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.

t = int(input())

for _ in range(t):
    n = int(input())
    a = [int(x) for x in input().split()]

    neg = []
    pos = []
    
    for x in a:
        if x < 0:
            neg.append(x)
        else:
            pos.append(x)

    neg.sort(reverse=True)
    pos.sort()

    print(max(
        pos[-1] * pos[-2] * pos[-3] * pos[-4] * pos[-5] if len(pos) >= 5 and len(neg) >= 0 else float('-inf'),
        neg[0]  * pos[0]  * pos[1]  * pos[2]  * pos[3]  if len(pos) >= 4 and len(neg) >= 1 else float('-inf'),
        neg[-1] * neg[-2] * pos[-1] * pos[-2] * pos[-3] if len(pos) >= 3 and len(neg) >= 2 else float('-inf'),
        neg[0]  * neg[1]  * neg[2]  * pos[0]  * pos[1]  if len(pos) >= 2 and len(neg) >= 3 else float('-inf'),
        neg[-1] * neg[-2] * neg[-3] * neg[-4] * pos[-1] if len(pos) >= 1 and len(neg) >= 4 else float('-inf'),
        neg[0]  * neg[1] *  neg[2]  * neg[3]  * neg[4]  if len(pos) >= 0 and len(neg) >= 5 else float('-inf')
    ))
