#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <map>
#include <set>
#include <vector>
#include <queue>
#include <stack>
#include <cctype>
#include <climits>
#include <cmath>
using namespace std;
int a[2];
void init() {
    a[0] = a[1] = -1;
}
void add(int x) {
    if(a[0] == -1) {
        a[0] = x;
    } else if(a[1] == -1) {
        a[1] = x;
    } else {
        if(x < a[0]) {
            a[1] = a[0];
            a[0] = x;
        } else if(x < a[1]) {
            a[1] = x;
        }
    }
}
int main() {
    int T, n, x;
    scanf("%d", &T);
    while(T--) {
        scanf("%d", &n);
        init();
        for(int i = 1; i <= n; i++) {
            scanf("%d", &x);
            for(int j = 2; j * j <= x; j++) {
                if(x % j == 0) {
                    while(x % j == 0) {
                        add(j);
                        x /= j;
                    }
                }
            }
            if(x > 1) add(x);
        }
        if(a[0] != -1 && a[1] != -1 && a[0] * a[1] != 2) {
            printf("%I64d\n", (long long)a[0] * a[1]);
        } else {
            printf("-1\n");
        }
    }
    return 0;
}