human
Write me a Python program to find any value of d which yields a beautiful coloring, or report that it is impossible given the following:
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":
assistant
#Here is Python program to find any value of d which yields a beautiful coloring, or report that it is impossible.
 import sys
import math
from itertools import accumulate
from fractions import gcd
from functools import reduce
    
def read_string(): return sys.stdin.readline().strip()
def read_int_arr(): return list(map(int, sys.stdin.readline().strip().split()))
def read_ints(): return map(int, sys.stdin.readline().strip().split())

def ggt(a, b):
    if a < b:
        a, b = b, a

    if b == 0:
        return a
    return ggt(b, a % b)

def ggt_l(l):
    return reduce(math.gcd, l)

def solve():
    n = int(input())
    ar = read_int_arr()

    l1 = []
    l2 = []

    for i in range(n):
        if i % 2 == 0:
            l1.append(ar[i])
        else:
            l2.append(ar[i])
    d1 = ggt_l(l1)
    d2 = ggt_l(l2)

    def works(l, x):
        for i in range(len(l) - 1):
            if l[i] % x == 0 and l[i+1] % x == 0:
                return False
        return True

    if works(ar, d1):
        print(d1)
        return
    elif works(ar, d2):
        print(d2)
        return
    else:
        print(0)
    
if __name__ == '__main__':
    T = int(input())
    for _ in range(T):
        solve()