#include <bits/stdc++.h>
using namespace std;
long long mod = 1e9 + 7;
int rx[4] = {0, 0, 1, -1};
int ry[4] = {-1, 1, 0, 0};
int rr[4] = {-1, -1, 1, 1};
int cr[4] = {-1, 1, -1, 1};
long long inf = 1e18 + 1;
int ed[3002][3002];
vector<int> g[3002];
long long max(long long a, long long b) {
  if (a >= b) {
    return a;
  }
  return b;
}
long long min(long long a, long long b) {
  if (a <= b) {
    return a;
  }
  return b;
}
int main() {
  std::ios::sync_with_stdio(false);
  cin.tie(NULL);
  int t, n;
  cin >> t;
  while (t--) {
    cin >> n;
    vector<long long> a(n);
    for (int i = 0; i < n; i++) {
      cin >> a[i];
    }
    sort(a.begin(), a.end());
    vector<long long> p;
    long long pr = (long long)a[0] * a[n - 1];
    long long i;
    for (i = 2; (long long)i * i <= pr; i++) {
      if (pr % i == 0) {
        p.push_back(i);
        if (i != pr / i) {
          p.push_back(pr / i);
        }
      }
    }
    sort(p.begin(), p.end());
    if (p == a) {
      cout << pr << endl;
    } else {
      cout << -1 << endl;
    }
  }
  return 0;
}
