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 input_int():
    return(int(input()))

def input_int_list():
    return(list(map(int,input().split())))

def input_int_map():
    return(map(int,input().split()))

import functools
import operator
prod = functools.partial(functools.reduce, operator.mul)

def run():
    q_num = input_int()

    for i in range(q_num):
        num_count = input_int()
        nums = input_int_list()
        nums.sort()
        p1 = nums[0:4] + [nums[-1]]
        p2 = nums[0:2] + nums[num_count-3:num_count]
        p3 = nums[num_count - 5:num_count]

        r1 = prod(p1)
        r2 = prod(p2)
        r3 = prod(p3)

        print(max(r1, r2, r3))


run()

# -10 -5 -3 -2 -1 0 1 2 4 5

# 左から
# -10 50 -150 -300 -300 0 0 0 0 0

# 右から
#                  0 40 40  20  5