#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cstdlib>
#include<cmath>
#include<vector>
#include<stack>
#include<set>
#include<string>
#include<iostream>
#include<map>
#pragma comment(linker,"/STACK:102400000,102400000") 
using namespace std;
int a[105];
int flag[100005],prime[100005],count1,vf[100005],vans[105],vn;
void getprime(int n){
    int i,j;
    memset(flag,0,sizeof(flag));
    for(i=2;i<=n;i++){
        if(flag[i]==0) prime[++count1]=i;
        for(j=1;j<=count1 && i*prime[j]<=n;j++){
            flag[i*prime[j]]=1;
            if(i%prime[j]==0) break;
        }
    }
}
int main(){
    int i,j,m,n,T,t;
    getprime(100000);
    scanf("%d",&T);
    while(T--){
        memset(vf,0,sizeof(vf));
        scanf("%d",&n);
        for(i=1;i<=n;i++){
            scanf("%d",&a[i]);
        }
        vn=0;
        for(i=1;i<=n;i++){
            t=a[i];
            for(j=1;j<=count1 && prime[j]*prime[j]<=t;j++){
                while(t%prime[j]==0){
                    t/=prime[j];
                    vf[j]++;
                }
            }
            if(t!=1){
                vans[++vn]=t;
            }
        }
        int cnt=0;
        for(j=1;j<=count1;j++){
            if(cnt==2) break;
            while(vf[j]){
                vans[++vn]=prime[j];
                vf[j]--;
                cnt++;
                if(cnt==2) break;
            }
        }
        sort(vans+1,vans+vn+1);
        if(vn<2) printf("-1\n");
        else printf("%I64d\n",1LL*vans[1]*vans[2]);
    }
    return 0;
}