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.
def mi():
    return map(int, input().split())
 
 
import sys, os
 
try:
    for _ in range(int(input())):
        noise = int(input())
        a = list(mi())
        a.sort()
 
        p, n = [], []
        for i in a:
            if i < 0:
                n.append(i)
            else:
                p.append(i)
        if len(p) == 0:
            ans = n[-1]*n[-2]*n[-3]*n[-4]*n[-5]
            print(ans)
            continue
 
        ans = p[-1]
        added = 1
        p.remove(p[-1])
        # print (p,n)
        if len(p) >= 2 and len(n) >= 2:
            if p[-1]*p[-2] > n[0]*n[1]:
                ans *= p[-1]*p[-2]
                added += 2
                p.remove(p[-1])
                p.remove(p[-1])
            else:
                ans *= n[0]*n[1]
                added += 2
                n.remove(n[0])
                n.remove(n[0])
        elif len(p) >= 4:
            added += 4
            ans *= p[-1]*p[-2]*p[-3]*p[-4]
        elif len(n)>=4:
            added += 4
            ans *= n[0]*n[1]*n[2]*n[3]
        # print (p, n)
        if added == 3:
            if len(p) >= 2 and len(n) >= 2:
                if p[-1]*p[-2] > n[0]*n[1]:
                    ans *= p[-1]*p[-2]
                    added += 2
                else:
                    ans *= n[0]*n[1]
                    added += 2
            elif len(p) >= 2:
                ans *= p[-1]*p[-2]
            elif len(n)>=2:
                ans *= n[0]*n[1]
        if added==1:
            ans = 1
            for i in range(5):
                ans*=a[i]
        print(ans)
 
 
except IndexError as e:
    for i in range(1010101010101010101):
        print ('lol, how did the index error creep in')