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<algorithm>
#include<iostream>
#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<cmath>
#include<list>
#include<set>
#include<map>

using namespace std;
long long MOD = 1000000007LL;
const double PI = 3.14159265358979323846;
#undef INT_MIN
#undef INT_MAX
#define INT_MIN -2147483648
#define INT_MAX 2147483647
#define endl "\n"

template<class T>
bool prime_factorization(T n, map<int, int>& ret, map<int, int> &ret2) {
	bool flags = false;
	map<int, int> tmp;
	for (long long i = 2; i * i <= n; ++i) {
		while (n % i == 0) {
			if (ret[i] != 0)flags = true;
			tmp[i]++;
			n /= i;
		}
	}

	if (n != 1) {
		if (ret[n] != 0)flags = true;
		tmp[n] += 1;
	}

	for (auto x : tmp) {
		ret[x.first] += x.second;
		ret2[x.first]++;
	}

	return flags;
}

int main() {
	int N;
	cin >> N;
	vector<long long> A;
	map<int, int> mp;
	map<int, int> mp2;
	bool flags = false;
	map<int, int> _A;
	for (int i = 0; i < N; ++i) {
		int a;
		cin >> a;
		_A[a] = 1;
	}
	for (auto x : _A) {
		A.push_back(x.first);
	}

	sort(A.begin(), A.end());
	for (int i = 0; i < A.size(); ++i) {
		flags = max(flags, prime_factorization(A[i], mp, mp2));
	}

	if (flags) {
		bool flags2 = false;
		for (auto x : mp2) {
			//cout << x.first << " " << (x.second == N) << endl;
			if (x.second == A.size()) {
				flags2 = true;
				break;
			}
		}
		if (flags2) {
			cout << "not coprime" << endl;
		}
		else {
			cout << "setwise coprime" << endl;
		}
	}
	else {
		cout << "pairwise coprime" << endl;
	}

	return 0;
}