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: //package codeforce.div3.r760;
  
  import java.io.BufferedReader;
  import java.io.File;
  import java.io.FileNotFoundException;
  import java.io.FileReader;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.InputStreamReader;
  import java.io.PrintWriter;
  import java.util.Collections;
  import java.util.Scanner;
  import java.util.StringTokenizer;
  import java.util.stream.Collectors;
  import java.util.stream.IntStream;
  import java.util.ArrayList;
  import java.util.List;
  import java.util.HashMap;
  import java.util.Map;
  import java.util.Set;
  import java.util.HashSet;
  
  import static java.lang.System.out;
  import static java.util.stream.Collectors.joining;
  
  
  /**
   * @author pribic (Priyank Doshi)
   * @see <a href="https://codeforces.com/contest/1618/problem/C" target="_top">https://codeforces.com/contest/1618/problem/C</a>
   * @since 14/12/21 8:34 PM
   */
  public class C {
    static FastScanner sc = new FastScanner(System.in);
  
    public static void main(String[] args) {
      try (PrintWriter out = new PrintWriter(System.out)) {
        int T = sc.nextInt();
        for (int tt = 1; tt <= T; tt++) {
          int n = sc.nextInt();
          long[] arr = new long[n];
          for (int i = 0; i < n; i++) {
            arr[i] = sc.nextLong();
          }
          long d = 0;
          for (int st1 = 0, st2 = 1; st1 < 2; st1++, st2--) {
            List<Long> first = new ArrayList<>();
            List<Long> second = new ArrayList<>();
            for (int i = st1; i < n; i += 2)
              first.add(arr[i]);
            for (int i = st2; i < n; i += 2)
              second.add(arr[i]);
            long gcd1 = gcd(first);
            boolean anydivide = second.stream().anyMatch(num -> num % gcd1 == 0);
            if (!anydivide) {
              d = gcd1;
              break;
            }
          }
          System.out.println(d);
        }
      }
    }
  
    private static long gcd(List<Long> first) {
      long gcd = 0;
      for (long f : first)
        gcd = gcd(gcd, f);
      return gcd;
    }
  
    private static long gcd(long a, long b) {
      if (b == 0)
        return a;
      return gcd(b, a % b);
    }
  
    static class FastScanner {
      BufferedReader br;
      StringTokenizer st;
  
      public FastScanner(File f) {
        try {
          br = new BufferedReader(new FileReader(f));
        } catch (FileNotFoundException e) {
          e.printStackTrace();
        }
      }
  
      public FastScanner(InputStream f) {
        br = new BufferedReader(new InputStreamReader(f), 32768);
      }
  
      String next() {
        while (st == null || !st.hasMoreTokens()) {
          String s = null;
          try {
            s = br.readLine();
          } catch (IOException e) {
            e.printStackTrace();
          }
          if (s == null)
            return null;
          st = new StringTokenizer(s);
        }
        return st.nextToken();
      }
  
      boolean hasMoreTokens() {
        while (st == null || !st.hasMoreTokens()) {
          String s = null;
          try {
            s = br.readLine();
          } catch (IOException e) {
            e.printStackTrace();
          }
          if (s == null)
            return false;
          st = new StringTokenizer(s);
        }
        return true;
      }
  
      int nextInt() {
        return Integer.parseInt(next());
      }
  
      long nextLong() {
        return Long.parseLong(next());
      }
  
      double nextDouble() {
        return Double.parseDouble(next());
      }
    }
  }