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.BufferedReader;
  import java.lang.*;
  import java.io.FileReader;
  import java.io.IOException;
  import java.math.BigInteger;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.math.BigDecimal;
  import java.math.BigInteger;
  import java.math.MathContext;
  import java.net.SocketOption;
  import java.nio.charset.StandardCharsets;
  import java.util.*;
  import java.util.LinkedList;
  
  public class Liked {
      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 sort(long[] arr) {
          ArrayList<Long> a = new ArrayList<>();
          for (long i : arr) {
              a.add(i);
          }
          Collections.sort(a);
          for (int i = 0; i < a.size(); i++) {
              arr[i] = a.get(i);
          }
      }
      static long gcd(long a, long b)
      {
          if (b == 0)
              return a;
          return gcd(b, a % b);
      }
      static String get(long h, long v) {
          StringBuilder str = new StringBuilder();
          long extra = (h-1)-v;
          long i = 0;
          str.append("0");
          while(h > 0) {
              if(i % 2 == 0) {
                  str.append("1");
                  h--;
              }else {
                  str.append("0");
                  v--;
                  if(extra > 0) {
                      str.append("0");
                      extra--;
                  }
              }
              i++;
          }
  
  
          str.append("0");
          if(v > 0) {
              str.append("1");
          }
           return str.toString();
      }
  
      static long lcm(long a, long b)
      {
          return (a / gcd(a, b)) * b;
      }
      static String comp(String ans) {
          StringBuilder ret = new StringBuilder();
          for(char ch: ans.toCharArray()) {
              if(ch == '1') {
                  ret.append("0");
              }else {
                  ret.append("1");
              }
          }
          return ret.toString();
      }
  
      public static long findGCD(long a, long b){
          //base condition
          if(b == 0)
              return a;
  
          return findGCD(b, a%b);
      }
      public static void main(String[] args) throws Exception {
          FastReader sc = new FastReader();
          int t = sc.nextInt();
         // long mod = 998244353;
         test :  while (t-- > 0) {
           int n = sc.nextInt();
           long[] arr = new long[n];
           for(int i = 0; i < n; i++) {
               arr[i] = sc.nextLong();
           }
           long lcm1 = arr[0];
           long gcd1 = arr[0];
             for(int i=2; i<n; i=i+2){
                 gcd1 = findGCD(arr[i], gcd1);
  
             }
  
             long lcm2 = arr[1];
             long gcd2 = arr[1];
             for(int i=3; i<n; i=i+2){
                 gcd2 = findGCD(arr[i], gcd2);
  
             }
  //        System.out.println(lcm1+" "+gcd1);
  //       System.out.println(lcm2+" "+gcd2);
             long ans = 0;
             int ind = 1;
  
             if(gcd1 != 1) {
                 ans = gcd1;
                 for (int i = 1; i < n; i += 2) {
                     if (arr[i] % gcd1 == 0) {
                         ans = 0;
                         break;
                     }
                 }
             }
             if(gcd2 != 1 && ans == 0) {
                 ans = gcd2;
                 for (int i = 0; i < n; i += 2) {
                     if ( arr[i] % gcd2 == 0) {
                         ans = 0;
                         break;
                     }
                 }
             }
             System.out.println(ans);
  
         }
      }
  }
  
  
  