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

rl = sys.stdin.readline
readInt = lambda: long(rl())

def solve(n, nums):
    sampleSpace = [(0,5),(1,4),(2,3),(3,2),(4,1),(5,0)]
    sortedNums = sorted(nums)
    negs = []
    pos = []
    for n in sortedNums:
        if n < 0:
            negs.append(n)
        else:
            pos.append(n)
    
    negCount = len(negs)
    posCount = len(pos)

    result = -243000000000000000L

    for x, y in sampleSpace:
        if negCount < x or posCount < y:
            continue

        prod1 = 1L
                    
        for i in range(x):
            prod1 *= negs[-(i+1)]
        for i in range(y):
            prod1 *= pos[i]

        prod2 = 1L

        for i in range(x):
            prod2 *= negs[i]
        for i in range(y):
            prod2 *= pos[-(i+1)]

        result = max(prod1, prod2, result)

    return result


if __name__ == '__main__':
    t = readInt()

    for i in range(t):
        n = readInt()
        ns = [long(x) for x in rl().split()]
        print(solve(n, ns))

