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: #Fast I/O
  import sys,os
  import math
  # To enable the file I/O i the below 2 lines are uncommented.
  # read from in.txt if uncommented
  if os.path.exists('in.txt'): sys.stdin=open('in.txt','r')
  # will print on Console if file I/O is not activated
  #if os.path.exists('out.txt'): sys.stdout=open('out.txt', 'w')
   
  # inputs template
  from io import BytesIO, IOBase
  from heapq import *
  from bisect import *
  from collections import *
  
  def main():
      for _ in range(mi()):
          x = mi()
          a = list(MI())
          if x == 1 : print(a[0]); continue
          eve = a[0]
          odd = a[1]
          for i in range(2,len(a)):
              if i&1:
                  odd = math.gcd(odd,a[i])
              else:
                  eve = math.gcd(eve,a[i])
          if eve == odd :
              print(0)
          else :
              flag1 = 0
              for i in range(0,len(a),2):
                  if a[i]%odd == 0:
                      flag1 = 1
                      break
              flag2 = 0
              for i in range(1,len(a),2):
                  if a[i]%eve == 0:
                      flag2 =1
                      break
              if flag1 and flag2:
                  print(0)
              elif not flag2:
                  print(eve)
              elif not flag1:
                  print(odd)
  
  # Sample Inputs/Output 
   
  # region fastio
   
  BUFSIZE = 8192
   
  class FastIO(IOBase):
      newlines = 0
   
      def __init__(self, file):
          self._fd = file.fileno()
          self.buffer = BytesIO()
          self.writable = "x" in file.mode or "r" not in file.mode
          self.write = self.buffer.write if self.writable else None
   
      def read(self):
          while True:
              b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
              if not b:
                  break
              ptr = self.buffer.tell()
              self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
          self.newlines = 0
          return self.buffer.read()
   
      def readline(self):
          while self.newlines == 0:
              b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
              self.newlines = b.count(b"\n") + (not b)
              ptr = self.buffer.tell()
              self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
          self.newlines -= 1
          return self.buffer.readline()
   
      def flush(self):
          if self.writable:
              os.write(self._fd, self.buffer.getvalue())
              self.buffer.truncate(0), self.buffer.seek(0)
   
   
  class IOWrapper(IOBase):
      def __init__(self, file):
          self.buffer = FastIO(file)
          self.flush = self.buffer.flush
          self.writable = self.buffer.writable
          self.write = lambda s: self.buffer.write(s.encode("ascii"))
          self.read = lambda: self.buffer.read().decode("ascii")
          self.readline = lambda: self.buffer.readline().decode("ascii")
   
   
  sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
  input = lambda: sys.stdin.readline().rstrip("\r\n")
  #for array of integers
  def MI():return (map(int,input().split()))
  def mi():return int(input())
  
  # endregion
  #for fast output, always take string
  def outP(var): sys.stdout.write(str(var)+'\n')  
  # end of any user-defined functions
   
  MOD=10**9+7
  mod=998244353
   
  # main functions for execution of the program.
   
  if __name__ == '__main__':  
      #This doesn't works here but works wonders when submitted on CodeChef or CodeForces 
      main()
  