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.
from functools import reduce
import operator


def calc_product(integers):
    return reduce(operator.mul, integers, 1)


num_cases = int(input())

for i in range(num_cases):
    case_len = input()
    case_str = input()

    integers = list(map(int, case_str.split(' ')))

    if len(integers) == 5:
        print(calc_product(integers))
        continue

    positives = list(filter(lambda x: x >= 0, integers))
    negatives = list(filter(lambda x: x < 0, integers))

    positives_sorted = sorted(positives, reverse=True)
    negatives_sorted = sorted(negatives)

    results = []
    # Positive cases
    if len(positives_sorted) >= 5:
        results.append(calc_product(positives_sorted[:5]))
    if len(negatives_sorted) >= 2 and len(positives_sorted) >= 3:
        results.append(calc_product(positives_sorted[:3] + negatives_sorted[:2]))
    if len(negatives_sorted) >= 4 and len(positives_sorted) >= 1:
        results.append(calc_product(positives_sorted[:1] + negatives_sorted[:4]))
    # Negative cases
    if len(negatives_sorted) >= 1 and len(positives_sorted) >= 4:
        results.append(calc_product(positives_sorted[-4:] + negatives_sorted[-1:]))
    if len(negatives_sorted) >= 3 and len(positives_sorted) >= 2:
        results.append(calc_product(positives_sorted[-2:] + negatives_sorted[-3:]))
    if len(negatives_sorted) >= 5:
        results.append(calc_product(negatives_sorted[-5:]))

    print(max(results))
