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.*;

public class F {
    public static class Edge{
        int to;
        int ind;
        public Edge(int t, int i){
            this.to = t;
            this.ind = i;
        }
    }
    public static class Graph{
        ArrayList<Edge>[] nn;
        public Graph(int size){
            this.nn = new ArrayList[size];
            for(int i = 0; i < size; ++i){
                nn[i] = new ArrayList<>();
            }
        }
        public void add(int f, int t, int i){
            nn[f].add(new Edge(t, i));
        }
        public ArrayList<Edge> get_n(int v){
            return nn[v];
        }
    }
    public static void dfs(int node){
        used[node] = 1;
        ArrayList<Edge> nn = graph.get_n(node);
        for(Edge e : nn){
            if(used[e.to] == 0){
                dfs(e.to);
                color[e.ind] = 1;
            }
            else if(used[e.to] == 2){
                color[e.ind] = 1;
            }
            else{
                color[e.ind] = 2;
                ans = 2;
            }
        }
        used[node] = 2;
    }
    public static Graph graph;
    public static int ans = 1;
    public static int[] used;
    public static int[] color;
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(reader.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        used = new int[n];
        color = new int[m];
        graph = new Graph(n);
        for(int i = 0; i < m; ++i){
            st = new StringTokenizer(reader.readLine());
            int from = Integer.parseInt(st.nextToken()) - 1;
            int to = Integer.parseInt(st.nextToken()) - 1;
            graph.add(from, to, i);
        }
        for(int i = 0; i < n; ++i){
            if(used[i] == 0){
                dfs(i);
            }
        }
        writer.println(ans);
        for(int i = 0; i < m; ++i){
            writer.print(color[i] + " ");
        }
        writer.close();
    }
}