Problem:
Score : 500 points

Problem Statement

We have N integers. The i-th number is A_i.

\{A_i\} is said to be pairwise coprime when GCD(A_i,A_j)=1 holds for every pair (i, j) such that 1\leq i < j \leq N.

\{A_i\} is said to be setwise coprime when \{A_i\} is not pairwise coprime but GCD(A_1,\ldots,A_N)=1.

Determine if \{A_i\} is pairwise coprime, setwise coprime, or neither.

Here, GCD(\ldots) denotes greatest common divisor.

Constraints

2 \leq N \leq 10^6

1 \leq A_i\leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 \ldots A_N

Output

If \{A_i\} is pairwise coprime, print pairwise coprime; if \{A_i\} is setwise coprime, print setwise coprime; if neither, print not coprime.

Sample Input 1

3
3 4 5

Sample Output 1

pairwise coprime

GCD(3,4)=GCD(3,5)=GCD(4,5)=1, so they are pairwise coprime.

Sample Input 2

3
6 10 15

Sample Output 2

setwise coprime

Since GCD(6,10)=2, they are not pairwise coprime. However, since GCD(6,10,15)=1, they are setwise coprime.

Sample Input 3

3
6 10 16

Sample Output 3

not coprime

GCD(6,10,16)=2, so they are neither pairwise coprime nor setwise coprime.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
public class Main{
    
    static final int MOD = (int)1e9+7;
    static final int MAX = (int)1e6+1;
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        int n = Integer.parseInt(sc.next());
        int[] a = new int[n];
        HashMap<Integer, Integer> h = new HashMap<>();
        for(int i=0; i<n; i++){
            a[i] = Integer.parseInt(sc.next());
            h.put(a[i], h.getOrDefault(a[i], 0)+1);
        }
        Arrays.sort(a);
        
        boolean[] prime = new boolean[MAX];
        Arrays.fill(prime, true);
        boolean pc = true;
        for(int i=2; i<MAX; i++){
            if(!prime[i]){
                continue;
            }
            int cnt = 0;
            for(int j=i; j<MAX; j+=i){
                prime[j] = false;
                cnt += h.getOrDefault(j, 0);
            }
            if(cnt > 1){
                pc = false;
            }
        }
        
        long gcd = a[0];
        for(int i=1; i<n; i++){
            gcd = gcd(a[i], gcd);
        }
        
        if(pc && gcd==1){
            System.out.println("pairwise coprime");
        }else if(gcd==1){
            System.out.println("setwise coprime");
        }else{
            System.out.println("not coprime");
        }
        
    }
    
    static long gcd (long a, long b){
        if(a < b){
            return gcd(b, a);
        }
        return b>0 ? gcd(b,a%b) : a;
    }
}