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.*;
public class ColoringEdges {
	static class Pair{
		int x;
		int y;
		Pair(int x,int y){
			this.x = x;
			this.y = y;
		}
	}
	static Map<Integer,ArrayList<Integer>> map = new HashMap<>();
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
			int n = sc.nextInt();
			int m = sc.nextInt();
			ArrayList<Pair> ar3 = new ArrayList<>();
			for(int i=0;i<m;i++) {
				int x = sc.nextInt();
				int y = sc.nextInt();
				Pair p1 = new Pair(x,y);
				ar3.add(p1);
				if(map.get(x)==null) {
					ArrayList<Integer> r = new ArrayList<>();
					r.add(y);
					map.put(x,r);
				}
				else {
					map.get(x).add(y);
				}
			}
            boolean visited[] = new boolean[n+1];
			boolean recStack[] = new boolean[n+1];
			boolean cycle = false;
			for(int i=1;i<=n;i++) {
				if(cycle(i,visited,recStack)) {
					cycle = true;
					break;
				}
			}
			if(!cycle) {
			    System.out.println("1");
				for(int i=0;i<m;i++) {
					System.out.print("1"+" ");
				}
			}
			else {
			    System.out.println("2");
				for(int i=0;i<m;i++) {
					int x = ar3.get(i).x;
					int y = ar3.get(i).y;
					if(x<y)
						System.out.print("1"+" ");
					else
						System.out.print("2"+" ");
				}
			}
	}
		static boolean cycle(int i,boolean visited[],boolean recStack[]) {
		if(recStack[i])
			return true;
		if(visited[i])
			return false;
		visited[i] = true;
		recStack[i] = true;
		if(map.get(i)==null){
		    recStack[i] = false;
		return false;
		}
		ArrayList<Integer> ar = map.get(i);
		for(Integer j : ar) {
			if(cycle(j,visited,recStack))
			return true;
		}
		recStack[i] = false;
			return false;
	}
}