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 java.io.*;
  import java.util.*;
  public class habd{
  
      public static void main(String[] args) throws IOException {
          Scanner sc = new Scanner(System.in);
          PrintWriter pw = new PrintWriter(System.out);
          int tc = sc.nextInt();
          while(tc-->0){
              int n = sc.nextInt();
              long[] arr = new long[n]; for(int i = 0; i<n; i++)arr[i] = sc.nextLong();
              long num1 = arr[0], num2 = arr[1];
              for(int i = 2; i<n; i+=2){
                  num1 = gcd(num1, arr[i]);
              }
              for(int i = 3; i<n; i+=2){
                  num2 = gcd(arr[i], num2);
              }
              boolean ok = true;
              for(int i = 1; i<n; i+=2){
                  if(arr[i] % num1 == 0){
                      ok = false;
                      break;
                  }
              }
              if(ok)pw.println(num1);
              else{
                  ok = true;
                  for(int i = 0; i<n; i+=2){
                      if(arr[i] % num2 == 0){
                          ok = false;
                          break;
                      }
                  }
                  if(ok)pw.println(num2);
                  else pw.println(0);
              }
              //System.out.println(num1 + " " + num2);
  
  
          }
          pw.flush();
  
      }
      public static long gcd(long a, long b)
      {
          if (b == 0)
              return a;
          return gcd(b, a % b);
      }
      public static class Pair{
          int x;
          int y;
          public Pair(int x, int y){
              this.x = x;
              this.y = y;
          }
      }
      public static boolean isSubsequence(char[] arr, String s){
          boolean ans = false;
          for(int i = 0, j = 0; i<arr.length; i++){
              if(arr[i] == s.charAt(j)){
                  j++;
              }
              if(j == s.length()){
                  ans = true;
                  break;
              }
          }
          return ans;
      }
  
      static class Scanner {
          StringTokenizer st;
          BufferedReader br;
  
          public Scanner(InputStream s) {
              br = new BufferedReader(new InputStreamReader(s));
          }
  
          public Scanner(FileReader r) {
              br = new BufferedReader(r);
          }
  
          public String next() throws IOException {
              while (st == null || !st.hasMoreTokens())
                  st = new StringTokenizer(br.readLine());
              return st.nextToken();
          }
  
          public int nextInt() throws IOException {
              return Integer.parseInt(next());
          }
  
          public long nextLong() throws IOException {
              return Long.parseLong(next());
          }
  
          public String nextLine() throws IOException {
              return br.readLine();
          }
  
          public double nextDouble() throws IOException {
              String x = next();
              StringBuilder sb = new StringBuilder("0");
              double res = 0, f = 1;
              boolean dec = false, neg = false;
              int start = 0;
              if (x.charAt(0) == '-') {
                  neg = true;
                  start++;
              }
              for (int i = start; i < x.length(); i++)
                  if (x.charAt(i) == '.') {
                      res = Long.parseLong(sb.toString());
                      sb = new StringBuilder("0");
                      dec = true;
                  } else {
                      sb.append(x.charAt(i));
                      if (dec)
                          f *= 10;
                  }
              res += Long.parseLong(sb.toString()) / f;
              return res * (neg ? -1 : 1);
          }
  
          public long[] nextlongArray(int n) throws IOException {
              long[] a = new long[n];
              for (int i = 0; i < n; i++)
                  a[i] = nextLong();
              return a;
          }
  
          public Long[] nextLongArray(int n) throws IOException {
              Long[] a = new Long[n];
              for (int i = 0; i < n; i++)
                  a[i] = nextLong();
              return a;
          }
  
          public int[] nextIntArray(int n) throws IOException {
              int[] a = new int[n];
              for (int i = 0; i < n; i++)
                  a[i] = nextInt();
              return a;
          }
  
          public Integer[] nextIntegerArray(int n) throws IOException {
              Integer[] a = new Integer[n];
              for (int i = 0; i < n; i++)
                  a[i] = nextInt();
              return a;
          }
  
          public boolean ready() throws IOException {
              return br.ready();
          }
  
      }
  
  
  }
  