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`.

Examples

Input

3
3 4 5


Output

pairwise coprime


Input

3
6 10 15


Output

setwise coprime


Input

3
6 10 16


Output

not coprime
#include <bits/stdc++.h>
using namespace std;

int main(){
    int A = 1000005;
    int n;
    cin>>n;
    vector<int> a(n);
    vector<int> c(A, 0);
    int max = 0;
    
    for(int i=0;i<n;i++){
        cin>>a[i];
        c[a[i]] += 1;
    }


    //素数に対しO(1)の計算量
    bool pairwise = true;
    for(int i=2;i<A;i++){
        int count = 0;
        for(int j=1;j*i<A;j++){
            count += c[j*i];
        }
        if(count>1) pairwise = false;
        if(count==n){
            cout<<"not coprime"<<endl;
            return 0;
        }
    }

    if(pairwise){
        cout<<"pairwise coprime"<<endl;
        return 0;
    }

    cout<<"setwise coprime"<<endl;
    
    return 0;

}