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.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder2 {
	class Program {
		static void Main(string[] args) {

			//出力の都度更新をやめる
			var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
			Console.SetOut(sw);


			Ans();

			//更新する
			Console.Out.Flush();
			
		}
public static void Ans() {

			var inputArray = retreiveLongArray();
			var inputCount = 1;

			// 不正な入力は処理しない
			if (inputArray.Length != inputCount) {
				Console.WriteLine("invalid input");
				return;
			}
			
			
			var N = (int)inputArray[0];
			var Aarray = retreiveLongArray();

			var AHash = new HashSet<long>();
			foreach (var a in Aarray) {
				if (!AHash.Contains(a)) {
					AHash.Add(a);
				}
			}
			var Num = AHash.Count();
			var aMax = AHash.Max();
			var primehurui = eleFuri((int)aMax);

			var primeCount = primehurui.Where(x => x == true).Count();

			var isPairwise = true;
			if (N > primeCount + 1) {//1も含めた素数より数が多かったら互いに素は無理
				isPairwise = false;
			}
			else {
				for (int i = 2; i <= aMax; i++) {
					if (!primehurui[i]) {
						continue;
					}
					var count = 0;

					foreach (var a in Aarray) {

						if (a % i == 0) {
							count++;
						}
					}
					if (count > 1) {
						isPairwise = false;
					}
				}
			}

			var isSetwise = true;

			var maxcheck = (aMax / Num);//Num種類必要だからmaxCheck以下が公約数である必要あり
			for (int i = 2; i <= maxcheck; i++) {
				if (!primehurui[i]) {
					continue;
				}
				var count = 0;

				foreach (var a in AHash) {

					if (a%i==0) {
						count++;
					}
				}

				if (count ==Num) {
					isSetwise = false;
					break;
				}

			}

			if (isPairwise) {
				Console.WriteLine("pairwise coprime");
				return;
			}

			if (isSetwise) {
				Console.WriteLine("setwise coprime");
				return;
			}

			var ans = "not coprime";
			Console.WriteLine(ans);

		}


		private static bool[] eleFuri(int N) {

			var hurui = Enumerable.Repeat(true,N+1).ToArray();
			var max = Math.Sqrt(N);

			for (int i = 2; i <= max; i++) {
				if (!hurui[i]) {
					continue;
				}
				var k = i+i;
				while (k<=N) {
					hurui[k] = false;
					k += i;
				}

			}

			return hurui;

		}
		

		

		/// <summary>
		/// スペースで区切られた文字列配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static string[] retreiveStringArray() {
			var inputArray = Console.ReadLine().Split(' ');
			return inputArray;
		}

		/// <summary>
		/// スペースで区切られた整数配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static long[] retreiveLongArray() {
			var inputArray = Console.ReadLine().Split(' ');
			var longArray = inputArray.Select(s => long.Parse(s));
			return longArray.ToArray();
		}


		/// <summary>
		/// 2組みずつの入力データ(数値)からTuppleListを作成する
		/// </summary>
		/// <param name="N"></param>
		/// <returns></returns>
		private static List<Tuple<long, long>> createLongTuppleList(long N) {
			var inpList = new List<Tuple<long, long>>();

			for (int i = 0; i < N; i++) {
				var inp = retreiveLongArray();
				var item1 = inp[0];
				var item2 = inp[1];
				inpList.Add(new Tuple<long, long>(item1, item2));
			}
			return inpList;
		}
	}
}