#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <vector>
#include <algorithm>
using namespace std;
typedef long long LL;
const int M=1000010;

int T;
vector<int> v;
vector<int> pr;

bool is[100100] = {false};

void init()
{
    for(int i=2; i*i<=100000; i++)
        if(is[i] == false)
            for(int j=i+i; j<=100000; j+=i)
                is[j] = true;
    for(int i=2; i<=100000; i++)
        if(is[i] == false)
            pr.push_back(i);
}

void solve(int x)
{
    int size = pr.size();
    for(int i =0; i<size; i++)
    {
        int tmp = pr[i];
        if(tmp > x) break;
        if(x % tmp == 0)
        {
            while(x%tmp == 0)
            {
                x/=tmp;
                v.push_back(tmp);
            }
        }
    }
    if(x!=1) v.push_back(x);
}

int main()
{
    init();
    cin>>T;
    int n;
    while(T--)
    {
        v.clear();
        cin>>n;
        for(int i=1,t; i<=n; i++)
        {
            scanf("%d", &t);
            solve(t);
        }
        unique(v.begin(), v.end());
        sort(v.begin(), v.end());
        int size = v.size();
        if(size < 2)
        {
            printf("-1\n");
            continue;
        }
        LL tmp = (LL)v[0] * (LL)v[1];
        cout<<tmp<<endl;
    }
    return 0;
}