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.
for _ in range(int(input())):
    n = int(input())
    a = list(map(int,input().split()))
    neg, pos, zero = [], [], []
    for i in sorted(a):
        if i<0:
            neg.append(i)
        elif i>0:
            pos.append(i)
        elif i==0:
            zero.append(i)
    neg = neg[::-1]
    
    pl, nl = len(pos), len(neg)
    
    ans = float('-inf')
    
    
    for i in range(min( nl + 1, 6)):
        t = None
        no = 0
        if i%2==0:
            for j in range(nl-1, nl-i-1, -1):
                if t==None:t = neg[j]
                else:t *= neg[j]
                no += 1
            for j in range(pl-1, pl-min(5-no, pl)-1,-1):
                if t==None:t = pos[j]
                else:t *= pos[j]
                no += 1
            
        else:
            for j in range(min(i, nl)):
                if t==None:t = neg[j]
                else:t *= neg[j]
                no += 1
            for j in range(min(5-no, pl)):
                if t==None:t = pos[j]
                else:t *= pos[j]
                no +=1
        #print(t,ans, no)
        if no==5:
            if ans<0 and zero:
                ans = 0
            ans = max(ans, t)
        elif len(zero)+no>=5:
            ans = max(ans, 0)
        
    print(ans)