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.lang.*;
import java.io.*;

public class Solution {
    static class Pair {
        int node;
        int index;
        Pair(int node, int index) {
            this.node = node;
            this.index = index;
        }
    }
    static int N = 5005;
    static Map<Integer, List<Pair>> map = new HashMap<>();
    static int[] color = new int[N];
    static int[] currState = new int[N];
    static int n, m;
    static boolean cycleFound = false;
    public static void main(String[] args) throws java.lang.Exception {
        out = new PrintWriter(new BufferedOutputStream(System.out));
        sc = new FastReader();
        int test = 1;
        for (int t = 0; t < test; t++) {
            solve();
        }
        out.close();
    }

    private static void solve() {
        n = sc.nextInt();
        m = sc.nextInt();
        Arrays.fill(color, 1);
        for (int i = 0; i < N; i++) {
            map.put(i, new ArrayList<>());
        }
        for (int i = 0; i < m; i++) {
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            map.get(u).add(new Pair(v, i));
        }
        for (int i = 0; i < n; i++) {
            if (currState[i] == 0) {
                dfs(i);
            }
        }
        out.println(cycleFound ? 2 : 1);
        for (int i = 0; i < m; i++) {
            out.print(color[i] + " ");
        }
        out.println();
    }

    private static void dfs(int currNode) {
        // here 1 represents -> node is in stack AND 2 represents -> node is visited
        // push the currNode into stack
        currState[currNode] = 1;
        for (Pair adj : map.get(currNode)) {
            if (currState[adj.node] == 0) {
                // not visited yet
                dfs(adj.node);
                color[adj.index] = 1;
            }else if (currState[adj.node] == 2) {
                // already visited node
                color[adj.index] = 1;
            }else {
                // found a cycle assign it a different color
                color[adj.index] = 2;
                cycleFound = true;
            }
        }
        // mark the currNode as visited
        currState[currNode] = 2;
    }

    public static FastReader sc;
    public static PrintWriter out;
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(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 nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}