description: 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
solution: import sys
  def get_ints(): return map(int, sys.stdin.readline().strip().split())
  def get_list(): return list(map(int, sys.stdin.readline().strip().split()))
  def get_string(): return sys.stdin.readline().strip()
  def get_int(): return int(sys.stdin.readline().strip())
  def get_list_strings(): return list(map(str, sys.stdin.readline().strip().split()))
  
  
  # Output for list
  # sys.stdout.write(" ".join(map(str, final)) + "\n")
  
  # Output for int or str
  # sys.stdout.write(str(best) + "\n")
  
  def gcd(a,b):
    if(b==0):
      return a
    else:
      return gcd(b,a%b)
  
  
  def solve():
    n = get_int()
    arr = get_list()
  
    arr1 = []
    arr2 = []
  
    for i, ele in enumerate(arr):
      if i%2 == 0:
        arr1.append(ele)
      else:
        arr2.append(ele)
  
    g1 = arr1[0]
    l1 = len(arr1)
    for i in range(1, l1):
      g1 = gcd(g1, arr1[i])
  
    g2 = arr2[0]
    l2 = len(arr2)
    for i in range(1, l2):
      g2 = gcd(g2, arr2[i])
    
    # print(g1, g2)
  
    if g1 == 1 and g2 == 1:
      print(0)
      return
    
    if g1 != 1:
      flag = 0
      for ele in arr2:
        if ele%g1 == 0:
          flag = 1
          break
      
      if flag == 0:
        print(g1)
        return
    
    if g2 != 1:
      flag = 0
      for ele in arr1:
        if ele%g2 == 0:
          flag = 1
          break
      
      if flag == 0:
        print(g2)
        return
    
    print(0)
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  T = get_int()
  while T:
    solve()
    T -= 1
  