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 cal(a,s):
    if(a[0]<0):
        k=a[0]*-1
        if(k>a[-1]):
             s=s*a[0]
             a.remove(a[0])                
        else:
             s=s*a[-1]
             a.remove(a[-1])
    elif(a[0]>=0):
        s=s*a[0]
        a.remove(a[0])  
    return s
for t in range(int(input())):
    n=int(input())
    a=list(map(int,input().split(' ')))
    a.sort()
    s,k=1,0
    s1,s2,s3,s4=0,0,0,0
    if(len(a)==5):
        for i in range(len(a)):
            s=s*a[i]
        print(s)
    else:
        for i in range(5):
            if(a[i]<0):
                k+=1
        l=len(a)
        if(k==2 or k==3):
            s1=a[0]*a[1]*a[-1]*a[-2]*a[-3]
            s2=a[-4]*a[-5]*a[-1]*a[-2]*a[-3]
        elif(k==4 or k>4):
            s1=a[0]*a[1]*a[-1]*a[-2]*a[-3]
            s2=a[0]*a[1]*a[-1]*a[3]*a[2]
            s3=a[0]*a[1]*a[2]*a[-1]*a[3]
            s4=a[-4]*a[-5]*a[-1]*a[-2]*a[-3]
        if(k==4 or k>4):
            for i in range(4):
                s=cal(a,s)
            if(s<0):
                s=s*a[0]
            elif(s>0):
                s=s*a[-1]
            else:
                s=s*a[-1]
        elif(k==2 or k==3):
            for i in range(2):
                s=cal(a,s)
            if(s<0):
                s=s*a[0]
                a.remove(a[0])
            elif(s>0):
                s=s*a[-1]
                a.remove(a[-1])
            else:
                s=s*a[-1]
                a.remove(a[-1])
            s=s*a[-1]*a[-2]
        else:
            for i in range(5):
                s=s*a[-1]
                a.remove(a[-1])
        print(max(s,s1,s2,s3,s4))            