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 Solution1{

	public static Integer INT(String s){
		return Integer.parseInt(s);
	}

	public static Long LONG(String s){
		return Long.parseLong(s);
	}

	//====================================================================================================================


	static class Node {
		int dest, index, color;
		Node(int dest, int index) {
			this.dest=dest;
			this.index=index;
		}
	}

	static LinkedList<Node> adj[];
	static boolean visited[];

	public static void dfs(int i, boolean flag[]) {

		flag[i]=true;
		visited[i]=true;

		for(Node item: adj[i]) {
			if(flag[item.dest])
				item.color=2;
			else 
				item.color=1;
			
			if(!visited[item.dest])
				dfs(item.dest, flag);
		}

		flag[i]=false;
	}


	public static void main(String args[])throws IOException{

		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringBuilder out=new StringBuilder();

		String line[]=br.readLine().split("\\s");
		int n=INT(line[0]),
			m=INT(line[1]);

		adj=new LinkedList[n+1];
		for(int i=0; i<=n; i++)
			adj[i]=new LinkedList<>();

		for(int i=0; i<m; i++){
			line=br.readLine().split("\\s");
			int u=INT(line[0]),
				v=INT(line[1]);
			
			adj[u].add(new Node(v, i));
		}

		visited=new boolean[n+1];

		for(int i=1; i<=n; i++)
			if(!visited[i]) {
				// System.out.println("i "+i);
				dfs(i, new boolean[n+1]);
			}

		int color[]=new int[m];
		boolean flag=true;
		for(int i=1; i<=n; i++)
			for(Node item: adj[i]) {
				color[item.index]=item.color;
				if(item.color==2)
					flag=false;
			}

		out.append(flag?1:2);
		out.append("\n");
		for(int i=0; i<m; i++)
			out.append(color[i]+" ");
		System.out.println(out);
	}
}