#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pr;
const double pi=acos(-1);
#define rep(i,a,n) for(int i=a;i<=n;i++)
#define per(i,n,a) for(int i=n;i>=a;i--)
#define Rep(i,u) for(int i=head[u];i;i=Next[i])
#define clr(a) memset(a,0,sizeof a)
#define pb push_back
#define mp make_pair
#define fi first
#define sc second
ld eps=1e-9;
ll pp=1000000007;
ll mo(ll a,ll pp){if(a>=0 && a<pp)return a;a%=pp;if(a<0)a+=pp;return a;}
ll powmod(ll a,ll b,ll pp){ll ans=1;for(;b;b>>=1,a=mo(a*a,pp))if(b&1)ans=mo(ans*a,pp);return ans;}
ll read(){
    ll ans=0;
    char last=' ',ch=getchar();
    while(ch<'0' || ch>'9')last=ch,ch=getchar();
    while(ch>='0' && ch<='9')ans=ans*10+ch-'0',ch=getchar();
    if(last=='-')ans=-ans;
    return ans;
}
//head
int main(){
    int T=read();
    while(T--){
        ll ans1=2000000000,ans2=2000000000;
        int n=read();
        while(n--){
            int t=read();
            int lim=1+(int)sqrt(t);
            for(int i=2;i<=ans2 && i<=lim;++i)
                while(t%i==0){
                    ll tt=i;
                    if(tt<ans1)swap(ans1,tt);
                    if(tt<ans2)swap(ans2,tt);
                    t/=i;
                }
            if(t>1){
                ll tt=t;
                if(tt<ans1)swap(ans1,tt);
                if(tt<ans2)swap(ans2,tt);
            }
        }
        if(ans2==2000000000)printf("-1\n");
        else printf("%I64d\n",ans1*ans2);
    }
    return 0;
}