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.util.*;
import java.io.*;
public class Main {
    public static class Edge implements Comparable<Edge> {
        int i, a, b;
        public Edge(int i, int a, int b) {
            this.i = i;
            this.a = a;
            this.b = b;
        }
        public int compareTo(Edge other) {
            return i - other.i;
        }
        public String toString() {
            return a + " - " + b;
        }
    }
    public static int n, m;
    public static boolean cycle;
    public static boolean[] back;
    public static int[] mark;
    public static TreeSet<Edge>[] adj;
    public static void dfs(int v) {
        mark[v] = 1;
        for (Edge e : adj[v]) {
            if (mark[e.b] == 0) {
                dfs(e.b);
            } else if (mark[e.b] == 1) {
                back[e.i] = true;
                cycle = true;
            }
        }
        mark[v] = 2;
    }
    public static void main(String[] args) throws IOException {
        BufferedReader rd = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        String[] line = rd.readLine().split(" ");
        n = Integer.parseInt(line[0]);
        m = Integer.parseInt(line[1]);
        adj = new TreeSet[n];
        for (int i = 0; i < n; i++) {
            adj[i] = new TreeSet<>();
        }
        for (int i = 0; i < m; i++) {
            line = rd.readLine().split(" ");
            int a = Integer.parseInt(line[0]) - 1;
            int b = Integer.parseInt(line[1]) - 1;
            adj[a].add(new Edge(i, a, b));
        }
        back = new boolean[m];
        mark = new int[n];
        for (int i = 0; i < n; i++) {
            if (mark[i] == 0) {
                dfs(i);
            }
        }
        if (!cycle) {
            pw.println(1);
            for (int i = 0; i < m; i++) {
                pw.print("1 ");
            }
            pw.println();
        } else {
            pw.println(2);
            for (int i = 0; i < m; i++) {
                if (back[i]) {
                    pw.print("1 ");
                } else {
                    pw.print("2 ");
                }
            }
            pw.println();
        }
        pw.flush();
        pw.close();
    }
}