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 itertools import combinations as permutations
import sys

def prod(A):
    return A[0] * A[1] * A[2] * A[3] * A[4]

def solve(A):
    A.sort()
    zero = False
 
    i_s = set([0, 1, 2, 3, 4])
    for x in range(len(A) - 5, len(A)):
        i_s.add(x)
    
    try:
        zindex = A.index(0)
        zero = True
    except:
        zindex = None
 
    if zindex is not None:
        #i_s.add(zindex)
        for x in range(zindex + 1, zindex + 6):
            if x < len(A):
                i_s.add(x)
        for x in range(zindex - 5, zindex):
            if x > 0:
                i_s.add(x)
 
    l = []
    for i in i_s:
        l.append(A[i])
    perms = permutations(l, 5)
    #print(len(perms))
    largest = None
    for x in perms:
        p = prod(x)
        if largest == None:
            largest = p
        
        elif p > largest:
            largest = p
 
    if largest < 0 and zero == True:
        largest = 0
    return largest


s = sys.stdin.readlines()
for i in range(1, len(s)):
    if i % 2 == 0:
        A = s[i].split(' ')
        A = [int(a) for a in A]
        print(solve(A))
