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 ans(n,a):
    ans = -float('inf')
    neg,pos = [],[]
    lp,ln=0,0
    for i in range(n):
        if a[i] >= 0:
            pos.append(a[i])
            lp+=1
        else:
            neg.append(a[i])
            ln+=1
    neg.sort()
    pos.sort(reverse=True)
    if ln==0:
        return pos[0]*pos[1]*pos[2]*pos[3]*pos[4]
    if lp==0:
        return neg[-1]*neg[-2]*neg[-3]*neg[-4]*neg[-5]
    if lp >= 1 and ln >= 4:
        ans = max(ans,neg[0]*neg[1]*neg[2]*neg[3]*pos[0])
    if lp >= 2 and ln >= 3:
        ans = max(ans,pos[0]*pos[1]*neg[-1]*neg[-2]*neg[-3])
    if lp >= 3 and ln >= 2:
        ans = max(ans,neg[0]*neg[1]*pos[0]*pos[1]*pos[2])
    if lp >= 4 and ln >=1:
        ans = max(ans,pos[0]*pos[1]*pos[2]*pos[3]*neg[-1])
    if lp >= 5:
        ans = max(ans,pos[0]*pos[1]*pos[2]*pos[3]*pos[4])
    if ln >= 5:
        ans = max(ans,neg[-1]*neg[-2]*neg[-3]*neg[-4]*neg[-5])
    return ans

t  = int(input())
while t > 0:
    n = int(input())
    a = list(map(int,input().split(" ")))
    out = ans(n,a)
    print(out)
    t-=1