Problem:
Score : 400 points

Problem Statement

There are N persons called Person 1 through Person N.

You are given M facts that "Person A_i and Person B_i are friends." The same fact may be given multiple times.

If X and Y are friends, and Y and Z are friends, then X and Z are also friends. There is no friendship that cannot be derived from the M given facts.

Takahashi the evil wants to divide the N persons into some number of groups so that every person has no friend in his/her group.

At least how many groups does he need to make?

Constraints

2 \leq N \leq 2\times 10^5

0 \leq M \leq 2\times 10^5

1\leq A_i,B_i\leq N

A_i \neq B_i

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
\vdots
A_M B_M

Output

Print the answer.

Sample Input 1

5 3
1 2
3 4
5 1

Sample Output 1

3

Dividing them into three groups such as \{1,3\}, \{2,4\}, and \{5\} achieves the goal.

Sample Input 2

4 10
1 2
2 1
1 2
2 1
1 2
1 3
1 4
2 3
2 4
3 4

Sample Output 2

4

Sample Input 3

10 4
3 1
4 1
5 9
2 6

Sample Output 3

3

Solution in Java (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;
import java.io.*;
public class Main {
	static ArrayList<Integer> primes;
	public static void main(String[] args) throws Exception{
		int num = 998244353;

		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 		int n = Integer.parseInt(bf.readLine());
 		primes = new ArrayList<Integer>();
 		StringTokenizer st = new StringTokenizer(bf.readLine());
 		long[] array = new long[n];
 		long gcd = array[0];
 		for(int j= 0 ;j<n;j++){
 			array[j] = Integer.parseInt(st.nextToken());
 			gcd = gcd(array[j], gcd);
 		}
 		boolean ans = true;
 		if (gcd == 1){
 		sieveOfEratosthenes(1001);
 		
 		Set<Integer> p = new HashSet<Integer>();
 		for(int j =0;j<n;j++){
 			for(int pr : primes){
 				if (pr*pr > array[j])
 					break;
 				if (array[j]%pr == 0){
 					if (p.contains(pr)){
 						ans = false;
 						break;
 					}
 					else{
 						p.add(pr);
 					}
 				}
 			}
 			if (!ans)
 				break;
 		}
 		}
 		
 		if (gcd > 1)
 			out.println("not coprime");
 		else if (ans)
 			out.println("pairwise coprime");
 		else
 			out.println("setwise coprime");
	 		
 		out.close();
 		
 		
 		
 	}
	public static long gcd(long a, long b){ 
	      if (b == 0) 
	        return a; 
	      return gcd(b, a % b);  
	    }
	public static void sieveOfEratosthenes(int n) {  
        boolean prime[] = new boolean[n+1]; 
        for(int i=0;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) { 
        	if(prime[p]){ 
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
        for(int i = 2; i <= n; i++){ 
            if(prime[i] == true) 
                primes.add(i);
        } 
    }
}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is