#include <bits/stdc++.h>
using namespace std;
long long arr[5000];
bool num[1000006];
void sieve() {
  int sz = sqrt(1000000);
  for (int i = 2; i <= sz; i++) {
    if (!num[i]) {
      for (int j = i * i; j < 1000001; j += i) num[j] = true;
    }
  }
}
int main() {
  sieve();
  int t;
  int n;
  cin >> t;
  while (t--) {
    cin >> n;
    for (int i = 0; i < n; i++) cin >> arr[i];
    sort(arr, arr + n);
    if (n == 1) {
      if (!num[arr[0]])
        cout << arr[0] * arr[0] << endl;
      else
        cout << -1 << endl;
      continue;
    }
    long long ans = arr[0] * arr[n - 1];
    for (int i = 1, j = n - 2; i <= j; i++, j--) {
      if (arr[i] * arr[j] != ans) ans = -1;
    }
    int cnt = 0;
    for (int i = 2; i <= sqrt(ans); i++) {
      if (ans % i == 0) {
        cnt++;
        if ((ans / i) != i) cnt++;
      }
    }
    if (cnt != n) ans = -1;
    cout << ans << endl;
  }
}
