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.util.*;
  import java.io.*;
  import java.lang.*;
  
  // Problem - Multiples of 3 onn codeforces MNedium difficulty level 
  // or check on youtube channel CodeNCode
  
  public class Problem {
       static int Mod = 1000000007;
      static long dp[][];
      static int g[][];
      static int fact[];
  
  
      public static void main(String[] args) {
          MyScanner scan = new MyScanner();
          PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
           int t = scan.nextInt();
          // int t = 1;
          while (t-- > 0) {
            int n= scan.nextInt();
            long a[]= new long[n];
            for(int i=0;i<n;i++) a[i]= scan.nextLong();
            long p1=a[0];
            for(int i=1;i<n;i++){
                if(i%2==0) p1= gcd(p1,a[i]);
            }
            long p2=a[1];
            for(int i=2;i<n;i++){
                if(i%2!=0) p2= gcd(p2,a[i]);
            }
  
            boolean ans1= true;
            boolean ans2= true;
  
            for(int i=0;i<n;i++){
                if(i%2==0){
                    if(a[i]%p2==0) ans1= false;
                }else{
                    if(a[i]%p1==0) ans2= false;
                }
            }
  
            if(ans1==true) out.println(p2);
            else if(ans2) out.println(p1);
            else out.println(0);
          }
  
          out.close();
      }
  
   
  
  
  
      static ArrayList<Integer> digits(int n){
          ArrayList<Integer> list= new ArrayList<>();
          while(n>0){
              list.add(n%10);
              n=n/10;
          }
          Collections.reverse(list);
          return list;
      }
  
      static class Pair {
          int l;
          int r;
  
          Pair(int l, int r) {
              this.l = l;
              this.r = r;
          }
  
          @Override
          public int hashCode() {
              final int prime = 31;
              int result = 1;
              result = prime * result + l;
              result = prime * result + r;
              return result;
          }
  
          @Override
          public boolean equals(Object obj) {
              if (this == obj)
                  return true;
              if (obj == null)
                  return false;
              if (getClass() != obj.getClass())
                  return false;
              Pair other = (Pair) obj;
              if (l != other.l)
                  return false;
              if (r != other.r)
                  return false;
              return true;
          }
  
          @Override
          public String toString() {
              return "Pair [l=" + l + ", r=" + r + "]";
          }
  
      }
  
      public static void reverse(int a[]) {
          int n = a.length;
          for (int i = 0; i < n / 2; i++) {
              int temp = a[i];
              a[i] = a[n - i - 1];
              a[n - i - 1] = temp;
          }
      }
  
      public static void sort(int[] array) {
          ArrayList<Integer> copy = new ArrayList<>();
          for (Integer i : array)
              copy.add(i);
          Collections.sort(copy);
          for (int i = 0; i < array.length; i++)
              array[i] = copy.get(i);
      }
  
      public static void sort(long[] array) {
          ArrayList<Long> copy = new ArrayList<>();
          for (Long i : array)
              copy.add(i);
          Collections.sort(copy);
          for (int i = 0; i < array.length; i++)
              array[i] = copy.get(i);
      }
  
      public static long gcd(long a, long b) {
          if (b == 0)
              return a;
          return gcd(b, a % b); // gcd(a,b) = gcd(a-b,b) or gcd(a,b) = gcd(b,a%b) where a>b
      }
  
      public static int gcd(int a, int b) {
          if (b == 0)
              return a;
          return gcd(b, a % b); // gcd(a,b) = gcd(a-b,b) or gcd(a,b) = gcd(b,a%b) where a>b
      }
  
      public static long lcm(long a, long b) {
          return (a / gcd(a, b)) * b;
      }
  
      static long power(long x, long y) {
          long temp;
          if (y == 0) // a^b= (a^b/2)^2 if b is even
              return 1; // = (a*a^(b-1)) if b is odd
          temp = power(x, y / 2);
          if (y % 2 == 0)
              return temp * temp;
          else
              return x * temp * temp;
      }
  
      static long mod(long x) {
          return ((x % Mod + Mod) % Mod);
      }
  
      static long add(long a, long b) {
          return mod(mod(a) + mod(b));
      }
  
      static int mod(int x) {
          return ((x % Mod + Mod) % Mod);
      }
  
      static int add(int a, int b) {
          return mod(mod(a) + mod(b));
      }
  
      static int sub(int a, int b) {
          return mod(mod(a) - mod(b) + Mod);
      }
  
      static long mul(long a, long b) {
          return mod(mod(a) * mod(b));
      }
  
      static long pow(long x, long y, long p) {
          long res = 1; // Initialize result
          x = x % p; // Update x if it is more than or equal to p
  
          if (x == 0)
              return 0; // In case x is divisible by p;
  
          while (y > 0) {
              // If y is odd, multiply x with result
              if ((y & 1) != 0)
                  res = (res * x) % p;
  
              // y must be even now
              y = y >> 1; // y = y/2
              x = (x * x) % p;
          }
          return res;
      }
  
      static long modInverse(long a, long m) {
          // int g = gcd(a, m);
          // if (g != 1)
          // System.out.println("Inverse doesn't exist");
          // else {
          // // If a and m are relatively prime, then modulo
          // // inverse is a^(m-2) mode m
          // return power(a, m - 2, m);
          // }
          return pow(a, m - 2, m);
      }
  
  }
  
  class MyScanner {
      BufferedReader br;
      StringTokenizer st;
  
      public MyScanner() {
          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;
      }
  
  }
  