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.IO;
using System.Linq;
using System.Collections.Generic;
using static System.Math;
using static System.Console;
using static System.Linq.Enumerable;
using static System.Numerics.BitOperations;
using System.Numerics;

namespace abc177{
    class SolverE{
        static void Main(){
            SetOut(new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false});
            new SolverE().Solve();
            Out.Flush();
        }

        public void Solve(){
            checked{
                ulong MOD = 1000000007;
                int N = Get.Int();
                ulong[] A = Get.Longs().Select(x => (ulong)x).ToArray();
                // BigInteger mul = 1;
                ulong lcm = 1;
                ulong gcd = A[0];
                bool isPairwise = true;
                for(int i=0; i<N; i++){
                    // mul *= A[i];
                    ulong tmpLcm = lcm;
                    lcm = Lcm(lcm, A[i]) % MOD;
                    if( tmpLcm * A[i] % MOD != lcm){
                        isPairwise = false;
                    }
                    gcd = Gcd(gcd, A[i]);
                }
                if( isPairwise ){
                    WriteLine("pairwise coprime");
                }else if (gcd == 1){
                    WriteLine("setwise coprime");
                }else{
                    WriteLine("not coprime");
                }



            }
        }

        ulong Lcm(ulong a, ulong b){
            return a / Gcd(a,b) * b;
        }

        ulong Gcd(ulong m, ulong n){
            if(m<n){
                ulong tmp = n;
                n = m;
                m = tmp;
            }
            if(n==0) return m;
            return Gcd(n, m%n); 
        }

        static class Debug{
            public static void Put(object obj, int padLeft = 0, bool newline = true){

                if (obj is Array arr){
                    if( arr.Rank == 1 ){
                        Write("[");
                        for(int i=0; i<arr.Length; i++){
                            Put(arr.GetValue(i), padLeft, false);
                            if( i < arr.Length - 1 ) Write(", ");
                        }
                        Write("]");
                    }
                    else if( arr.Rank == 2 ){
                        Write("[\n");
                        for(int i=0; i<arr.GetLength(0); i++){
                            Write(" [");
                            for(int j=0; j<arr.GetLength(1); j++){
                                Put(arr.GetValue(i,j), padLeft, false);
                                if (j < arr.GetLength(1) - 1) Write(", ");
                            }
                            if (i < arr.GetLength(0) - 1 ) Write("],\n");
                            else Write("]\n");
                        }
                        Write("]");
                    }
                }
                else if( obj is ValueType val ){
                    Write(val.ToString().PadLeft(padLeft));
                }
                else if( obj is string str ){
                    Write(str.PadLeft(padLeft));
                }
                else{
                    Write(obj.ToString().PadLeft(padLeft));
                }

                if(newline) Write("\n");
            }

            public static void Put(object obj, string label, int padLeft = 0, bool newline = true){
                Write("\u001b[32m{0}:\u001b[0m ", label);
                Put(obj, padLeft, newline);
            }
            public static void Put(params object[] args){
                if (args.Length % 2 != 0){
                    WriteLine("Debug.Put(params): arg length shall be multiple of 2.");
                }
                for(int i=0; i<args.Length; i += 2){
                    Put(args[i], (string)args[i+1],0, false);
                    Write("   ");
                }
                Write("\n");
            }
        }

        
        private static class Get{
            public static string Str() => ReadLine().Trim();
            public static int Int() => int.Parse(Str());
            public static long Long() => long.Parse(Str());
            public static double Double() => double.Parse(Str());
            public static string[] Strs() => Str().Split(' ', StringSplitOptions.RemoveEmptyEntries);
            public static int[] Ints() => Strs().Select(int.Parse).ToArray();
            public static long[] Longs() => Strs().Select(long.Parse).ToArray();
            public static double[] Doubles() => Strs().Select(double.Parse).ToArray();
            static bool TypeEq<T,U>() => typeof(T).Equals(typeof(U));
            static T TypeConv<T,U>(U u) => (T)Convert.ChangeType(u, typeof(T));
            static T TypeConv<T>(string s) => TypeEq<T, int>() ?   TypeConv<T, int>(int.Parse(s))
                                        : TypeEq<T, long>() ?       TypeConv<T, long>(long.Parse(s))
                                        : TypeEq<T, double>() ?     TypeConv<T, double>(long.Parse(s))
                                        : TypeConv<T, string>(s);
            public static (T,U) Tuple<T,U>() {string[] strs = Strs(); T t = TypeConv<T>(strs[0]); U u = TypeConv<U>(strs[1]); return(t,u);}
            public static (T,U,V) Tuple<T,U,V>() {string[] strs = Strs(); T t = TypeConv<T>(strs[0]); U u = TypeConv<U>(strs[1]); V v = TypeConv<V>(strs[2]); return(t,u,v);}
        }
    }
}