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, collections, math, bisect, heapq, random, functools,io,os,copy
  input = sys.stdin.readline
  out = sys.stdout.flush
  def rep():
      a = list(map(int,input().split()))
      return a
  
  def sep():
      a = list(input().split())
      return a
  
  
  class UnionFind:
      def __init__(self, x) -> None:
          self.uf = [-1] * x
  
      def find(self, x):
          r = x
          while self.uf[x] >= 0:
              x = self.uf[x]
  
          while r != x:
              self.uf[r], r = x, self.uf[r]
          return x
  
      def union(self, x, y):
          ux, uy = self.find(x), self.find(y)
          if ux == uy:
              return
          if self.uf[ux] >= self.uf[uy]:
              self.uf[uy] += self.uf[ux]
              self.uf[ux] = uy
          else:
              self.uf[ux] += self.uf[uy]
              self.uf[uy] = ux
          return
  
      def __print__(self):
          return self.uf
  
  
  def spfa(x,g,n):
      dis = [float('inf') for i in range(n)]
      dis[x] = 0
      state = [False for i in range(n)]
      state[x] = True
      queue = collections.deque()
      queue.append(x)
      while queue:
          cur = queue.popleft()
          state[cur] = False
          for next_ in g[cur]:
              if dis[next_] > dis[cur] + 1:
                  dis[next_] = dis[cur] + 1
                  if state[next_] == False:
                      state[next_] = True
                      queue.append(next_)
      return dis
  
  
  def gcd(x,y):
      if y == 0:
          return x
      return gcd(y,x % y)
  
  
  
  
  def solve():
      n = int(input())
      a = rep()
      if n == 2:
          if a[0] == a[1]:
              print(0)
          else:
              print(max(a))
      else:
          b1 = a[0]
          b2 = a[1]
          l = 2
          r = 3
          while r < n:
              b2 = gcd(b2,a[r])
              r += 2
  
          while l < n:
              b1 = gcd(b1,a[l])
              l += 2
  
  
  
          flag1 = 1
          l = 1
          while l < n:
                  if a[l] % b1 == 0:
                      flag1 = 0
                      break
                  l += 2
  
          flag2 = 1
          l = 0
          while l < n:
                  if a[l] % b2 == 0:
                      flag2 = 0
                      break
                  l += 2
          if not flag1 and not flag2:
                  print(0)
          else:
                  if flag1:
                      print(b1)
                  else:
                      print(b2)
  
  if __name__ == '__main__':
      for i in range(int(input())):
          solve()