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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
#define all(x) x.begin(),x.end()
#define endl '\n'
#define pb push_back
#define ff first
#define ss second
#define PI 3.1415926535897932384626
#define mod 1000000007
#define modd 998244353

void io() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	#ifndef ONLINE_JUDGE
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
	#endif
}

int main() {
	io();
	
	int n;
	cin>>n;
	ll a;
	cin>>a;
	ll lcm = a, gcd = a, pro = a;
	for(int i=1;i<n;i++) {
		cin>>a;
		pro*=a;
		gcd = __gcd(gcd,a);
		lcm = lcm*a/__gcd(lcm,a);
	}
	if(lcm == pro) cout<<"pairwise coprime";
	else if(gcd == 1) cout<<"setwise coprime";
	else cout<<"not coprime";
	return 0;
}