human
PYTHON3 solution for "You are given an array a consisting of n positive integers. You have to choose a positive integer d and paint all elements into two colors. All elements which are divisible by d will be painted red, and all other elements will be painted blue.

The coloring is called beautiful if there are no pairs of adjacent elements with the same color in the array. Your task is to find any value of d which yields a beautiful coloring, or report that it is impossible.

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.

The first line of each testcase contains one integer n (2 ≤ n ≤ 100) — the number of elements of the array.

The second line of each testcase contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^{18}).

Output

For each testcase print a single integer. If there is no such value of d that yields a beautiful coloring, print 0. Otherwise, print any suitable value of d (1 ≤ d ≤ 10^{18}).

Example

Input

5
5
1 2 3 4 5
3
10 5 15
3
100 10 200
10
9 8 2 6 6 2 8 6 5 4
2
1 3

Output

2
0
100
0
3":



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What is a Python code to find any value of d which yields a beautiful coloring, or report that it is impossible?
assistant
#Here is Python code to find any value of d which yields a beautiful coloring, or report that it is impossible.
 def hcf(a, b):

	if a%b == 0:
		return b

	return hcf(b, a%b)

t = int(input())

for ii in range(t):
	n = int(input())
	l = list(map(int, input().split()))

	num1 = l[0]

	for i in range(2, n, 2):
		num1 = hcf(num1, l[i])

	num2 = l[1]

	for i in range(3, n, 2):
		num2 = hcf(num2, l[i])

	tf = False

	for i in range(0, n, 2):
		if l[i]%num2 == 0:
			tf = True
			break

	tf2 = False

	for i in range(1, n, 2):
		if l[i]%num1 == 0:
			tf2 = True
			break

	if tf and not tf2:
		print(num1)
	elif tf2 and not tf:
		print(num2)
	elif tf2 and tf:
		print(0)
	else:
		print(max(num1, num2))