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

public class ColoringEdges {
    static ArrayList<Integer>[] adjList;
    static Color[] color = new Color[5000];
    static int[] edgeColor = new int[5000];
    static int[][] edgeID = new int[5000][5000];
    static int count = 1;
    static enum Color {
        progress, done, none;
    }
    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        adjList = new ArrayList[n];
        for (int i = 0 ; i < n; i++) {
            adjList[i] = new ArrayList<>();
            color[i] = Color.none;
        }
        for (int i = 0; i < m; i++) {
            st = new StringTokenizer(f.readLine());
            int a = Integer.parseInt(st.nextToken())-1;
            int b = Integer.parseInt(st.nextToken())-1;
            edgeID[a][b] = i;
            adjList[a].add(b);
        }
        for (int i = 0; i < n; i++) {
            if (color[i] == Color.none) {
                dfs(i, 0);
            }
        }
        PrintWriter out = new PrintWriter(System.out);
        out.println(count);
        for (int i = 0; i < m; i++) {
            out.print(edgeColor[i]+1 + " ");
        }
        out.close();
    }
    public static void dfs(int node, int col) {
        color[node] = Color.progress;
        for (int next : adjList[node]) {
            if (color[next] == Color.progress) {
                count = 2;
                edgeColor[edgeID[node][next]] = (col + 1)%2;
            }
            else if (color[next] == Color.none){
                edgeColor[edgeID[node][next]] = col;
                dfs(next, col);
            }
        }
        color[node] = Color.done;
    }
}