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 C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Linq;

namespace ProgramingStydying
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split().Select(long.Parse).ToArray();

            var ans = "pairwise coprime";

            for(int divider = 2; divider <= Math.Sqrt(a.Max()); divider++)
            {
                var flag = 0;

                for(int i = 0; i < n; i++)
                {
                    if(a[i] % divider == 0)
                    {
                        flag++;
                    }
                    if (flag == 2)
                    {
                        break;
                    }
                }

                if(flag == 2)
                {
                    ans = "setwise coprime";
                    break;
                }
            }

            if(ans == "setwise coprime")
            {
                for(int divider = 2; divider <= Math.Sqrt(a.Max()); divider++)
                {
                    var flag = 0;

                    for(int i = 0; i < n; i++)
                    {
                        if(a[i] % divider == 0)
                        {
                            flag++;
                        }
                    }

                    if(flag == n)
                    {
                        ans = "not coprime";
                        break;
                    }
                }
            }

            Console.WriteLine(ans);
        }
    }
}