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.
import sys
input = lambda: sys.stdin.readline().rstrip()
t = int(input())
for _ in range(t):
    n = int(input())
    a = []
    b = []
    z = 0
    for u in map(int,input().split()):
        if u<0:
            a.append(u)
        if u>0:
            b.append(u)
        if u==0:
            z+=1
    res = -10 ** 50
    if z:
        res = 0
    for aa in range(0,2):
        for bb in range(0,2):
                a.sort(reverse=aa)
                b.sort(reverse=bb)
                for i in range(0,6):
                    j = 5-i
                    if len(a)>=i and len(b)>=j:
                        aux = 1
                        for ii in range(0,i):
                            aux*=a[ii]
                        for ii in range(0,j):
                            aux*=b[ii]
                        res = max(res,aux)



    print(res)
