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;
#define ll long long int
ll gcd(int a,int b)
{
    if(b==0)
        return a;
    return gcd(b,a%b);
}
ll cnt[1000009];
int main()
{
   long long int a[100000],p=0,i,j;

   int n;
   ll ans=0;
   cin>>n;
   long long int b[n+9];
   for( i=0;i<n;i++){
        cin>>p;
        cnt[p]++;
        ans=gcd(ans,p);
   }
 if(ans>1) cout<<"not coprime"<<endl;

 else{  ll x=0;
       for(i=2;i<=1000000;i++){
          x=0;
        for(j=i;j<=1000000;j+=i){
              x+=cnt[j];

        }
        if(x>1) break;

       }


   if(x>1)cout<<"setwise coprime"<<endl;
   else cout<<"pairwise coprime"<<endl;
 }
}




