#include <bits/stdc++.h>
#define _ ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
using namespace std;
void solve()
{
long long n, res; cin>>n;
vector<long long>d(n);
vector<long long>comp;
for(long long i(0); i<n; i++)
{
cin>>d[i];
}
sort(d.begin(), d.end());
res=d[0]*d[n-1];
for(long long i(2); i*i<=res; i++)
{
if(res%i==0)
{
comp.push_back(i);
if(i!=res/i)
{
comp.push_back(res/i);
}
}
}
sort(comp.begin(), comp.end());
if(comp==d)
{
cout<<res<<"\n";
}
else
{
cout<<-1<<"\n";
}
}
int main()
{_
long long t; cin>>t;
for(long long i(0); i<t; ++i)
{
solve();
}
}
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