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: // हर हर महादेव
  import java.util.*;
  import java.lang.*;
  import java.io.*;
  import java.math.BigInteger;
  import java.text.DecimalFormat;
  
  public final class Solution {
  
      static int inf = Integer.MAX_VALUE;
      static long mod = 1000000000 + 7;
  
   static void ne(Scanner sc, BufferedWriter op) throws Exception {
    int n=sc.nextInt();
    long[] arr= new long[n];
    for(int i=0;i<n;i++){
        arr[i]=sc.nextLong();
    }
  
    long gc1=0;
    long gc2=0;
    for(int i=0;i<n;i+=2){
        gc1=gcd(arr[i],gc1);
    }
    for(int i=1;i<n;i+=2){
       gc2=gcd(arr[i],gc2);
    }
    long min=Math.min(gc1,gc2);
    
  //   if(gc1==1 || gc2==1){
  //       if(gc1==1){
  //         if(check(arr,gc2,0)){
  //            op.write(gc2+"\n");
  //            return;
  //         }else{
  //             op.write("0\n");
  //             return;
  //         }
  //       }else{
  //         if(check(arr,gc1,1)){
  //             op.write(gc1+"\n");
  //         }else{
  //             op.write("0\n");
  //         }
  //         return;
  
  //       }
  //   }
  
   
    if(gc2!=gc1){
        
      //   gc1=Math.max(gc1,gc2);
        boolean f=true;
       
        for(int i=1;i<n;i+=2){
            if(arr[i]%gc1==0){
                f=false;
                break;
            }
        }
        boolean f2=true;
        for(int i=0;i<n;i+=2){
            if(arr[i]%gc2==0){
                f2=false;
            }
        }
      
        if(f || f2){
          //   print(f+" "+f2);
            if(f){
              op.write(gc1+"\n");
            }else{
              op.write(gc2+"\n");
            }
            
            return;
        }
  
        op.write("0\n"); 
       
        return;
    }
  
    op.write("0\n");
    
   }
  
  
  
   static boolean check(long[] arr, long gc, int st){
       boolean f=true;
       int n=arr.length;
       for(int i=st;i<n;i+=2){
           if(arr[i]%gc==0){
               f=false;
               break;
           }
       }
       return f;
   }
    public static void subset(ArrayList<Long> list, int id, long[] arr, long sum){
        if(id==3){
            list.add(sum);
            return;
        }
        subset(list,id+1,arr,sum+arr[id]);
        subset(list,id+1,arr,sum);
    }
  
    static long gcd(long a, long b){
          if(a==0L) return b;
          return gcd(b%a,a);
    }
  
  
      public static void main(String[] args) throws Exception {
          BufferedWriter op = new BufferedWriter(new OutputStreamWriter(System.out));
          // Reader sc = new Reader();
          Scanner sc= new Scanner(System.in);
          int t = sc.nextInt();
          while (t-->0){ ne(sc, op); }
          
          // ne(sc,op);
             
                     
          op.flush();
      }
  
      static void print(Object o) {
          System.out.println(String.valueOf(o));
      }
      static int[] toIntArr(String s){
          int[] val= new int[s.length()];
          for(int i=0;i<s.length();i++){
              val[i]=s.charAt(i)-'a';
          }
          return val;
      }
  
      static void  sort(int[] arr){
          ArrayList<Integer> list= new ArrayList<>();
          for(int i=0;i<arr.length;i++){
              list.add(arr[i]);
  
          }
          Collections.sort(list);
          for(int i=0;i<arr.length;i++){
              arr[i]=list.get(i);
          }
      }
         static void  sort(long[] arr){
          ArrayList<Long> list= new ArrayList<>();
          for(int i=0;i<arr.length;i++){
              list.add(arr[i]);
  
          }
          Collections.sort(list);
          for(int i=0;i<arr.length;i++){
              arr[i]=list.get(i);
          }
      }
  
  }
  
  
  
  // return -1 to put no ahed in array
  class pair {
      int  xx;
      int yy;
      pair(int xx, int yy ) {
          this.xx = xx;
          this.yy = yy;
      }
  }
  
  
  class sortY implements Comparator<pair> {
      public int compare(pair p1, pair p2) {
          if (p1.yy > p2.yy) {
              return 1;
          } else if (p1.yy == p2.yy) {
              if (p1.xx > p2.xx) {
                  return 1;
              } else if (p1.xx < p2.xx) {
                  return -1;
              }
              return 0;
  
          }
          return -1;
      }
  }
  
  class sortX implements Comparator<pair> {
      public int compare(pair p1, pair p2) {
          if (p1.xx > p2.xx) {
              return 1;
          } else if (p1.xx == p2.xx) {
              if (p1.yy > p2.yy) {
                  return 1;
              } else if (p1.yy < p2.yy) {
                  return -1;
              }
              return 0;
  
          }
          return -1;
      }
  }
  
  class debug {
  
      static void print1d(long[] arr) {
          System.out.println();
          for (int i = 0; i < arr.length; i++) {
              System.out.print(arr[i] + " ");
          }
  
      }
  
      static void print1d(int[] arr) {
          System.out.println();
          for (int i = 0; i < arr.length; i++) {
              System.out.println(i+" = "+arr[i]);
          }
  
      }
  
      static void print1d(boolean[] arr) {
          System.out.println();
          for (int i = 0; i < arr.length; i++) {
              System.out.println(i + "= " + arr[i]);
          }
  
      }
  
      static void print2d(int[][] arr) {
          System.out.println();
          int n = arr.length;
          int n2 = arr[0].length;
          for (int i = 0; i < n; i++) {
              for (int j = 0; j < n2; j++) {
                  System.out.print(arr[i][j] + " ");
              }
              System.out.println();
          }
  
      }
  
      static void print2d(long[][] arr) {
          System.out.println();
          int n = arr.length;
          int n2 = arr[0].length;
          for (int i = 0; i < n; i++) {
              for (int j = 0; j < n2; j++) {
                  System.out.print(arr[i][j] + " ");
              }
              System.out.println();
          }
  
      }
       static void printPair(ArrayList<pair> list) {
          if(list.size()==0){
              System.out.println("empty list");
              return;
          }
         System.out.println();
         for(int i=0;i<list.size();i++){
            System.out.println(list.get(i).xx+"-"+list.get(i).yy);
         }
      }
  
  }
  
  class Reader {
      final private int BUFFER_SIZE = 1 << 16;
      private DataInputStream din;
      private byte[] buffer;
      private int bufferPointer, bytesRead;
  
      public Reader() {
          din = new DataInputStream(System.in);
          buffer = new byte[BUFFER_SIZE];
          bufferPointer = bytesRead = 0;
      }
  
      public Reader(String file_name) throws IOException {
          din = new DataInputStream(new FileInputStream(file_name));
          buffer = new byte[BUFFER_SIZE];
          bufferPointer = bytesRead = 0;
      }
  
      public String readLine() throws IOException {
          byte[] buf = new byte[64]; // line length
          int cnt = 0, c;
          while ((c = read()) != -1) {
              if (c == '\n') {
                  if (cnt != 0) {
                      break;
                  } else {
                      continue;
                  }
              }
              buf[cnt++] = (byte) c;
          }
          return new String(buf, 0, cnt);
      }
  
      public int nextInt() throws IOException {
          int ret = 0;
          byte c = read();
          while (c <= ' ') {
              c = read();
          }
          boolean neg = (c == '-');
          if (neg)
              c = read();
          do {
              ret = ret * 10 + c - '0';
          } while ((c = read()) >= '0' && c <= '9');
  
          if (neg)
              return -ret;
          return ret;
      }
  
      public long nextLong() throws IOException {
          long ret = 0;
          byte c = read();
          while (c <= ' ')
              c = read();
          boolean neg = (c == '-');
          if (neg)
              c = read();
          do {
              ret = ret * 10 + c - '0';
          } while ((c = read()) >= '0' && c <= '9');
          if (neg)
              return -ret;
          return ret;
      }
  
      public double nextDouble() throws IOException {
          double ret = 0, div = 1;
          byte c = read();
          while (c <= ' ')
              c = read();
          boolean neg = (c == '-');
          if (neg)
              c = read();
  
          do {
              ret = ret * 10 + c - '0';
          } while ((c = read()) >= '0' && c <= '9');
  
          if (c == '.') {
              while ((c = read()) >= '0' && c <= '9') {
                  ret += (c - '0') / (div *= 10);
              }
          }
  
          if (neg)
              return -ret;
          return ret;
      }
  
      private void fillBuffer() throws IOException {
          bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
          if (bytesRead == -1)
              buffer[0] = -1;
      }
  
      private byte read() throws IOException {
          if (bufferPointer == bytesRead)
              fillBuffer();
          return buffer[bufferPointer++];
      }
  
      public void close() throws IOException {
          if (din == null)
              return;
          din.close();
      }
  }
   
   