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

t = int(input())

for i in range(t):
    n = int(sys.stdin.readline())
    arr = list(map(int, sys.stdin.readline().split()))

    negative = []
    positive = []
    for x in arr:
        if x >= 0:
            positive.append(x)
        else:
            negative.append(x)

    positive.sort(reverse=True)
    negative.sort()

    # print(positive)
    # print(negative)

    poslen = len(positive)
    neglen = len(negative)
    maxNum = float('-inf')

    if n == 5:
        maxNum = max(maxNum, arr[0] * arr[1] * arr[2] * arr[3] * arr[4])
    if poslen == 0:
        maxNum = max(maxNum, negative[-1] * negative[-2] * negative[-3] * negative[-4] * negative[-5])
    if poslen >= 1 and neglen >= 4:
        maxNum = max(maxNum, positive[0] * negative[0] * negative[1] * negative[2] * negative[3])
    if poslen >= 3 and neglen >= 2:
        maxNum = max(maxNum, positive[0] * positive[1] * positive[2] * negative[0] * negative[1])
    if poslen >= 5:
        maxNum = max(maxNum, positive[0] * positive[1] * positive[2] * positive[3] * positive[4])

    print(maxNum)