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: //package Codeforces.Round760Div3;
  
  import java.io.*;
  import java.util.*;
  
  public class C {
      static long gcd(long a, long b){
          if(a%b==0)
              return b;
          else return gcd(b, a%b);
      }
      public static void main(String[] args) throws IOException {
          Soumit sc = new Soumit();
  
          int t = sc.nextInt();
          StringBuilder sb = new StringBuilder();
          while (t-->0){
              int n = sc.nextInt();
              long[] arr = sc.nextLongArray(n);
  
              long oddgcd = arr[0];
              for(int i=2;i<n;i+=2){
                  oddgcd = gcd(oddgcd, arr[i]);
              }
  
              long evengcd = arr[1];
              for(int i=3;i<n;i+=2){
                  evengcd = gcd(evengcd, arr[i]);
              }
  
              boolean oddflag = true;
              boolean evenflag = true;
              for(int i=0;i<n;i++){
                  if(i%2==0){
                      if(arr[i]%evengcd==0)
                          evenflag = false;
                  }
                  else{
                      if(arr[i]%oddgcd==0)
                          oddflag = false;
                  }
              }
  
              if(oddflag){
                  sb.append(oddgcd).append("\n");
              }
              else if(evenflag){
                  sb.append(evengcd).append("\n");
              }
              else{
                  sb.append("0\n");
              }
          }
  
          System.out.println(sb);
  
          sc.close();
      }
  
      static class Soumit {
          final private int BUFFER_SIZE = 1 << 18;
          final private DataInputStream din;
          final private byte[] buffer;
          private PrintWriter pw;
          private int bufferPointer, bytesRead;
          StringTokenizer st;
  
          public Soumit() {
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public Soumit(String file_name) throws IOException {
              din = new DataInputStream(new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public void streamOutput(String file) throws IOException {
              FileWriter fw = new FileWriter(file);
              BufferedWriter bw = new BufferedWriter(fw);
              pw = new PrintWriter(bw);
          }
  
          public void println(String a) {
              pw.println(a);
          }
  
          public void print(String a) {
              pw.print(a);
          }
  
          public String readLine() throws IOException {
              byte[] buf = new byte[3000064]; // line length
              int cnt = 0, c;
              while ((c = read()) != -1) {
                  if (c == '\n')
                      break;
                  buf[cnt++] = (byte) c;
              }
              return new String(buf, 0, cnt);
          }
  
          String next() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          public void sort(int[] arr) {
              ArrayList<Integer> arlist = new ArrayList<>();
              for (int i : arr)
                  arlist.add(i);
  
              Collections.sort(arlist);
              for (int i = 0; i < arr.length; i++)
                  arr[i] = arlist.get(i);
          }
  
          public void sort(long[] arr) {
              ArrayList<Long> arlist = new ArrayList<>();
              for (long i : arr)
                  arlist.add(i);
  
              Collections.sort(arlist);
              for (int i = 0; i < arr.length; i++)
                  arr[i] = arlist.get(i);
          }
  
          public int[] nextIntArray(int n) throws IOException {
              int[] arr = new int[n];
              for (int i = 0; i < n; i++) {
                  arr[i] = nextInt();
              }
  
              return arr;
          }
  
          public long[] nextLongArray(int n) throws IOException {
              long[] arr = new long[n];
              for (int i = 0; i < n; i++) {
                  arr[i] = nextLong();
              }
  
              return arr;
          }
  
          public double[] nextDoubleArray(int n) throws IOException {
              double[] arr = new double[n];
              for (int i = 0; i < n; i++) {
                  arr[i] = nextDouble();
              }
  
              return arr;
          }
  
          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;*/
              if (din != null) din.close();
              if (pw != null) pw.close();
          }
      }
  }
  