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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jenish
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DColoringEdges solver = new DColoringEdges();
        solver.solve(1, in, out);
        out.close();
    }

    static class DColoringEdges {
        ArrayList<pair>[] arrayList;
        int[] ans;
        boolean[] visited;
        boolean[] incycle;

        void dfs(int node) {
            visited[node] = true;
            incycle[node] = true;

            for (pair p : arrayList[node]) {
                int k = p.b;
                if (incycle[k]) {
                    ans[p.index] = 2;
                }
                if (!visited[k]) {
                    dfs(k);
                }
            }
            incycle[node] = false;
        }

        public void solve(int testNumber, ScanReader in, PrintWriter out) {

            int n = in.scanInt();
            int m = in.scanInt();
            int k = 1;


            visited = new boolean[n + 1];
            incycle = new boolean[n + 1];
            arrayList = new ArrayList[n + 1];
            ans = new int[m];
            for (int i = 0; i <= n; i++) arrayList[i] = new ArrayList<>();


            for (int i = 0; i < m; i++) {
                int a = in.scanInt();
                int b = in.scanInt();
                arrayList[a].add(new pair(b, i));
            }
            Arrays.fill(ans, 1);
            for (int i = 1; i <= n; i++) if (!visited[i]) dfs(i);
            for (int i = 0; i < m; i++) if (ans[i] == 2) k = 2;
            out.println(k);
            for (int i = 0; i < m; i++) out.print(ans[i] + " ");


        }

        class pair {
            int b;
            int index;

            public pair(int b, int index) {
                this.b = b;
                this.index = index;
            }

        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int INDEX;
        private BufferedInputStream in;
        private int TOTAL;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (INDEX >= TOTAL) {
                INDEX = 0;
                try {
                    TOTAL = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (TOTAL <= 0) return -1;
            }
            return buf[INDEX++];
        }

        public int scanInt() {
            int I = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    I *= 10;
                    I += n - '0';
                    n = scan();
                }
            }
            return neg * I;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}