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 D {
    static ArrayList<Edge>[] graph;
    static int[] col;
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int n = scanner.nextInt(), m = scanner.nextInt();
        graph = new ArrayList[n];
        for(int i = 0; i <n; i++) graph[i] = new ArrayList<>();
        Edge[] edges = new Edge[m];
        for(int i= 0; i < m; i++) {
            int u = scanner.nextInt()-1, v = scanner.nextInt()-1;
            Edge edge = new Edge(u, v);
            graph[u].add(edge);
            edges[i] = edge;
        }
        int max = 1;
        col = new int[n];
        for(int i = 0; i < n; i++) if(col[i] == 0) dfs(i);
        for(int i = 0; i < m; i++) max = Math.max(edges[i].c, max);
        out.println(max);
        for(int i =0;i < m; i++) out.print(edges[i].c + " ");
        out.println();
        out.flush();
    }
    static void dfs(int v) {
        col[v] = 1;
        for(Edge edge: graph[v]) {
            if (edge.c != 0) continue;
            else if (col[edge.v]==1) {
                edge.c = 2;
            }
            else {
                edge.c = 1;
                dfs(edge.v);
            }
        }
        col[v] = 2;
    }
    static class Edge {
        int u,v,c;
        public Edge(int aa, int bb) {
            u = aa; v = bb;c = 0;
        }
    }
    public static Edge[] cupidShuffle(Edge[] arr) {
        Random random = new Random();
        for(int i = 0; i < arr.length; i++) {
            int ind = random.nextInt(arr.length-i)+i;
            Edge temp = arr[i];
            arr[i] = arr[ind];
            arr[ind] = temp;
        }
        return arr;
    }
    
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        
        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }
        
        public FastScanner() {
            this(new InputStreamReader(System.in));
        }
        
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        int nextInt() {
            return Integer.parseInt(next());
        }
        
        long nextLong() {
            return Long.parseLong(next());
        }
        
        double nextDouble() {
            return Double.parseDouble(next());
        }
        
        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}