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>

#define rep(i, n) for (ll i = 0; i < (n); i++)
using namespace std;
typedef long long ll;

ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }

int main() {
  ll n, g = 0, cnt[1000005] = {};
  cin >> n;

  rep(i, n) {
    ll a;
    cin >> a;
    cnt[a]++;
    g = gcd(g, a);
  }
  bool ok = true;
  for (ll i = 2; i < 1000005; i++) {
    ll sum = 0;
    for (ll j = i; j < 1000005; j += i) sum += cnt[j];
    if (sum > 1) ok = false;
  }
  cout << (ok ? "pairwise coprime" : g == 1 ? "setwise coprime" : "not coprime")
       << endl;
  return 0;
}