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 com.company;
  
  import java.util.*;
  import java.lang.*;
  import java.io.*;
  
  public class Rough_Work {
      public static void main(String[] args) throws IOException {
          FastReader sc = new FastReader();
          PrintWriter out = new PrintWriter(System.out);
  
          int t = sc.nextInt();
          while (t-->0) {
              int n = sc.nextInt();
              long[] a = new long[(n+1)/2];
              long[] b = new long[n/2];
  
              for (int i = 0; i < n/2; i++) {
                  a[i] = sc.nextLong();
                  b[i] = sc.nextLong();
              }
              if ((n&1) == 1) a[a.length-1] = sc.nextLong();
  
              long g = a[0];
              for (int i = 1; i < a.length; i++) g = gcd(g,a[i]);
  
              boolean x = true;
              if (g != 1) {
                  for (long j : b) {
                      if (j%g == 0) {
                          x = false;
                          break;
                      }
                  }
                  if (x) {
                      out.println(g);
                      continue;
                  }
              }
  
              g = b[0];
              for (int i = 1; i < b.length; i++) g = gcd(g,b[i]);
  
              x = true;
              if (g != 1) {
                  for (long j : a) {
                      if (j%g == 0) {
                          x = false;
                          break;
                      }
                  }
                  if (x) {
                      out.println(g);
                      continue;
                  }
              }
              
              out.println(0);
          }
  
          sc.close();
          out.close();
      }
  
      static long gcd(long a, long b)
      {
          if (b == 0)
              return a;
          return gcd(b, a % b);
      }
  
      static class FastReader {
          final private int BUFFER_SIZE = 1 << 17;
          private DataInputStream din;
          private byte[] buffer;
          private int bufferPointer, bytesRead;
  
          public FastReader()
          {
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public FastReader(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[128]; // 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;
          }
  
          public int[] nextIntArray(int size) throws IOException {
              int[] arr = new int[size];
              for (int i = 0; i < size; i++) {
                  arr[i] = nextInt();
              }
              return arr;
          }
  
          public long[] nextLongArray(int size) throws IOException {
              long[] arr = new long[size];
              for (int i = 0; i < size; i++) {
                  arr[i] = nextLong();
              }
              return arr;
          }
  
          public Double[] nextDoubleArray(int size) throws IOException {
              Double[] arr = new Double[size];
              for (int i = 0; i < size; i++) {
                  arr[i] = nextDouble();
              }
              return arr;
          }
  
          public int[][] nextIntMatrix(int n, int m) throws IOException {
              int[][] arr = new int[n][m];
              for (int i = 0; i < n; i++) {
                  arr[i] = nextIntArray(m);
              }
              return arr;
          }
  
          public long[][] nextLongMatrix(int n, int m) throws IOException {
              long[][] arr = new long[n][m];
              for (int i = 0; i < n; i++) {
                  arr[i] = nextLongArray(m);
              }
              return arr;
          }
  
          public ArrayList<Integer> nextIntList(int size) throws IOException {
              ArrayList<Integer> arrayList = new ArrayList<>(size);
              for (int i = 0; i < size; i++) {
                  arrayList.add(nextInt());
              }
              return arrayList;
          }
  
          public ArrayList<Long> nextLongList(int size) throws IOException {
              ArrayList<Long> arrayList = new ArrayList<>(size);
              for (int i = 0; i < size; i++) {
                  arrayList.add(nextLong());
              }
              return arrayList;
          }
  
          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();
          }
      }
  }
  