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: Wrong Answer)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;

public class Main {
    
    public static void main(String[] args) {
    
        var sc = new Scanner(System.in);
    
        int n = Integer.parseInt(sc.next());
        var a = new int[n];
        var set = new HashSet<Integer>();
        for(int i = 0; i < n; i++){
            a[i] = Integer.parseInt(sc.next());
            set.add(a[i]);
        }
        
        List<Integer> list = sieve(1000);
        boolean b = true;
        if(set.size() < n){
            b = false;
        }else{
            for(int x : list){
                int count = 0;
                for(int i = 0; i < n; i++){
                    if(a[i] % x == 0){
                        count++;
                    }
                }
                if(count >= 2){
                    b = false;
                    break;
                }
            }
        }
        
        if(b){
            System.out.println("pairwise coprime");
        }else{
            long gcd = gcd(a[0], a[1]);
            for(int i = 2; i < n; i++){
                gcd = gcd(gcd, a[i]);
            }
            if(gcd == 1){
                System.out.println("setwise coprime");
            }else{
                System.out.println("not coprime");
            }
        }
    }
    
    static List<Integer> sieve(int x){
        
        var p = new boolean[x+1];
        Arrays.fill(p, true);
        int sqrt = (int)Math.sqrt(x+1);
        for(int i = 2; i <= sqrt; i++){
            if(!p[i]) continue;
            for(int j = i*i; j <= x; j += i){
                p[j] = false;
            }
        }
        var list = new ArrayList<Integer>();
        if(x >= 2) list.add(2);
        for(int i = 3; i <= x; i += 2){
            if(p[i]) list.add(i);
        }
        return list;
    }
    
    static long gcd(long a, long b){
        return b == 0 ? a : gcd(b, a%b);
    }
}