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.io.IOException;
  import java.io.InputStreamReader;
  import java.io.OutputStreamWriter;
  import java.io.PrintWriter;
  import java.util.StringTokenizer;
  
  public class C_Paint_the_Array {
     
      static Scanner in=new Scanner();
      
      static PrintWriter out=new PrintWriter( new OutputStreamWriter(System.out) );
      
      static int testCases,n;
      
      static long a[];
      
      static void solve(){
          
          long x=a[0],y=a[1];
          
          for(int i=0;i<n;i+=2 ){
              
              x=gcd(x,a[i]);
              
          }
          
          for(int i=1;i<n;i+=2){
              
              y=gcd(y,a[i]);
              
          }
          
          boolean yes=true;    
              
            for(int i=0;i<n;i+=2){
                
                if(a[i]%y==0 ){
                    
                    yes=false;
                    
                    break;
                    
                }
                
            }
          
          if(yes){
              
              out.println(y);
              out.flush();
              
          }else{
              
              yes=true;
              
            for(int i=1;i<n;i+=2){
                
                if(a[i]%x==0){
                    
                    yes=false;
                    
                    break;
                    
                }
                
            }
            
            if(yes){
                
                out.println(x);
                out.flush();
                
            }else{
                
                out.println(0);
                out.flush();
                
            }
            
          }
          
      }
      
      public static void main(String[] amit) throws IOException {
          
          testCases=in.nextInt();
          
          for(int t=0;t<testCases;t++){
              
              n=in.nextInt();
              
              a=new long[n];
              
              for(int i=0;i<n;i++){
                  
                  a[i]=in.nextLong();
                  
              }
              
              solve();
              
          }
          
      }
       
      static String sum(String a,String b){
          
          StringBuilder ans=new StringBuilder();
          
          int n1=a.length(),m=b.length();
          
          if(n1>m ){
              
              String t=a;
              a=b;
              b=t;
              
          }
          
          n1=a.length();
          m=b.length();
          
          StringBuilder str1=new StringBuilder(a).reverse();
          StringBuilder str2=new StringBuilder(b).reverse();
          
          char first[]=str1.toString().toCharArray();
          char second[]=str2.toString().toCharArray();
          
          int carry=0;
          
          for(int i=0;i<n1;i++){
              
              int sum=(first[i]-'0')+(second[i]-'0')+carry;
              
              ans.append(sum%10 );
              
              carry=sum/10;
              
          }
          
          for(int i=n1;i<m;i++){
              
             int sum=(second[i]-'0')+carry;
             
             ans.append(sum%10 );
              
             sum/=10;
             
          }
          
          if(carry>0){
              
              ans.append(carry);
              
          }
          
          ans.reverse();
          
          return ans.toString();
          
      }
      
      static String mul(String num1, String num2)
  {
      int len1 = num1.length();
      int len2 = num2.length();
      if (len1 == 0 || len2 == 0)
          return "0";
   
      
      int result[] = new int[len1 + len2];
   
      
      int i_n1 = 0;
      int i_n2 = 0;
       
    
      for (int i = len1 - 1; i >= 0; i--)
      {
          int carry = 0;
          int n1 = num1.charAt(i) - '0';
   
          
          i_n2 = 0;
           
                   
          for (int j = len2 - 1; j >= 0; j--)
          {
              
              int n2 = num2.charAt(j) - '0';
   
             
              int sum = n1 * n2 + result[i_n1 + i_n2] + carry;
   
              
              carry = sum / 10;
   
           
              result[i_n1 + i_n2] = sum % 10;
   
              i_n2++;
          }
   
         
          if (carry > 0)
              result[i_n1 + i_n2] += carry;
   
         
          i_n1++;
      }
   
     
      int i = result.length - 1;
      while (i >= 0 && result[i] == 0)
      i--;
   
     
      if (i == -1)
      return "0";
   
      
      String s = "";
       
      while (i >= 0)
          s += (result[i--]);
   
      return s;
  }
      
      static int multiply(int x, int res[], int res_size) {
   
      
      int carry = 0;
   
      
      for (int i = 0; i < res_size; i++) {
      int prod = res[i] * x + carry;
   
      
      res[i] = prod % 10;
   
     
      carry = prod / 10;
      }
   
     
      while (carry > 0) {
      res[res_size] = carry % 10;
      carry = carry / 10;
      res_size++;
      }
      return res_size;
  }
   
  
  static long power(int x, int n) {
       
      int MAX = 100000;
      
      
      if(n == 0 ){
     
          
      return 1;
  }
      int res[] = new int[MAX];
      int res_size = 0;
      int temp = x;
   
     
      while (temp != 0) {
      res[res_size++] = temp % 10;
      temp = temp / 10;
      }
   
      
      for (int i = 2; i <= n; i++)
      res_size = multiply(x, res, res_size);
   
     StringBuilder sb=new StringBuilder();
      
      for (int i = res_size - 1; i >= 0; i--)
      sb.append(res[i]);
      
      return Long.parseLong(sb.toString());
      
  }
                    
     static class Node<T>{
      
      T data;
      
      Node<T> next;
  
      public Node() {
      
          this.next=null;
      
      }
  
      public Node(T data) {
          
          this.data = data;
      
          this.next=null;
          
      }
  
      public T getData() {
          return data;
      }
  
      public void setData(T data) {
          this.data = data;
      }
  
      public Node<T> getNext() {
          return next;
      }
  
      public void setNext(Node<T> next) {
          this.next = next;
      }
      
      @Override
      public String toString(){
          
          return this.getData().toString()+"  ";
          
      }
      
  }
  
     static class ArrayList<T>{
             
      Node<T> head,tail;
      
      int len;
  
      public ArrayList() {
      
      this.head=null;    
          
      this.tail=null;
      
      this.len=0;
      
      }
      
      int size(){
          
          return len;
          
      }
      
      boolean isEmpty(){
          
          return len==0;
          
      }
      
      int indexOf(T data){
          
          if( isEmpty() ){
              
              throw new ArrayIndexOutOfBoundsException();
              
          }
          
          Node<T> temp=head;
          
          int index=0,i=0;
          
          while(temp!=null){
              
              if( temp.getData()==data ){
                  
                  index=i;
                  
              }
              
              i++;
              
              temp=temp.getNext();
              
          }
          
          return index;
          
      }
      
      void add(T data){
          
          Node<T> newNode=new Node<>(data);
          
          if( isEmpty() ){
              
              head=newNode;
              
              tail=newNode;
              
              len++;
              
          }else{
          
          tail.setNext(newNode);
              
          tail=newNode;
          
          len++;
          
          }
          
      }
      
      void see(){
          
          if( isEmpty() ){
              
              throw new ArrayIndexOutOfBoundsException();
              
          }
          
          Node<T> temp=head;
          
          while( temp!=null ){
              
              out.print(temp.getData().toString()+" ");
              out.flush();
              
              temp=temp.getNext();
              
          }
          
          out.println();
          out.flush();
          
      }
              
      void inserFirst(T data){
          
          Node<T> newNode=new Node<>(data);
          
          Node<T> temp=head;
          
          if( isEmpty() ){
              
              head=newNode;
              tail=newNode;
              
              len++;
              
          }else{
              
              newNode.setNext(temp);
              
              head=newNode;
              
              len++;
              
          }
          
      }
      
      T get(int index){
          
          if( isEmpty() || index>=len ){
              
              throw new ArrayIndexOutOfBoundsException();
              
          }
          
          Node<T> temp=head;
          
          if(index==0){
              
              return temp.getData();
              
          }
          
          int i=0;
          
          T data=null;
          
          while(temp!=null){
              
              if( i==index ){
                  
                  data=temp.getData();
                  
              }
              
              i++;
              
              temp=temp.getNext();
              
          }
          
          return data;
          
      }
      
      void addAt(T data,int index){
          
          if( index>=len ){
              
              throw new ArrayIndexOutOfBoundsException();
              
          }
          
          Node<T> newNode=new Node<>(data);
          
          int i=0;
          
          Node<T> temp=head;
          
          while( temp.next!=null ){
              
              if(i==index){
                  
                  newNode.setNext(temp.next);
                  
                  temp.next=newNode;
                  
              }
              
              i++;
              
              temp=temp.getNext();
              
          }
          
      //    temp.setNext(temp);
          
          len++;
          
      }
      
      T popFront(){
          
          if( isEmpty() ){
              
              throw new ArrayIndexOutOfBoundsException();
              
          }
          
          T data=head.getData();
          
          if( head==tail ){
              
              head=null;
              tail=null;
              
          }else{
              
              head=head.getNext();
              
          }
          
          len--;
          
          return data;
          
      }
      
      void removeAt(int index){
          
          if( index>=len ){
              
              throw new ArrayIndexOutOfBoundsException();
              
          }
          
          if(index==0){
              
              this.popFront();
              
              return;
              
          }
          
          Node<T> temp=head;
          
          int i=0;
          
          Node<T> n=new Node<>();
          
          while(temp!=null){
              
              if(i==index){
                  
                  n.next=temp.next;
                  
                  temp.next=n;
                  
                  break;
                  
              }
              
              i++;
              
              n=temp;
              
              temp=temp.getNext();
              
          }
          
          tail=n;
          
          --len;
          
      }
      
      void clearAll(){
          
          this.head=null;
          this.tail=null;
          
      }
         
     }
     
      static long gcd(long a, long b)
      {
        if (b == 0)
          return a;
        return gcd(b, a % b);
      }
  	
     static void merge(long a[],int left,int right,int mid){
          
          int n1=mid-left+1,n2=right-mid;
          
          long L[]=new long[n1];
          
          long R[]=new long[n2];
          
          for(int i=0;i<n1;i++){
              
              L[i]=a[left+i];
              
          }
          
          for(int i=0;i<n2;i++){
              
              R[i]=a[mid+1+i];
              
          }
          
          int i=0,j=0,k1=left;
          
          while(i<n1 && j<n2){
              
              if( L[i]<=R[j] ){
                  
                  a[k1]=L[i];
                  
                  i++;
                  
              }else{
                  
                  a[k1]=R[j];
                  
                  j++;
                  
              }
              
              k1++;
              
          }
          
          while(i<n1){
              
              a[k1]=L[i];
              
              i++;
              
              k1++;
              
          }
          
          while(j<n2){
              
              a[k1]=R[j];
              
              j++;
              k1++;
              
          }
          
      }
      
      static void sort(long a[],int left,int right){
          
          if(left>=right){
              
              return;
              
          }
          
          int mid=(left+right)/2;
          
          sort(a,left,mid);
          
          sort(a,mid+1,right);
          
          merge(a,left,right,mid);
          
      }
  	
      static class Node1<T>{
          
          T data;
          
          Node1 next;
  
          public Node1(T data) {
              this.data = data;
          
              this.next=null;
              
          }
  
          public T getData() {
              return data;
          }
  
          public void setData(T data) {
              this.data = data;
          }
  
          public Node1 getNext() {
              return next;
          }
  
          public void setNext(Node1 next) {
              this.next = next;
          }
          
      }
      
      static class Stack<T>{
          
          int len;
          
          Node1<T> node;
  
          public Stack() {
          
              len=0;
              
              node=null;
              
          }
          
          boolean isEmpty(){
              
              return len==0;
              
          }
          
          int size(){
              
              return len;
              
          }
          
          void push(T data){
              
              Node1<T> temp=new Node1<>(data);
              
              temp.setNext(this.node);
              
              node=temp;
              
              len++;
              
          }
          
          T top(){
              
              if( isEmpty() ){
                  
                  throw new ArrayIndexOutOfBoundsException();
                  
              }
              
              return this.node.getData();
              
          }
          
          T pop(){
              
              if( isEmpty() ){
                  
                  throw new ArrayIndexOutOfBoundsException();
                  
              }
              
              T data=this.node.getData();
              
              this.node=this.node.getNext();
              
              len--;
              
              return data;
              
          }
          
      }
      
  	  static class Scanner{
          
          BufferedReader in;
          StringTokenizer st;
  
          public Scanner() {
          
              in=new BufferedReader( new InputStreamReader(System.in) );
              
          }
          
          String next() throws IOException{
              
              while(st==null || !st.hasMoreElements()){
                  
                  st=new StringTokenizer(in.readLine());
                  
              }
              
              return st.nextToken();
              
          }
          
          int nextInt() throws IOException{
              
              return Integer.parseInt(next());
              
          }
          
          long nextLong() throws IOException{
              
              return Long.parseLong(next());
              
          }
          
          String nextLine() throws IOException{
              
              return in.readLine();
              
          }
          
          char nextChar() throws IOException{
              
              return next().charAt(0);
              
          }
          
          double nextDouble() throws IOException{
              
              return Double.parseDouble(next());
              
          }
          
          float nextFloat() throws IOException{
              
              return Float.parseFloat(next());
              
          }
          
          boolean nextBoolean() throws IOException{
              
              return Boolean.parseBoolean(next());
              
          }
          
          void close() throws IOException{
              
              in.close();
              
          }
          
      }
  	
  }
  /*
  
  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
  
  
  */
  
  /*
  
  1
  5
  1 2 3 4 5
  
  */
  
  /*
  
  1
  3
  100 10 200
  
  */