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.


for _ in range(int(input())):
    n = int(input())
    l = sorted(list(map(int, input().split())))

    if n == 5:
        print(l[0] * l[1] * l[2] * l[3] * l[4])
        continue

    neg_arr = []
    pos_arr = []
    for i in l:
        if i < 0:
            neg_arr.append(i)
        elif i > 0:
            pos_arr.append(i)

    if len(neg_arr) + len(pos_arr) < 5:
        print(0)
        continue

    neg_arr.sort()
    pos_arr.sort()

    arr = []

    if 0 in l:
        arr.append(0)


    if len(neg_arr) >= 2 and len(pos_arr) >= 3:
        arr.append(neg_arr[0] * neg_arr[1] * pos_arr[-1] * pos_arr[-2] * pos_arr[-3])


    if len(neg_arr) >= 4 and len(pos_arr) >= 1:
        arr.append(neg_arr[0] * neg_arr[1] * neg_arr[2] * neg_arr[3] * pos_arr[-1])

    if len(pos_arr) >= 5:
        arr.append(pos_arr[-1] * pos_arr[-2] * pos_arr[-3] * pos_arr[-4] * pos_arr[-5])
    if len(pos_arr) == 0:
        arr.append(neg_arr[-1] * neg_arr[-2] * neg_arr[-3] * neg_arr[-4] * neg_arr[-5])
    if len(pos_arr) == 4:
        arr.append(pos_arr[-1] * pos_arr[-2] * pos_arr[-3] * pos_arr[-4] * neg_arr[0])

    print(max(arr))


