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:
/*Author: Satyajeet Singh, Delhi Technological University*/
    import java.io.*;
    import java.util.*;
    import java.text.*; 
    import java.lang.*;
    import java.math.*;
 
public class Main{
/*********************************************Constants******************************************/
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));        
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static long mod=(long)1e9+7;
    static long mod1=998244353;
    static boolean sieve[];
    static ArrayList<Integer> primes;
    static long factorial[],invFactorial[];
    static HashSet<Pair> graph[];
    static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
/****************************************Solutions Begins***************************************/
    static boolean vis[];
    static int fs=0;
    public static void main (String[] args) throws Exception {
        String st[]=nl();
        int n=pi(st[0]);
        int m=pi(st[1]);
        int indeg[]=new int[n+1];
        Makegraph(n+1);
        ArrayList<Integer> list=new ArrayList<>();
        for(int i=0;i<m;i++){
            st=nl();
            int a=pi(st[0]);
            int b=pi(st[1]);
            addEdge(a,b);
            list.add(a);
            list.add(b);
            indeg[b]++;
        }
        Queue<Integer> q=new ArrayDeque<>();
        vis=new boolean[n+1];
        for(int i=1;i<=n;i++){
            if(indeg[i]==0){
                q.add(i);
                vis[i]=true;
            }
        }
        int ans=0;
        boolean flag=true;
        if(q.size()==0){
            flag=false;
        }
     //   debug(flag);
        while(!q.isEmpty()){
            int sz=q.size();
            ans++;
            while(sz>0){
                int a=q.remove();
                sz--;
                for(Pair p:graph[a]){
                    if(vis[p.u]){
                        debug(p.u);
                        flag=false;
                        break;
                    }
                    indeg[p.u]--;
                    if(indeg[p.u]==0){
                        q.add(p.u);
                    }
                }
                if(!flag)break;
            }
            if(!flag)break;         
        }

       /// debug(graph);
        for(int i=1;i<=n;i++){
            if(indeg[i]!=0){
                flag=false;
                break;
            }
        }
    
        if(flag){
            out.println(1);
            for(int i=1;i<=m;i++){
                out.print(1+" ");
            }
        }
        else{
            out.println(2);
            for(int i=0;i<list.size();i+=2){
                if(list.get(i)<list.get(i+1)){
                    out.print(1+" ");
                }
                else{
                    out.print(2+" ");
                }
            }
        }
/****************************************Solutions Ends**************************************************/
        out.flush();
        out.close();
    }
/****************************************Template Begins************************************************/
    static String[] nl() throws Exception{
        return br.readLine().split(" ");
    }
    static String[] nls() throws Exception{
        return br.readLine().split("");
    }
    static int pi(String str) {
        return Integer.parseInt(str);
    }
    static long pl(String str){
        return Long.parseLong(str);
    }
    static double pd(String str){
        return Double.parseDouble(str);
    }
/***************************************Precision Printing**********************************************/
    static void printPrecision(double d){
        DecimalFormat ft = new DecimalFormat("0.000000000000000000000"); 
        out.println(ft.format(d));
    }
/**************************************Bit Manipulation**************************************************/
    static void printMask(long mask){
        System.out.println(Long.toBinaryString(mask));
    }
    static int countBit(int mask){
        int ans=0;
        while(mask!=0){
            if(mask%2==1){
                ans++;
            }
            mask/=2;
        }
        return ans;
    }
/******************************************Graph*********************************************************/
    static void Makegraph(int n){
        graph=new HashSet[n];
        for(int i=0;i<n;i++){
            graph[i]=new HashSet<>();
        }
    }
    static void addEdge(int a,int b){
        graph[a].add(new Pair(b,1));
    }
    static void addEdge(int a,int b,int c){
        graph[a].add(new Pair(b,c));
    }    
/*********************************************PAIR********************************************************/
    static class PairComp implements Comparator<Pair>{
        public int compare(Pair p1,Pair p2){
            return p1.u-p2.u;
        }
    }
    static class Pair implements Comparable<Pair> {
        int u;
        int v;
        int index=-1;
        public Pair(int u, int v) {
            this.u = u;
            this.v = v;
        }
        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }
        public boolean equals(Object o) {
            Pair other = (Pair) o;
            return u == other.u && v == other.v;
        }
        public int compareTo(Pair other) {
            if(index!=other.index)
                return Long.compare(index, other.index);
            return Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u);
        }
        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
/******************************************Long Pair*******************************************************/
    static class PairCompL implements Comparator<Pairl>{
        public int compare(Pairl p1,Pairl p2){
            if(p1.u-p2.u<0){
                return -1;
            }
            else if(p1.u-p2.u>0){
                return 1;
            }
            else{
                if(p1.v-p2.v<0){
                    return -1;
                }
                else if(p1.v-p2.v>0){
                    return 1;
                }
                else{
                    return 0;
                }
            }
        }
    }
    static class Pairl implements Comparable<Pairl> {
            long u;
            long v;
            int index=-1;
            public Pairl(long u, long v) {
                this.u = u;
                this.v = v;
            }
    
            public int hashCode() {
                int hu = (int) (u ^ (u >>> 32));
                int hv = (int) (v ^ (v >>> 32));
                return 31 * hu + hv;
            }
    
            public boolean equals(Object o) {
                Pairl other = (Pairl) o;
                return u == other.u && v == other.v;
            }
    
            public int compareTo(Pairl other) {
                if(index!=other.index)
                    return Long.compare(index, other.index);
                return Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u);
            }
    
            public String toString() {
                return "[u=" + u + ", v=" + v + "]";
            }
        }
/*****************************************DEBUG***********************************************************/
    public static void debug(Object... o) {
        if(!oj)
        System.out.println(Arrays.deepToString(o));
    }
/************************************MODULAR EXPONENTIATION***********************************************/
    static long modulo(long a,long b,long c) {
        long x=1;
        long y=a;
        while(b > 0){
            if(b%2 == 1){
                x=(x*y)%c;
            }
            y = (y*y)%c; // squaring the base
            b /= 2;
        }
        return  x%c;
    }
/********************************************GCD**********************************************************/
    static long gcd(long x, long y)
    {
        if(x==0)
            return y;
        if(y==0)
            return x;
        long r=0, a, b;
        a = (x > y) ? x : y; // a is greater number
        b = (x < y) ? x : y; // b is smaller number
        r = b;
        while(a % b != 0)
        {
            r = a % b;
            a = b;
            b = r;
        }
        return r;
    }
/******************************************SIEVE**********************************************************/
    static void sieveMake(int n){
        sieve=new boolean[n];
        Arrays.fill(sieve,true);
        sieve[0]=false;
        sieve[1]=false;
        for(int i=2;i*i<n;i++){
            if(sieve[i]){
                for(int j=i*i;j<n;j+=i){
                    sieve[j]=false;
                }
            }
        }
        primes=new ArrayList<Integer>();
        for(int i=0;i<n;i++){
            if(sieve[i]){
                primes.add(i);
            }
        }        
    }
/********************************************End***********************************************************/
}