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 <iostream>

using namespace std;

const int kMaxV = 1000001;

int b[kMaxV], f[kMaxV], d;
int n, a, g;

int G(int a, int b) { return !b ? a : G(b, a % b); }

void R(int i, int a) {
  for (; a > 1; a /= f[a]) {
    d |= b[f[a]] > 0 && b[f[a]] < i;
    b[f[a]] = i;
  }
}

int main() {
  for (int i = 2; i < kMaxV; i++) {
    if (!f[i]) {
      for (int j = i; j < kMaxV; j += i) {
        f[j] = i;
      }
    }
  }
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a;
    g = G(a, g);
    R(i, a);
  }
  if (!d) {
    cout << "pairwise coprime";
  } else if (g == 1) {
    cout << "setwise coprime";
  } else {
    cout << "not coprime";
  }
  return 0;
}