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 math
from collections import Counter
from functools import lru_cache

t = int(input())
for _ in range(t):
    n = int(input())
    arr = [int(i) for i in input().split()]
    positive, negative = [], []
    for i in arr:
        if i < 0:
            negative.append(abs(i))
        else:
            positive.append(i)
    ans = 1
    positive.sort(reverse=True)
    negative.sort(reverse=True)

    count = 0
    # print(positive)
    # print(negative)
    for i in range(min(5, len(positive))):
        ans *= positive[i]
        count += 1
    for i in range(5-count):
        ans *= -negative[len(negative)-1-i]
    temp2 = 1
    count = 0
    if len(negative) >= 2:
        for i in range(min(3, len(positive))):
            temp2 *= positive[i]
            count += 1
        for i in range(5-count):
            temp2 *= -negative[i]
        ans = max(ans, temp2)
    if len(negative) >= 4:
        temp2 = 1
        count = 0
        for i in range(min(1, len(positive))):
            temp2 *= positive[i]
            count += 1
        for i in range(5-count):
            temp2 *= -negative[i]
        ans = max(ans, temp2)
    print(ans)
