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 REP(i,n) for(int(i)=0;i<(n);i++)
#define MAX_N 2000001
int pr[MAX_N];

map<int,int> prime_factor(int m){
  map<int,int> rtn;
  for(int i=2;i*i<=m;i++) while(!(m%i)){
    ++rtn[i];
    m/=i;
  }
  if(m!=1) rtn[m]=1;
  return rtn;
}

int main(){
  int n;cin>>n;
  REP(i,n){
    int tmp;cin>>tmp;
    map<int,int> mp=prime_factor(tmp);
    for(auto p:mp) pr[p.first]++;
  }
  REP(i,MAX_N) if(pr[i]==n){
    cout<<"not coprime";
    return 0;
  }
  REP(i,MAX_N) if(pr[i]>1){
    cout<<"setwise coprime";
    return 0;
  }
  cout<<"pairwise coprime";
}