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 maxVal(arr):
    arr.sort()
    positives = 0
    negatives = 0
    zero = False
    for i in range(len(arr)):
        if arr[i] < 0:
            negatives += 1
        elif arr[i] > 0:
            positives += 1
        else:
            zero = True
    
    #if at least 2 negatives, use the smallest ones
    #if less than 2 negatives, use the largest 5
    if negatives < 2 or arr[-1] < 0:
        total = 1
        for i in range(len(arr)-1,len(arr)-6,-1):
            total *= arr[i]
        return total
    else:
        l = 0
        r = len(arr) - 2
        total = arr[-1] 
        if total == 0:
            return 0
        for i in range(2):
            if arr[l] * arr[l+1] > arr[r] * arr[r-1]:
                total *= arr[l] * arr[l+1]
                l += 2
            else:
                total *= arr[r] * arr[r-1]
                r -= 2
        return total

T = int(input())
for t in range(T):
    N = int(input())
    arr = [int(i) for i in input().split(' ')]
    print(maxVal(arr))
