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.
# -*- coding: utf-8 -*-
"""
Created on Sat Sep 12 20:38:35 2020

@author: Dark Soul
"""
def solve(a):
    n=len(a)
    sol=a[0]*a[1]*a[2]*a[3]*a[5]
    for i in range(n):
        for j in range(i+1,n):
            for k in range(j+1,n):
                for x in range(k+1,n):
                    for y in range(x+1,n):
                        sol=max(sol,a[i]*a[j]*a[k]*a[x]*a[y])
    return sol
t=int(input(''))
arr=[]
for i in range(t):
    n=int(input(''))
    arr.append(list(map(int,input().split())))
for i in arr:
    sol=1
    if len(i)==5:
        for j in i:
            sol*=j
        print(sol)
        continue
    if len(i)<=10:
        print(solve(i))
        continue
    i.sort()
    sol=[]
    n=len(i)
    for j in range(0,5):
        sol.append(i[j])
    for j in range(n-1,n-6,-1):
        sol.append(i[j])
    print(solve(sol))
        
    