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 t1 in range(t):

    n = int(input())

    a = list(map(int,input().split(' ')))

    s = -1000000000000000000

    if n<=10:
        for i1 in range(0,n):
            for i2 in range(i1+1,n):
                for i3 in range(i2+1,n):
                    for i4 in range(i3+1,n):
                        for i5 in range(i4+1,n):
                            x = a[i1]*a[i2]*a[i3]*a[i4]*a[i5]
                            s = max(s,x)

    else:
        a.sort()
        b = []

        for i in range(0,5):
            b.append(a[i])

        for i in range(len(a)-5,len(a)):
            b.append(a[i])

        n = len(b)

##        print(a)
##
##        print(b)

        for i1 in range(0,n):
            for i2 in range(i1+1,n):
                for i3 in range(i2+1,n):
                    for i4 in range(i3+1,n):
                        for i5 in range(i4+1,n):
                            x = b[i1]*b[i2]*b[i3]*b[i4]*b[i5]
                            s = max(s,x)

    print(s)

        
        
