#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <queue>
#include <vector>
#include <map>
using namespace std;
typedef long long LL;
const int N = 100005;
int T, flag[N], p0, p[N], n, a[N];
int p1;
int sum[N];
LL ans1,ans2,ans3,tot;
map<int, int> mp;
struct Node {
    int x, y;
}ans[N];
bool cmp(const Node &a, const Node &b) {
    return a.x < b.x;
}
int main() {
    scanf("%d", &T);
    memset(flag, 0, sizeof(flag));
    for (int i = 2; i <= 100000; ++i) {
        if (flag[i] != 0) continue;
        ++p0;
        p[p0] = i;
        for (int j = i; j <= 100000; j += i) {
            flag[j] = 1;
        }
    }
    while (T--) {
        scanf("%d", &n);
        for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
        mp.clear();
        p1 = p0;
        memset(sum,0,sizeof(sum));
        for (int i = 1; i <= n; ++i) {
            int now = a[i];
            int j = 1;
            while (j <= p0 && now != 1) {
                while (now % p[j] == 0) {
                    ++sum[j];
                    now /= p[j];
                }
                ++j;
            }
            if (now != 1) {
                if (mp.count(now) != 0) {
                    ++mp[now];    
                }
                else {
                    ++p1;
                    p[p1] = now;
                    mp[now] = 1;
                }
            }
        }
        for (int i = 1; i <= p0; ++i) ans[i].x = p[i], ans[i].y = sum[i];
        for (int i = p0 + 1; i <= p1; ++i) ans[i].x = p[i], ans[i].y = mp[ans[i].x];
        sort(ans + 1, ans + p1 + 1,cmp);
        tot = 0; 
        for (int i=1;i<=p1;++i) {
            tot+=ans[i].y;
        }
        if (tot<2) {
            printf("-1\n");
            continue;
        }
        ans1 = 0; 
        ans2 = 0;
        for (int i = 1; i <= p1; ++i) {
            if (ans[i].y==0) continue;
            if (ans1==0)
            {
                if (ans[i].y>=2)
                {
                    ans1=ans[i].x;
                    ans2=ans[i].x;
                    break;
                }
                else
                    ans1=ans[i].x;
            }
            else
            {
                ans2=ans[i].x;
                break;
            }
        }
        ans3=ans1*ans2;
        printf("%I64d\n",ans3);
    }
    return 0;
}