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 static System.Math;
using System.Linq;
using System.Collections.Generic;
using System;

public class Hello
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine().Trim());
        string[] line = Console.ReadLine().Trim().Split(' ');
        var a = Array.ConvertAll(line, int.Parse);
        if (n == 2)
        {
            Console.WriteLine(gcd(a[0], a[1]) == 1 ? "pairwise coprime" : "not coprime");
            goto exit;
        }
        var gcd0 = gcd(a[0], a[1]);
        if (gcd0 != 1) { Console.WriteLine("not coprime"); goto exit; }
        var ok = true;
        for (int i = 2; i < n; i++)
        {
            var t = gcd(gcd0, a[i]);
            if (t != 1) { ok = false; break; }
            gcd0 = t;
        }
        if (!ok) { Console.WriteLine("not coprime"); goto exit; }
        getAns(n, a);
    exit:;
    }
    static void getAns(int n, int[] a)
    {
        var amax = a.Max();
        if (amax == 1) { Console.WriteLine("pairwise coprime"); return; }
        var pr = GeneratePrime(amax);
        var b = new int[amax + 1];
        for (int i = 0; i < n; i++) b[a[i]]++;
        foreach (var x in pr)
        {
            var p = x;
            var check = 0;
            while (p <= amax)
            {
                check += b[p];
                if (check > 1) { Console.WriteLine("setwise coprime"); return; }
                p += x;
            }
        }
        Console.WriteLine("pairwise coprime");
    }
    static List<int> GeneratePrime(int m)
    {
        var a = new List<int>();
        int p;
        var sqrtMax = Sqrt(m);
        var s = Enumerable.Range(2, m - 1).ToList();
        do
        {
            p = s.First();
            a.Add(p);
            s.RemoveAll(n => n % p == 0);
        }
        while (p < sqrtMax);
        a.AddRange(s);
        return a;
    }
    static int gcd(int a, int b)
    {
        if (a < b) return gcd(b, a);
        while (b != 0)
        {
            var w = a % b;
            a = b;
            b = w;
        }
        return a;
    }
}