#include<cstdio>
#include<cstring>
#include<vector>

using namespace std;

typedef long long LL;
int n;
const int maxn = 110;
const int N = 100000;
vector<int> primes;
int vis[N*10];

LL gcd(LL a,LL b)
{
    return !b?a:gcd(b,a%b);
}

void init()
{
    primes.clear();
    memset(vis,0,sizeof vis);
    for(int i=2; i<N ;++i)
    {
        if(!vis[i])
        {
            primes.push_back(i);
            for(int j = i+i ; j <N ;j+=i) vis[j] = 1;
        }
    }
}

void solve(int x)
{
    for(int i=0;i<primes.size();++i)
    {
        int t = primes[i];
        if(x%t == 0)
        {
            int cnt = 0;
            while(x%t==0) x/=t,++cnt;
            vis[i] += cnt;
        }
        if(x == 1) break;
    }
    if(x!=1)
    {
           vis[primes.size()] = 1;
        primes.push_back(x);
    }
}


int main()
{
    //freopen("test.txt","r",stdin);
    init();
    int T;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d",&n);
        memset(vis,0,sizeof vis);
        LL mx = 9;
        for(int i=0;i<n;++i)
        {
            int x;
            scanf("%d",&x);
            solve(x);
        }
        LL res = 1;
        int cnt = 1;
        for(int i=0;i < primes.size();++i)
        {
            while(vis[i] && cnt<3)
            {
                --vis[i];
                ++cnt;
                res*=primes[i];
            }
            if(cnt>=3) break;
        }
        if(cnt<3) res = -1;
        printf("%lld\n",res);
    }
    return 0;
}