#include <map>
#include <set>
#include <stack>
#include <queue>
#include <cmath>
#include <ctime>
#include <vector>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;
#define INF 0x3f3f3f3f
#define mem(a, b) memset(a, b, sizeof(a))
#define FIN freopen("in.txt", "r", stdin)
#define FOUT freopen("out.txt", "w", stdout)

//typedef __int64 LL;
typedef long long LL;
const int MAXN = 4002;
const int MAXM = 110000;
const double eps = 1e-12;
const double PI = 4.0 * atan(1.0);
const int MOD = 1000000007;

LL f, s, x;
int n, T;

void fun(LL p, int num) {
    if(p < f) {
        if(num == 1) s = f, f = p;
        else s = f = p;
    }
    else if(p < s) s = p;
}

void calc(LL x) {
    LL m = (LL) sqrt(1.0 * x + 0.5);
    for (LL i = 2; i <= m; i ++) if(x % i == 0) {
        int cnt = 0;
        while(x % i == 0) {
            cnt ++;
            x /= i;
        }
        fun(i, cnt);
    }
    if(x > 1) fun(x, 1);
}

int main()
{
    cin  >> T;
    while(T--) {
        cin >> n;
        f = s = (1LL << 33);
        for(int i = 1; i <= n; i ++) {
            cin >> x;
            calc(x);
        }
        if(s == (1LL << 33)) {
            puts("-1");
        }
        else {
            cout << (f * s) << endl;
        }
    }
    return 0;
}