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

N = int(sys.stdin.readline().strip())
MOST_NEG = -2425952699100149990000

def mult(a):
    prod = 1
    for i in a: prod *= i
    return prod

def mx(a, b, ai, bi):
    if ai == 0:
        return b[bi]
    if bi == 0:
        return a[ai]

    if a[ai] == MOST_NEG or b[bi] == MOST_NEG:
        return MOST_NEG

    return a[ai] * b[bi]

for _ in range(N):
    m = int(sys.stdin.readline().strip())
    nums = [int(i) for i in sys.stdin.readline().strip().split(" ")]
    nums.sort()
    neg = []
    pos = []
    zeros = 0
    for n in nums:
        if n > 0:
            pos.append(n)
        elif n < 0:
            neg.append(n)
        else:
            zeros += 1
    sp, lp, sn, ln = [MOST_NEG] * 6, [MOST_NEG] * 6, [MOST_NEG] * 6, [MOST_NEG] * 6
    for i in range(1,6):
        if len(pos) >= i:
            sp[i] = mult(pos[0:i])
            lp[i] = mult(pos[len(pos) - i:len(pos)])
        if len(neg) >= i:
            sn[i] = mult(neg[0:i])
            ln[i] = mult(neg[len(neg) - i:len(neg)])

    best = MOST_NEG
    for i in range(6):
        for j in range(6):
            for k in range(min(6,zeros+1)):
                if i+j+k != 5: continue
                if k > 0:
                    best = max(best, 0)
                else:
                    best = max(best,
                           mx(sp, sn, i, j),
                           mx(sp, ln, i, j),
                           mx(lp, sn, i, j),
                           mx(lp, ln, i, j))
    print(best)
        
        
        

    
