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 N;
const int M=1000001;
int cnt[M];
int gcd(int a,int b){return a?gcd(b%a,a):b;}

int main()
{
    cin>>N;
    int g=0;
    bool ok=true;
    for(int i=0;i<N;++i){
        int A;cin>>A;
        g=gcd(g,A);
        ++cnt[A];
    }
    for(int i=2;i<M;++i){
        int s=0;
        for(int j=i;j<M;j+=i)s+=cnt[j];
        if(s>1)ok=false;
    }
    cout<<(ok?"pairwise coprime":g==1?"setwise coprime":"not coprime")<<endl;
}