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 io, os
  import sys 
  from sys import stdin
  
  from bisect import bisect_left, bisect_right
  from collections import defaultdict, deque, namedtuple
  from heapq import heappush, heappop
  from math import gcd, ceil, floor, factorial, sqrt
  from itertools import combinations, permutations
  
  input = sys.stdin.buffer.readline
  # input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
  # input = sys.stdin.readline
  
  def work():
      ans = 0 
  
      return 
  
  # sys.setrecursionlimit(200010)
  def main():
      test = int(input())
  
      for idt in range(test):
          n = int(input())
          # n, m = map(int, input().split())
          nums = list(map(int, input().split()))
          a, b = [], []
          for i in range(n):
              if i % 2 == 0:
                  a.append(nums[i])
              else:
                  b.append(nums[i])
  
          flag = False 
          for i in a:
              if i in b:
                  flag = True 
                  break 
  
          max_gcd1 = a[0]
          for i in range(1, len(a)):
              max_gcd1 = gcd(max_gcd1, a[i])
  
          max_gcd2 = b[0]
          for i in range(1, len(b)):
              max_gcd2 = gcd(max_gcd2, b[i])
          ans = 0 
          if max_gcd1 == max_gcd2 or flag:
              ans = 0 
          else:
              flag = True
              for i in b:
                  if i % max_gcd1 == 0:
                      flag = False 
                      break 
              if flag:
                  ans = max_gcd1 
              
              flag = True 
              for i in a:
                  if i % max_gcd2 == 0:
                      flag = False 
                      break 
              if flag:
                  ans = max_gcd2 
          print(ans)                 
              
  
  
      return 
  
  
  if __name__ == '__main__':
      main()