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.
from collections import Counter
for _ in range(int(input())):
    n=int(input())
    arr=list(map(int,input().split()))
    ne=[]
    p=[]
    for i in range(n):
        if arr[i]<0:
            ne.append(-1*arr[i])
        else:
            p.append(arr[i])
    ne.sort()
    p.sort(reverse=True)
    if n==5:
        out=1
        for i in arr:
            out*=i
        print(out)
    elif len(p)==0:
        out=1
        i=0
        while i<5:
            out*=ne[i]
            i+=1
        print(-1*out)
    else:
        out=p[0]
        p=p[1:]
        ne.reverse()
        i=0
        while i<4:
            if len(ne)>=2:
                if len(p)>=2:
                    if ne[0]*ne[1]>p[0]*p[1]:
                        out*=ne[0]*ne[1]
                        ne=ne[2:]
                    else:
                        out*=p[0]*p[1]
                        p=p[2:]
                else:
                    out*=ne[0]*ne[1]
                    ne=ne[2:]
            else:
                out*=p[0]*p[1]
                p=p[2:]
            i+=2
        print(out)   
        
        
        