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: 
  /*****  --->         :)    Vijender  Srivastava      (:       <---       *****/
  
  
  import java.util.*;
  import java.lang.*;
  import java.io.*;
  public class Main
  {
      static FastReader sc =new FastReader();
      static PrintWriter out=new PrintWriter(System.out);
      static int mod=10000007;
      /* start */
      public static void main(String [] args)throws Exception {
          int t = i();
          while(t-->0)
          {
              int n = i();
              long a[] = inputL(n);
              long g1=a[0],g2=a[1];
              for(int i=2;i<n;i++)
              {
                  if(i%2==0)
                      g1=gcd(g1,a[i]);
                  else g2=gcd(g2,a[i]);
              }
              if(g1==g2) pl('0');
              else
              {
                  int f1=0,f2=0;
                  for(int i=0;i<n;i++)
                  {
                      if(i%2==1 && a[i]%g1==0) f1=1;
                      if(i%2==0 && a[i]%g2==0) f2=1;
                  }
                  if(f1==0)
                      pl(g1);
                  else if(f2==0)pl(g2);
                  else pl("0");
              }
          }
          out.close();
      }
  
      /* end */
      static class FastReader
      {
          BufferedReader br;
          StringTokenizer st;
  
          public FastReader()
          {
              br = new BufferedReader(new
                      InputStreamReader(System.in));
          }
  
          String next()
          {
              while (st == null || !st.hasMoreElements())
              {
                  try
                  {
                      st = new StringTokenizer(br.readLine());
                  }
                  catch (IOException  e)
                  {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          int nextInt()
          {
              return Integer.parseInt(next());
          }
  
          long nextLong()
          {
              return Long.parseLong(next());
          }
  
          double nextDouble()
          {
              return Double.parseDouble(next());
          }
  
          String nextLine()
          {
              String str = "";
              try
              {
                  str = br.readLine();
              }
              catch (IOException e)
              {
                  e.printStackTrace();
              }
              return str;
          }
      }
  
      static void p(Object o)
      {
          out.print(o);
      }
      static void pl(Object o)
      {
          out.println(o);
      }
      static int i() {
          return sc.nextInt();
      }
  
      static String s() {
          return sc.next();
      }
  
      static long l() {
          return sc.nextLong();
      }
  
      static char[] inputC()
      {
          String s = sc.nextLine();
          return s.toCharArray();
      }
  
      static int[] input(int n) {
          int A[]=new int[n];
          for(int i=0;i<n;i++) {
              A[i]=sc.nextInt();
          }
          return A;
      }
  
      static long[] inputL(int n) {
          long A[]=new long[n];
          for(int i=0;i<n;i++) {
              A[i]=sc.nextLong();
          }
          return A;
      }
  
      static long[] putL(long a[]) {
          long A[]=new long[a.length];
          for(int i=0;i<a.length;i++) {
              A[i]=a[i];
          }
          return A;
      }
  
      static String[] inputS(int n) {
          String A[]=new String[n];
          for(int i=0;i<n;i++) {
              A[i]=sc.next();
          }
          return A;
      }
  
      static int gcd(int a, int b)
      {
          if (a == 0)
              return b;
          return gcd(b % a, a);
      }
  
      static long gcd(long a, long b)
      {
          if (a == 0)
              return b;
          return gcd(b % a, a);
      }
  
      static int lcm(int a, int b)
      {
          return (a / gcd(a, b)) * b;
      }
  
      static String reverse(String s) {
          StringBuffer p=new StringBuffer(s);
          p.reverse();
          return p.toString();
      }
  
      static int min(int a,int b) {
          return Math.min(a, b);
      }
      static int min(int a,int b,int c) {
          return Math.min(a, Math.min(b, c));
      }
      static int min(int a,int b,int c,int d) {
          return Math.min(a, Math.min(b, Math.min(c, d)));
      }
  
      static int max(int a,int b) {
          return Math.max(a, b);
      }
      static int max(int a,int b,int c) {
          return Math.max(a, Math.max(b, c));
      }
      static int max(int a,int b,int c,int d) {
          return Math.max(a, Math.max(b, Math.max(c, d)));
      }
      static long min(long a,long b) {
          return Math.min(a, b);
      }
      static long min(long a,long b,long c) {
          return Math.min(a, Math.min(b, c));
      }
      static long min(long a,long b,long c,long d) {
          return Math.min(a, Math.min(b, Math.min(c, d)));
      }
      static long max(long a,long b) {
          return Math.max(a, b);
      }
      static long max(long a,long b,long c) {
          return Math.max(a, Math.max(b, c));
      }
      static long max(long a,long b,long c,long d) {
          return Math.max(a, Math.max(b, Math.max(c, d)));
      }
  
      static long sum(int A[]) {
          long sum=0;
          for(int i : A) {
              sum+=i;
          }
          return sum;
      }
  
      static long sum(long A[]) {
          long sum=0;
          for(long i : A) {
              sum+=i;
          }
          return sum;
      }
  
      static void print(int A[]) {
          for(int i : A) {
              System.out.print(i+" ");
          }
          System.out.println();
      }
  
      static void print(long A[]) {
          for(long i : A) {
              System.out.print(i+" ");
          }
          System.out.println();
      }
  
      static long mod(long x) {
          return ((x%mod + mod)%mod);
      }
  
      static long power(long x, long y)
      {
  
          if(y==0)
              return 1;
          if(x==0)
              return 0;
          long res = 1;
          while (y > 0) {
  
              if (y % 2 == 1)
                  res = (res * x) ;
  
              y = y >> 1;
              x = (x * x);
          }
  
          return res;
      }
  
      static boolean prime(int n)
      {
          if (n <= 1)
              return false;
          if (n <= 3)
              return true;
          if (n % 2 == 0 || n % 3 == 0)
              return false;
          double sq=Math.sqrt(n);
  
          for (int i = 5; i <= sq; i = i + 6)
              if (n % i == 0 || n % (i + 2) == 0)
                  return false;
          return true;
      }
      static long[] sort(long a[]) {
          ArrayList<Long> arr = new ArrayList<>();
          for(long i : a) {
              arr.add(i);
          }
          Collections.sort(arr);
          for(int i = 0; i < arr.size(); i++) {
              a[i] = arr.get(i);
          }
          return a;
      }
  
      static int[] sort(int a[])
      {
          ArrayList<Integer> arr = new ArrayList<>();
          for(Integer i : a) {
              arr.add(i);
          }
          Collections.sort(arr);
          for(int i = 0; i < arr.size(); i++) {
              a[i] = arr.get(i);
          }
          return a;
      }
      static boolean prime(long n)
      {
          if (n <= 1)
              return false;
          if (n <= 3)
              return true;
          if (n % 2 == 0 || n % 3 == 0)
              return false;
          double sq=Math.sqrt(n);
  
          for (int i = 5; i <= sq; i = i + 6)
              if (n % i == 0 || n % (i + 2) == 0)
                  return false;
          return true;
      }
      //pair class
      private static class Pair implements Comparable<Pair> {
          int first, second;
          public Pair(int f, int s) {
              first = f;
              second = s;
          }
          @Override
          public int compareTo(Pair p) {
              if (first > p.first)
                  return 1;
              else if (first < p.first)
                  return -1;
              else {
                  if (second > p.second)
                      return 1;
                  else if (second < p.second)
                      return -1;
                  else
                      return 0;
              }
          }
  
      }
  }
  