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.
t = int(input())
def prod(u):
    e = 1
    for j in u:
        e*=j
    return e
for _ in range(t):
    n = int(input())
    a = list(map(int,input().split()))
    p = []
    r = []
    z = []
    for x in a:
        if x > 0:
            p.append(x)
        elif x < 0:
            r.append(x)
        else:
            z.append(x)
    lz = len(z)
    lp = len(p)
    lr = len(r)
    if lp == 0:
        if lz == 0:
            r.sort()
            m = prod(r[-5:])
        else:
            m = 0
    elif lp == 1:
        if lr >= 4:
            r.sort()
            m = prod(r[:4])*p[0]
        else:
            m = 0
    elif lp == 2:
        if lr >= 4:
            r.sort()
            m = prod(r[0:4])*max(p)
        else:
            if lz == 0:
                r.sort()
                m = prod(r[-3:])*p[0]*p[1]
            else:
                m = 0
    elif lp == 3:
        p.sort()
        if lr < 4:
            if lr >= 2:
                r.sort()
                m = prod(r[0:2])*prod(p)
            else:
                m = 0
        else:
            r.sort()
            m = max(prod(r[0:4])*max(p), prod(r[0:2])*prod(p))
    elif lp == 4:
        p.sort()
        if lr == 1:
            if lz == 0:
                m = prod(p)*r[0]
            else:
                m = 0
        elif lr == 2 or lr == 3:
            r.sort()
            m = prod(r[0:2])*prod(p[-3:])
        elif lr >= 4:
            r.sort()
            m = max(prod(r[0:2])*prod(p[-3:]), prod(r[0:4])*max(p))
        else:
            m = 0
    elif lp >= 5:
        p.sort()
        mb = prod(p[-5:])
        m1 = -float('inf') #2 3
        m2 = -float('inf') #4 1
        if lr <= 1:
            m = mb
        elif lr >= 2 and lr < 4:
            r.sort()
            m1 = prod(r[0:2])*prod(p[-3:])
            m = max(mb,m1)
        elif lr >= 4:
            r.sort()
            m1 = prod(r[0:2])*prod(p[-3:])
            m2 = prod(r[0:4])*max(p)
            m = max(max(m1,m2),mb)
        else:
            m = mb
    print(m)
        
                
            
            
    