You are given an array of integers a_1,a_2,…,a_n. Find the maximum possible value of a_ia_ja_ka_la_t among all five indices (i, j, k, l, t) (i<j<k<l<t).

Input

The input consists of multiple test cases. The first line contains an integer t (1≤ t≤ 2 ⋅ 10^4) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer n (5≤ n≤ 10^5) — the size of the array.

The second line of each test case contains n integers a_1,a_2,…,a_n (-3× 10^3≤ a_i≤ 3× 10^3) — given array.

It's guaranteed that the sum of n over all test cases does not exceed 2⋅ 10^5.

Output

For each test case, print one integer — the answer to the problem.

Example

Input


4
5
-1 -2 -3 -4 -5
6
-1 -2 -3 1 2 -1
6
-1 0 0 0 -1 -1
6
-9 -7 -5 -3 -2 1


Output


-120
12
0
945

Note

In the first test case, choosing a_1,a_2,a_3,a_4,a_5 is a best choice: (-1)⋅ (-2) ⋅ (-3)⋅ (-4)⋅ (-5)=-120.

In the second test case, choosing a_1,a_2,a_3,a_5,a_6 is a best choice: (-1)⋅ (-2) ⋅ (-3)⋅ 2⋅ (-1)=12.

In the third test case, choosing a_1,a_2,a_3,a_4,a_5 is a best choice: (-1)⋅ 0⋅ 0⋅ 0⋅ (-1)=0.

In the fourth test case, choosing a_1,a_2,a_3,a_4,a_6 is a best choice: (-9)⋅ (-7) ⋅ (-5)⋅ (-3)⋅ 1=945.
import sys as _sys


def main():
    t = int(input())
    for i in range(t):
        n, = _read_ints()
        a = tuple(_read_ints())
        result = find_max_possible_n_elements_product(a, product_members_n=5)
        print(result)


def _read_line():
    result = _sys.stdin.readline()
    assert result[-1] == "\n"
    return result[:-1]


def _read_ints():
    return map(int, _read_line().split(" "))


def find_max_possible_n_elements_product(sequence, product_members_n):
    sequence = sorted(sequence)
    assert len(sequence) >= product_members_n
    best_products = []
    for lowest_n in range(0, product_members_n + 1):
        highest_n = product_members_n - lowest_n
        best_lowest = sequence[:lowest_n]
        best_highest = sequence[len(sequence)-highest_n:]
        product = 1
        for x in best_lowest + best_highest:
            product *= x
        best_products.append(product)
    return max(best_products)


if __name__ == '__main__':
    main()
