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
if sys.subversion[0] == "PyPy":
    import io, atexit
    sys.stdout = io.BytesIO()
    atexit.register(lambda: sys.__stdout__.write(sys.stdout.getvalue()))
    
    sys.stdin = io.BytesIO(sys.stdin.read())
    input = lambda: sys.stdin.readline().rstrip()

RS = raw_input
RI = lambda x=int: map(x,RS().split())
RN = lambda x=int: x(RS())
''' ...................................................................... '''

def sum1(arr):
    v=1
    for i in arr:
        v*=i
    return v

for _ in xrange(RN()):
    n = RI()
    arr = RI()
    less = []
    more = []
    
    for i in arr:
        if i<0: less.append(i)
        else: more.append(i)

    less.sort(reverse=True)
    more.sort()

    a=b=c=d=e=f=float('-inf')

    if len(more)>=5:
        a = sum1(more[-5:])

    if len(more)>=4 and len(less)>=1:
        b = sum1(more[:4]) * less[0]

    if len(more)>=3 and len(less)>=2:
        c = sum1(more[-3:]) * sum1(less[-2:])

    if len(more)>=2 and len(less)>=3:
        d = sum1(more[:2]) * sum1(less[:3])

    if len(more)>=1 and len(less)>=4:
        e = more[-1] * sum1(less[-4:])

    if len(less)>=5:
        f = sum1(less[:5])

    print max(a,b,c,d,e,f)
        
    

    
