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.
K = 5

def solve(n, a):
	neg = []
	pos = []
	hasZero = False
	for v in a:
		if v < 0:
			neg.append(-v)
		elif v > 0:
			pos.append(v)
		else:
			hasZero = True
	pos.sort()
	neg.sort()
	negRes = True
	for i in range(0, K + 1, 2):
		if len(pos) >= K - i and len(neg) >= i:
			negRes = False
			break
	if negRes:
		if hasZero:
			return 0
		i = 0
		j = 0
		ans = -1
		need = K
		while need > 0 and i < len(pos) and j < len(neg):
			if pos[i] < neg[j]:
				ans *= pos[i]
				i += 1
			else:
				ans *= neg[j]
				j += 1
			need -= 1
		while need > 0 and i < len(pos):
			need -= 1
			ans *= pos[i]
			i += 1
		while need > 0 and j < len(neg):
			need -= 1
			ans *= neg[j]
			j += 1
		return ans

	if len(pos) + len(neg) < K:
		return 0
	pos.reverse()
	neg.reverse()
	best = 1
	for i in range(K):
		best *= a[i]
	for i in range(0, K + 1, 2):
		if len(neg) < i or len(pos) < K - i:
			continue
		t = 1
		for z in range(i):
			t *= neg[z]
		for z in range(K - i):
			t *= pos[z]
		best = max(best , t)
	return best
		
		
tests = int(input())
for test in range(tests):
	n = int(input())
	a = list(map(int, input().split()))
	print(solve(n, a))
