#include <cstdio>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <set>
#include <cctype>
#include <utility>
#include <queue>
#include <cmath>

using namespace std;
 
typedef long long LL;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<PII> VPII;
typedef pair<LL, LL> PLL;
typedef pair<int, LL> PIL;
typedef pair<LL, int> PLI;
typedef double DB;
typedef long double LD;
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define bit(x) (1 << (x))
#define bitl(x) (1LL << (x))
#define sqr(x) ((x) * (x))
#define sz(x) ((int)(x.size()))
#define counti(x) (__builtin_popcount(x))
#define countl(x) (__builtin_popcountll(x))
#define rep(i, n) for (int (i) = 0; (i) < (int)(n); ++(i))
#define X first
#define Y second
 
template <typename T, typename U> 
inline void chkmax(T& x, U y) {
    if (x < y) x = y;
}
 
template <typename T, typename U>
inline void chkmin(T& x, U y) {
    if (y < x) x = y;
}
int get() {
    char c;
    while (c = getchar(), (c < '0' || c > '9') && (c != '-'));
    bool flag = (c == '-');
    if (flag) c = getchar();
    int x = 0;
    while (c >= '0' && c <= '9') {
        x = x * 10 + c - 48;
        c = getchar();
    }
    return flag ? -x : x;
}
 
void output(int x) {
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    int len = 0, data[20];
    while (x) {
        data[len++] = x % 10;
        x /= 10;
    }
    if (!len) data[len++] = 0;
    while (len--) putchar(data[len] + 48);
    putchar('\n');
}
int n;
int main() {
    
    int Tcase;
    for (scanf("%d", &Tcase); Tcase--;) {
        
        scanf("%d", &n);
        int i, a;
        VI v;
        for (i = 0; i < n; i++) {
            scanf("%d", &a);
            if (a == 1) continue;
            int j;
            int cnt = 0;
            for (j = 2; j * j <= a && cnt < 2; j++) {
                if (a % j == 0) {
                    while (a % j == 0 && cnt < 2) a /= j, v.pb(j), cnt++;
                }
            }
            if (a > 1 && cnt < 2) v.pb(a);
        }
        sort(v.begin(), v.end());
        if (v.size() <= 1) puts("-1");
        else {
            LL x = 1LL * v[0] * v[1];
            cout << x << endl;
        }
    }
    return 0;
}