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.
t = int(input())
for _ in range(t):
    n = int(input())
    a = list(map(int, input().split()))
    m1 = -10000
    m2 = -10000
    m3 = -10000
    m4 = -10000
    m5 = -10000
    mi1 = 10000
    mi2 = 10000
    mi3 = 10000
    mi4 = 10000
    mi5 = 10000
    for i in a:
        if i >= m1:
            m1, m2, m3, m4, m5 = i, m1, m2, m3, m4
        elif i >= m2:
            m2, m3, m4, m5 = i, m2, m3, m4
        elif i >= m3:
            m3, m4, m5 = i, m3, m4
        elif i >= m4:
            m4, m5 = i, m4
        elif i >= m5:
            m5 = i
        if i <= mi1:
            mi1, mi2, mi3, mi4, mi5 = i, mi1, mi2, mi3, mi4
        elif i <= mi2:
            mi2, mi3, mi4, mi5 = i, mi2, mi3, mi4
        elif i <= mi3:
            mi3, mi4, mi5 = i, mi3, mi4
        elif i <= mi4:
            mi4, mi5 = i, mi4
        elif i <= mi5:
            mi5 = i
    a = m1 * m2 * m3 * m4 * m5
    b = m1 * mi1 * mi2 * mi3 * mi4
    c = m1 * m2 * m3 * mi1 * mi2
    print(max(a,b,c))
            
