#include <bits/stdc++.h>
using namespace std;
int t;
bool isLack(long long num, int prev, int next) {
  bool answer = false;
  int divisor = prev + 1;
  while (1) {
    if (divisor >= next) {
      break;
    }
    if (num % divisor == 0) {
      answer = true;
      break;
    } else {
      ++divisor;
    }
  }
  return answer;
}
int main() {
  scanf("%d", &t);
  for (int test = 0; test < t; ++test) {
    int n = 0;
    scanf("%d", &n);
    vector<int> divisors;
    for (int i = 0; i < n; ++i) {
      int input;
      scanf("%d", &input);
      divisors.push_back(input);
    }
    long long answer = -1;
    sort(divisors.begin(), divisors.end());
    long long num = (long long)divisors[0] * (long long)divisors[n - 1];
    int start = 0;
    int end = n - 1;
    while (1) {
      if (start > end) {
        answer = num;
        break;
      }
      if (num == (long long)divisors[start] * (long long)divisors[end]) {
        ++start;
        --end;
        continue;
      } else {
        answer = -1;
        break;
      }
    }
    bool cancel = false;
    for (int i = 0; i < n; ++i) {
      if (i == 0) {
        cancel = isLack(num, 1, divisors[i]);
      } else {
        cancel = isLack(num, divisors[i - 1], divisors[i]);
      }
      if (cancel) {
        answer = -1;
        break;
      }
    }
    printf("%lld\n", answer);
  }
  return 0;
}
