#include <bits/stdc++.h>
using namespace std;
void fastIO() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
}
bool chk(long long int x, long long int *v, long long int n) {
  long long int divs[100000], j = 0;
  for (long long int i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      divs[j++] = i;
      if (i != x / i) divs[j++] = x / i;
    }
  }
  if (n != j) return false;
  sort(divs, divs + j);
  for (int i = 0; i < j; i++) {
    if (v[i] != divs[i]) return false;
  }
  return true;
}
int main() {
  fastIO();
  int t;
  cin >> t;
  while (t--) {
    long long int n, num;
    cin >> n;
    long long int v[n + 5];
    for (int i = 0; i < n; i++) cin >> v[i];
    sort(v, v + n);
    num = v[0] * v[n - 1];
    if (chk(num, v, n))
      cout << num << '\n';
    else
      cout << -1 << '\n';
  }
  return 0;
}

### Prompt

Generate a Cpp solution to the following problem:

We guessed some integer number x. You are given a list of almost all its divisors. Almost all means that there are all divisors except 1 and x in the list.

Your task is to find the minimum possible integer x that can be the guessed number, or say that the input data is contradictory and it is impossible to find such number.

You have to answer t independent queries.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 25) — the number of queries. Then t queries follow.

The first line of the query contains one integer n (1 ≤ n ≤ 300) — the number of divisors in the list.

The second line of the query contains n integers d_1, d_2, ..., d_n (2 ≤ d_i ≤ 10^6), where d_i is the i-th divisor of the guessed number. It is guaranteed that all values d_i are distinct.

Output

For each query print the answer to it.

If the input data in the query is contradictory and it is impossible to find such number x that the given list of divisors is the list of almost all its divisors, print -1. Otherwise print the minimum possible x.

Example

Input


2
8
8 2 12 6 4 24 16 3
1
2


Output


48
4

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void fastIO() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
}
bool chk(long long int x, long long int *v, long long int n) {
  long long int divs[100000], j = 0;
  for (long long int i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      divs[j++] = i;
      if (i != x / i) divs[j++] = x / i;
    }
  }
  if (n != j) return false;
  sort(divs, divs + j);
  for (int i = 0; i < j; i++) {
    if (v[i] != divs[i]) return false;
  }
  return true;
}
int main() {
  fastIO();
  int t;
  cin >> t;
  while (t--) {
    long long int n, num;
    cin >> n;
    long long int v[n + 5];
    for (int i = 0; i < n; i++) cin >> v[i];
    sort(v, v + n);
    num = v[0] * v[n - 1];
    if (chk(num, v, n))
      cout << num << '\n';
    else
      cout << -1 << '\n';
  }
  return 0;
}

```