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.*;
  import java.lang.*;
  import static java.lang.Math.*;
  
  // Sachin_2961 submission //
  public class Codeforces {
  
  
      static void solve() {
  
          int n = fs.nInt();
          long[]ar = new long[n];
          for(int i=0;i<n;i++)
              ar[i] = fs.nLong();
          long g1 = ar[0], g2 = ar[1];
          for(int i=2;i<n;i++){
              if(i%2 == 0)
                  g1 = gcd(g1,ar[i]);
              else
                  g2 = gcd(g2,ar[i]);
          }
          if(gcd(g1,g2) == 1){
              if(g1 != 1 && check(ar,g1,0)){
                  out.println(g1);
                  return;
              }
              if(g2 != 1 && check(ar,g2,1)){
                  out.println(g2);
                  return;
              }
              out.println("0");
          }else{
              if(g1 != 1 && check(ar,g1,0)){
                  out.println(g1);
                  return;
              }
              if(g2 != 1 && check(ar,g2,1)){
                  out.println(g2);
                  return;
              }
              long g = gcd(g1,g2);
              g1 /= g;
              g2 /= g;
              if(g1 != 1 && check(ar,g1,0)){
                  out.println(g1);
                  return;
              }
              if(g2 != 1 && check(ar,g2,1)){
                  out.println(g2);
                  return;
              }
              out.println("0");
          }
      }
      static boolean check(long[]ar,long g,int type){
  
          for(int i=0;i<ar.length;i++){
              if(i%2 == type && ar[i]%g != 0){
                  return false;
              }
              if(i%2 != type && ar[i]%g == 0){
                  return false;
              }
          }
          return true;
      }
      static long gcd(long a, long b)
      {
          if(a > b)
              a = (a+b)-(b=a);
          if(a == 0L)
              return b;
          return gcd(b%a, a);
      }
      static class PairI{
          int f,s,ind;
          PairI(int f,int s,int ind){
              this.f = f;
              this.s = s;
              this.ind = ind;
          }
      }
      static class Pair{
          int f,s;
          Pair(int f,int s) {
              this.f = f;
              this.s = s;
          }
      }
      static boolean multipleTestCase = true;
      static FastScanner fs;
      static PrintWriter out;
      public static void main(String[]args){
          try{
              out = new PrintWriter(System.out);
              fs = new FastScanner();
              int tc = multipleTestCase?fs.nInt():1;
              while (tc-->0)solve();
              out.flush();
              out.close();
          }catch (Exception e){
              e.printStackTrace();
          }
      }
      static class FastScanner {
          BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
          StringTokenizer st=new StringTokenizer("");
          String n() {
              while (!st.hasMoreTokens())
                  try {
                      st=new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              return st.nextToken();
          }
          String Line()
          {
              String str = "";
              try
              {
                  str = br.readLine();
              }catch (IOException e)
              {
                  e.printStackTrace();
              }
              return str;
          }
          int nInt() {return Integer.parseInt(n()); }
          long nLong() {return Long.parseLong(n());}
          double nDouble(){return Double.parseDouble(n());}
          int[]aI(int n){
              int[]ar = new int[n];
              for(int i=0;i<n;i++)
                  ar[i] = nInt();
              return ar;
          }
      }
      public static void sort(int[] arr){
          ArrayList<Integer> ls = new ArrayList<>();
          for(int x: arr)
              ls.add(x);
          Collections.sort(ls);
          for(int i=0; i < arr.length; i++)
              arr[i] = ls.get(i);
      }
      public static void sort(long[] arr){
          ArrayList<Long> ls = new ArrayList<>();
          for(long x: arr)
              ls.add(x);
          Collections.sort(ls);
          for(int i=0; i < arr.length; i++)
              arr[i] = ls.get(i);
      }
  }