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.
def highest_product_of_5(list_of_ints):
    lowest = highest = list_of_ints[0]

    lowest_product_of_2 = highest_product_of_2 = highest * list_of_ints[1]

    lowest_product_of_3 = highest_product_of_3 = lowest_product_of_2 * list_of_ints[2]

    lowest_product_of_4 = highest_product_of_4 = highest_product_of_3 * list_of_ints[3]

    highest_product_of_5 = highest_product_of_4 * list_of_ints[4]

    for i, current in enumerate(list_of_ints[1:]):

        if i + 1 >= 5:
            highest_product_of_5 = max(
                highest_product_of_5,
                current * highest_product_of_4,
                current * lowest_product_of_4)

        if i + 1 >= 4:
            highest_product_of_4 = max(
                highest_product_of_4,
                current * highest_product_of_3,
                current * lowest_product_of_3)

            lowest_product_of_4 = min(
                lowest_product_of_4,
                current * highest_product_of_3,
                current * lowest_product_of_3)

        if i + 1 >= 3:
            highest_product_of_3 = max(
                highest_product_of_3,
                current * highest_product_of_2,
                current * lowest_product_of_2)

            lowest_product_of_3 = min(
                lowest_product_of_3,
                current * highest_product_of_2,
                current * lowest_product_of_2)

        if i + 1 >= 2:
            highest_product_of_2 = max(
                highest_product_of_2,
                current * highest,
                current * lowest)

            lowest_product_of_2 = min(
                lowest_product_of_2,
                current * highest,
                current * lowest)

        highest = max(highest, current)

        lowest = min(lowest, current)

        # print(current, ":", lowest, highest, "|", lowest_product_of_2, highest_product_of_2, "|", lowest_product_of_3, highest_product_of_3, "|", lowest_product_of_4, highest_product_of_4, "|", highest_product_of_5)

    return highest_product_of_5


t = int(input())
for req in range(t):
    n = int(input())
    a = list(map(int, input().split()))

    print(highest_product_of_5(a))
