#include <cstring>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cassert>
#include <iomanip>

using namespace std;

#define repu(i, a, b) for (int i = (a); i < (b); ++i)
#define repd(i, a, b) for (int i = (a); i > (b); --i)
#define mem(a, x) memset(a, x, sizeof(a))
#define all(a) a.begin(), a.end()
#define uni(a) a.erase(unique(all(a)), a.end())
#define count_bits(x) __builtin_popcount(x)
#define count_bitsll(x) __builtin_popcountll(x)

typedef long long ll;
const int MOD = 1000000007;

template<class T, class U> inline T tmin(T a, U b) {return (a < b) ? a : b;}
template<class T, class U> inline T tmax(T a, U b) {return (a > b) ? a : b;}
template<class T, class U> inline void amax(T &a, U b) {if (b > a) a = b;}
template<class T, class U> inline void amin(T &a, U b) {if (b < a) a = b;}
template<class T> inline T tabs(T a) {return (a > 0) ? a : -a;}
template<class T> T gcd(T a, T b) {while (b != 0) {T c = a; a = b; b = c % b;} return a;}

const int N = 44800;
int f[N];

int main(int argc, char *argv[]) {
    ios_base::sync_with_stdio(false);
    
    int ntest, n, x;
    
    vector<int> primes;
    vector<bool> is_prime(N, true);
    
    repu(i, 2, N) {
        if (is_prime[i]) {
            primes.push_back(i);
            for (int j = i * i; j < N; j += i) is_prime[j] = false;
        }
    }
    
    cin >> ntest;
    
    while (ntest--) {
        cin >> n;
        mem(f, 0);
        vector<ll> rem;
        repu(i, 0, n) {
            cin >> x;
            repu(j, 0, primes.size()) {
                int p = primes[j], cnt = 0;
                while (x % p == 0) {
                    cnt++;
                    x /= p;
                }
                f[p] += cnt;
            }
            if (x > 1) rem.push_back(x);
        }
        ll ret = 5e18;
        repu(i, 0, primes.size()) {
            if (f[primes[i]] > 1) {
                amin(ret, primes[i] * 1LL * primes[i]);
            }
            if (f[primes[i]] > 0) {
                rem.push_back(primes[i]);
            }
        }
        sort(all(rem));
        if (rem.size() > 1) amin(ret, rem[0] * 1LL * rem[1]);
        if (ret == 5e18) ret = -1;
        cout << ret << '\n';
    }
    
    return 0;    
}