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.
from math import ceil
from collections import Counter
def get_array_int():
    li = list(map(int, input().split()))
    return li
t = int(input())


def solve():
    n = int(input())
    arr = get_array_int()
    
    temp = sorted(arr)
    product = 1
    if temp[-1] == 0:
        print(0)
    elif temp[-1] <= 0:
        for i in range(n - 1, n - 5 -1, -1): 
            product *= temp[i] 
        print(product)
    else:
        j = n-1
        i = 0
        product *= temp[j] 
        j-= 1
        k = 4
        k>>=1
        
        for itr in range(k):
            left_product = temp[i]*temp[i+1]
            right_product = temp[j]*temp[j-1]
            if (left_product > right_product) : 
                product *= left_product 
                i += 2
            else : 
                product *= right_product 
                j -= 2
        print(product)



while t:
    solve()
    t-=1