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


#Une fonction qui insére l'élément x à la bonne place dans le tableau A.
#A est supposé trié par ordre croissant

def insertion(x,A):
    i=0
    while (i<len(A) and A[i]<x):
        i=i+1
    if(i==len(A)):
        A.append(x)
    else:
        A.append(0)
        for j in range(len(A)-i-1):
            A[len(A)-j-1]=A[len(A)-j-2]
        A[i]=x

def F(A):
    
    #On va récupérer les cinqs plus grands et les 5 plus petits elts de A 
    Max = []
    Min = []

    for i in range(5):
        insertion(A[i],Max)
        insertion(A[i],Min)
        
    for i in range(5,len(A)):
        if A[i]>Max[0]:
            del Max[0]
            insertion(A[i],Max)
        if A[i]<Min[4]:
            del Min[4]
            insertion(A[i],Min)

    res1 =  Max[4] * Max[3] * Max[2] * Max[1] * Max[0]
    res2 =  Max[4] * Max[3] * Max[2] * Min[0] * Min[1]
    res3 =  Max[4] * Min[0] * Min[1] * Min[2] * Min[3]
    res=max(res1,res2,res3)
    print(res)

for j in range(int(input())):
    _ = input()
    A = list(map(int, input().split()))
    F(A)
