// #include C {
#include<cstring>
#include<cassert>
#include<cstdio>
#include<cctype>
#include<cmath>
// }

// #include C++ {
#include<functional>
#include<algorithm>
#include<iostream>
#include<numeric>
#include<vector>
#include<string>
#include<bitset>
#include<queue>
#include<deque>
#include<stack>
#include<list>
#include<map>
#include<set>
// }
using namespace std;
// #typedef {
typedef long long int64;
typedef pair <int, int> PII;
typedef pair <int64, int64> PLL;
// }

// #parameter{
#ifdef DEBUG_MODE

#define TYPE decltype
#define RF(filename) {freopen((filename), "r", stdin);}
#define WF(filename) {freopen((filename), "w", stdout);}
#define EF(filename) {freopen((filename), "w", stderr);}
#define eprintf(...) fprintf(stderr, __VA_ARGS__)

#else

#define TYPE __typeof
#define RF(filename) {;}
#define WF(filename) {;}
#define EF(filename) {;}
#define eprintf(...)
#define fprintf(...)

#endif

// #define {
#define SZ(a) ((int)(a).size())
#define X first
#define Y second
#define MP make_pair
#define L(x) ((x)<<1)
#define R(x) ((x)<<1 | 1)
#define max3(x, y, z) (max(max((x), (y)), (z)))
#define min3(x, y, z) (min(min((x), (y)), (z)))
#define BIT(x, i) (((x) >> (i)) & 1)
#define ALL(it) (it).begin(), (it).end()
#define FILL(__space, __val) memset(__space, __val, sizeof(__space))
#define MOVE(__spaceTo, __spaceFrom) memmove(__spaceTo, __spaceFrom, sizeof(__spaceTo))
#define UNIQUE(__vector) sort(ALL(__vector)), __vector.resize(unique(ALL(__vector)) - __vector.begin())
#define FOR(it, c) for( TYPE((c).begin()) it = (c).begin(); it != (c).end(); it++)
/////////////////////////////////////////////////////////////
const double PI = acos(-1.0);
const double EPS = 1e-6;

#define MAX_N 45000
#define MAX_M 5005
#define MOD (int)(1e9+7)
#define INF ((1 << 30) - 1)
#define BINF ((1LL << 62) - 1LL)
#define NONE -1
#define NIL 0
// }

/////////////////////////////////////////////////////////////
vector <int> primes;
bitset <MAX_N> seive;
void Setup(){
    for (int64 i = 2; i < MAX_N; i++) if (!seive[i]){
        primes.push_back((int)i);
        for (int64 j = i*i; j < MAX_N; j += i)
            seive[j] = true;
    }
}
/////////////////////////////////////////////////////////////
int main(){
    RF("input.txt");
    //    WF("output.txt");
    EF("err.txt");

    Setup();
    int T;
    scanf("%d", &T);
    while (T--){
        int n;
        scanf("%d", &n);
        vector <int> V;
        for (int i = 0; i < n; i++){
            int a;
            scanf("%d", &a);
            for (int k = 0; k < SZ(primes) && a > 1; k++) while (a%primes[k] == 0){
                V.push_back(primes[k]);
                a /= primes[k];
            }
            if (a > 1)
                V.push_back(a);
        }
        sort(ALL(V));
        if (SZ(V) <= 1)
            puts("-1");
        else
            printf("%I64d\n", 1LL * V[0] * V[1]);
    }
    return 0;
}