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.
#Python Template

from sys import stdin, stdout

def main():
	t = int(stdin.readline())
	for _ in range(t):
		n = int(stdin.readline())
		a = [int(i) for i in stdin.readline().split()]
		lp = [[0]*5 for i in range(n)]
		sp = [[0]*5 for i in range(n)]
		lp[0][0] = a[0]
		sp[0][0] = a[0]
		for i in range(1, n):
			for k in range(min(5, i+1)):
				#print("evaluating i={0}, k={1}".format(i, k))
				c = []
				if k != i:
					c1 = lp[i-1][k]
					c2 = sp[i-1][k]
					c.append(c1)
					c.append(c2)
				if k != 0:
					c3 = a[i] * lp[i-1][k-1]
					c4 = a[i] * sp[i-1][k-1]
					c.append(c3)
					c.append(c4)
				if k == 0:
					c5 = a[i]
					c.append(c5)
				#print(c)
				lp[i][k] = max(c)
				sp[i][k] = min(c)
		#print("largest:", lp)
		#print("smallest:", sp)
		print(lp[n-1][4])

main()