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: Runtime Error)

import java.util.*;
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] arr = new int[n];
        for(int i = 0; i < n; i++){
            arr[i] = sc.nextInt();
        }
        Arrays.sort(arr);
        int[] div = new int[arr[0] + 1];
        for(int i = 0; i < n; i++){
            helper(arr[i],div);
        }
        boolean pair = true, set = true;
        for(int i = 2; i < div.length; i++){
            if(div[i] > 1)
                pair = false;
            if(div[i] == n)
                set = false;
        }
        if(pair)
            System.out.println("pairwise coprime");
        else if(set)
            System.out.println("setwise coprime");
        else
            System.out.println("not coprime");
    }
    public static void helper(int num, int[] div){
        for(int i = 2; i <= Math.min(Math.sqrt(num) + 1, div.length - 1); i++){
            if(num % i == 0){
                div[i]++;
                if(i * i < num)
                    div[num / i]++;
            }
        }
    }
}