc.nextInt();
            graph = new DColoringEdges.Node[n];
            visited = new boolean[n];
            stack = new boolean[n];
            for (int i = 0; i < n; i++) {
                graph[i] = new DColoringEdges.Node();
                graph[i].edges = new ArrayList<>();
            }
            int m = sc.nextInt();
            for (int i = 0; i < m; i++) {
                int x = sc.nextInt() - 1;
                int y = sc.nextInt() - 1;
                graph[x].edges.add(new DColoringEdges.Pair(y, i));
            }
            ans = new int[m];
            for (int i = 0; i < n; i++) {
                if (!visited[i]) {
                    dfs(i);
                }
            }
            int max = 0;
            for (int i : ans)
                max = Math.max(max, i);
            out.println(max);
            for (int i : ans) {
                out.print(i + " ");
            }
        }

        static class Node {
            ArrayList<DColoringEdges.Pair> edges;

        }

        static class Pair {
            int x;
            int y;

            public Pair(int x, int y) {
                this.x = x;
                this.y = y;
            }

        }

    }

    static class inputClass {
        BufferedReader br;
        StringTokenizer st;

        public inputClass(InputStream in) {

            br = new BufferedReader(new InputStreamReader(in));
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}