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.
from sys import stdin
    
class Input:
    def __init__(self):
        self.next = self.readline()
    
    def readline(self):
        return stdin.readline().strip()

    def line(self):
        try:
            return self.next
        finally:
            self.next = self.readline()

    def array(self, sep = ' ', cast = int):
        return list(map(cast, self.line().split(sep = sep)))

    def known_tests(self):
        num_of_cases, = self.array()
    
        for case in range(num_of_cases):
            yield self

    def unknown_tests(self):
        while self.next:
            yield self

class Problem:
    def __init__(self, input):
        n, = input.array()
        a = input.array()
        a.sort()

        ans = max(
            a[0] * a[1] * a[2] * a[3] * a[4],
            a[0] * a[1] * a[2] * a[3] * a[-1],
            a[0] * a[1] * a[2] * a[-2] * a[-1],
            a[0] * a[1] * a[-3] * a[-2] * a[-1],
            a[0] * a[-4] * a[-3] * a[-2] * a[-1],
            a[-5] * a[-4] * a[-3] * a[-2] * a[-1]
        )

        print(ans)

for tc in Input().known_tests():
    Problem(tc)
