#include <bits/stdc++.h>   using namespace std;   int main() {     int T;     cin >> T;     while (T--) {       int n;       cin >> n;       vector<long long> v;       for (int i = 1; i <= n; i++) {         int x;         cin >> x;         v.push_back(x);       }       sort(v.begin(), v.end());       long long ans = v[0] * v[v.size() - 1];       int sum = 0, flag = 1;       for (long long i = 2; i * i <= ans; i++) {         if (ans % i == 0) {           if (find(v.begin(), v.end(), i) == v.end() ||               find(v.begin(), v.end(), ans / i) == v.end()) {             flag = 0;             break;           }           sum += 2;           if (i * i == ans) sum--;         }       }       if (sum == n && flag == 1)         cout << ans << endl;       else         cout << -1 << endl;     }     return 0;   }   