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(void){
  int m=0,n,l=0; cin>>n;
  unordered_map<int,int> mp;
  for(int i=0; i<n; ++i){
    int a; cin>>a;
    ++mp[a]; m=max(m,a);
  }
  vector<bool> b(m+1,true);
  for(int i=2; i<=m; ++i){
    int s=0;
    if(b[i]==true) for(int j=1; i*j<=m; ++j) {b[i*j]=false; s+=mp[i*j];}
    if(s==n){ cout<<"not coprime"; return 0;}
    else l=max(l,s);
  }
  if(l<2){ cout<<"pairwise coprime"; return 0;}
  else cout<<"setwise coprime";
  return 0;
}
