#include <bits/stdc++.h>
using namespace std;
const int32_t INFint = 1e9;
const long long INFll = 1e18;
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long t;
  cin >> t;
  while (t--) {
    long long n;
    cin >> n;
    long long arr[n];
    for (long long i = 0; i < n; i++) cin >> arr[i];
    ;
    sort(arr, arr + n);
    long long ans = arr[0] * arr[n - 1];
    long long fact[100000];
    long long index = 0;
    for (long long i = 2; i <= sqrt(ans); i++) {
      if (ans % i == 0) {
        fact[index] = i;
        index++;
        if (i != ans / i) {
          fact[index] = ans / i;
          index++;
        }
      }
    }
    sort(fact, fact + index);
    if (index != n) {
      cout << -1 << '\n';
    } else {
      long long flag = 0;
      for (long long i = 0; i < n; i++) {
        if (fact[i] != arr[i]) {
          flag = 1;
          break;
        }
      }
      ans = flag ? -1 : ans;
      cout << ans << '\n';
    }
  }
}
