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.
def solve(n, a):
    min1 = a.copy()
    max1 = a.copy()

    min2 = [0] * n
    max2 = [0] * n

    for m in range(2, 6):
        minv = min1[m - 2]
        maxv = max1[m - 2]

        for i in range(m - 1, n):
            ai = a[i]
            if ai > 0:
                min2[i] = minv * ai
                max2[i] = maxv * ai
            elif ai < 0:
                min2[i] = maxv * ai
                max2[i] = minv * ai
            else:
                min2[i] = 0
                max2[i] = 0

            minv = min(minv, min1[i])
            maxv = max(maxv, max1[i])

        min1, max1, min2, max2 = min2, max2, min1, max1

    return max(max1[4:])


def main():
    t = int(input())
    anss = [0] * t

    for i in range(t):
        n = int(input())
        a = list(map(int, input().split()))
        anss[i] = solve(n, a)

    for ans in anss:
        print(ans)


main()
