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

t = int(input())
f = -1000000000000000000000000000


if 1 <= t <= 2 * 10**4:
    for x in range(t):
        product, x1, x2, x3 = int(1), int(f), int(f), int(f)
        x4, x5, x6, x7 = int(f), int(f), int(f), int(f)
        
        neg_arr, pos_arr, zero_arr, arr = [], [], [], []

        n = int(input())
        arr = list(map(int, input().split())) 
        
        if len(arr) == n:
            for x in range(len(arr)):
                if arr[x] > 0:
                    pos_arr.append(arr[x])
                elif arr[x] < 0:
                    neg_arr.append(arr[x])
                elif arr[x] == 0:
                    zero_arr.append(arr[x])
                        
            pos_arr.sort()
            neg_arr.sort()
        
            if len(pos_arr) >= 5:
                x1 = 1 
                for y in range(len(pos_arr)-5, len(pos_arr)):
                    x1 = x1 * pos_arr[y]
            if len(pos_arr) >= 3 and len(neg_arr) >= 2:
                x2 = 1
                for y in range(len(pos_arr)-3, len(pos_arr)):
                    x2 = x2 * pos_arr[y]
                for y in range(2):
                    x2 = x2 * neg_arr[y]
            if len(pos_arr) >= 1 and len(neg_arr) >= 4:
                x3 = pos_arr[len(pos_arr)-1]
                for y in range(4):
                    x3 = x3 * neg_arr[y]
            if len(zero_arr) >= 1:
                x4 = 0
            if len(neg_arr) >= 5:
                x5 = 1
                for y in range(len(neg_arr)-5, len(neg_arr)):
                    x5 = x5 * neg_arr[y]
            if len(neg_arr) >= 3 and len(pos_arr) >= 2:
                x6 = 1
                for y in range(len(neg_arr)-3, len(neg_arr)):
                    x6 = x6 * neg_arr[y]
                for y in range(2):    
                    x6 = x6 * pos_arr[y]
            if len(neg_arr) >= 1 and len(pos_arr) >= 4:
                x7 = neg_arr[len(neg_arr)-1]
                for y in range(4):
                    x7 = x7 * pos_arr[y]
        else:
            raise ValueError('Invalid User Input')
        
        product = max(x1, x2, x3, x4, x5, x6, x7)
        
        print(product)
