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()


def prod(L):
    s = 1
    for l in L:
        s *= l
    return s

T = int(input())
for _ in range(T):
    N = int(input())
    A = [int(a) for a in input().split()]
    NE = []
    PO = []
    po, ne, ze = 0, 0, 0
    for a in A:
        if a > 0:
            PO.append(a)
            po += 1
        elif a < 0:
            NE.append(-a)
            ne += 1
        else:
            ze += 1
    PO = sorted(PO)
    NE = sorted(NE)
    ans = - 10 ** 100
    if ze:
        ans = max(ans, 0)
    if ne >= 5:
        ans = max(ans, -prod(NE[:5]))
    if po >= 5:
        ans = max(ans, prod(PO[-5:]))
    if po >= 3 and ne >= 2:
        ans = max(ans, prod(PO[-3:]) * prod(NE[-2:]))
    if po >= 1 and ne >= 4:
        ans = max(ans, prod(PO[-1:]) * prod(NE[-4:]))
    if po >= 4 and ne >= 1:
        ans = max(ans, -prod(PO[:4]) * prod(NE[:1]))
    if po >= 2 and ne >= 3:
        ans = max(ans, -prod(PO[:2]) * prod(NE[:3]))
    print(ans)
