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 heapq
inputed = []
count = int(input())

linesPer = 2
for i in range(count*linesPer):
    inputed.append(input())


t = 0
for i in range(count):
    
    try:
        inputed[t+1] = inputed[t+1].split(" ")
        inputed[t+1] = [int(x) for x in inputed[t+1]]
        neg = [-x for x in inputed[t+1]]
        heapq.heapify(inputed[t+1])
        heapq.heapify(neg)
        heap = inputed[t+1]
        topFive = []
        botFive = []
        for i in range(5):
            topFive.append(-heapq.heappop(neg))
            botFive.append(heapq.heappop(heap))
        mult = 1
        for num in topFive:
            mult *= num
        op1 = mult
        op2 = topFive[0]*botFive[0]*botFive[1]*botFive[2]*botFive[3]
        op3 = topFive[0]*topFive[1]*topFive[2]*botFive[0]*botFive[1]
        print(max(op1,op2,op3))
    except:
        print(0)
    

    t += linesPer
