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 = sys.stdin.readline


def solve(n, a):
    a = [0] + a
    min_table = [[float('inf')] * (n + 1) for _ in range(6)]
    max_table = [[float('-inf')] * (n + 1) for _ in range(6)]

    # min_table[1][0] =
    # max_table[1][0] = float
    for j in range(1, n + 1):
        min_table[1][j] = min(a[j], min_table[1][j - 1])
        max_table[1][j] = max(a[j], max_table[1][j - 1])
    for i in range(2, 6):
        for j in range(i, n + 1):
            if a[j] > 0:
                min_table[i][j] = min(a[j] * min_table[i - 1][j - 1], min_table[i][j - 1])
                max_table[i][j] = max(a[j] * max_table[i - 1][j - 1], max_table[i][j - 1])
            else:  # a[j] < 0
                min_table[i][j] = min(a[j] * max_table[i - 1][j - 1], min_table[i][j - 1])
                max_table[i][j] = max(a[j] * min_table[i - 1][j - 1], max_table[i][j - 1])
    return max_table[5][n]


# assert solve(5, list(map(int, '-1 -2 -3 -4 -5'.split()))) == -120
# assert solve(6, list(map(int, '-1 -2 -3 1 2 -1'.split()))) == 12
# assert solve(6, list(map(int, '-1 0 0 0 -1 -1'.split()))) == 0
# assert solve(6, list(map(int, '-9 -7 -5 -3 -2 1'.split()))) == 945

for _ in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    v = solve(n, a)
    print(v)
