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> P;
#define forin(in) for(int i=0; i<(int)in.size(); i++) cin>>in[i]
#define forout(out) for(int i=0; i<(int)out.size(); i++) cout<<out[i]<<endl
#define rep(i, n) for(int i=0; i<(n); i++)

bool pairwise = true;
vector<bool> seen(1e+6, false);

vector<pair<int, int> > prime_factorize(int n) {
    vector<pair<int, int> > res;
    for (int p = 2; p * p <= n; ++p) {
        if (n % p != 0) continue;
        int num = 0;
        while (n % p == 0) { ++num; n /= p; }
        if(seen[p - 1]) pairwise = false;
        res.push_back(make_pair(p, num)); seen[p - 1] = true;
    }
    if (n != 1) res.push_back(make_pair(n, 1));
  		if(seen[n-1]){
          pairwise=false;
        }
  		seen[n - 1] = true;
    return res;
}


int gcd(int a, int b) {
    if (b==0) return a;
    else return gcd(b, a%b);
}

int main(){
    int N; cin>> N;
    vector<int> A(N);
    bool setwise = true;

    cin>> A[0];
    int cur = A[0];

    for(int i = 1; i < N; i++){
        cin>> A[i];

        cur = gcd(cur, A[i]);
    }

    //setwise
    if(cur != 1) setwise = false;

    //pairwise
    rep(i, N){
        prime_factorize(A[i]);
    }

    //result
    if(pairwise){
        cout<< "pairwise coprime" << endl;
        return 0;
    }
    if(setwise){
        cout<< "setwise coprime" << endl;
        return 0;
    }
    cout<< "not coprime" << endl;
    return 0;
}