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;
long long gcd(long long a, long long b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}
int B[1000001];
int main() {
  int N;
  cin >> N;
  vector<int> A(N);
  int d = 0;
  bool c = false;
  for (int i = 0; i < N; i++) {
    cin >> A[i];
    d = gcd(d, A[i]);
    B[A[i]]++;
  }
  for (int i = 2; i < 1000001; i++) {
    int count = 0;
    for (int j = 1; j * i < 1000001; j++) {
      count += B[i * j];
    }
    if (count > 1)
      c = true;
  }
  if (d != 1)
    puts("not coprime");
  else if (c)
    puts("setwise coprime");
  else
    puts("pairwise coprime");
}