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.*;
  import java.util.*;
  
  public class PaintTheArray {
      static PrintWriter out = new PrintWriter((System.out));
  
      static Reader sc = new Reader();
  
      public static void main(String args[]) throws Exception {
  
          int t = sc.nextInt();
          int i = 0;
          while (t-- > 0) {
              // out.print("Case #" + (i + 1) + ": ");
              solve();
              // i++;
          }
  
          out.close();
  
      }
  
      public static long gcd(long a, long b) {
          if (a == 0) {
              return b;
          } else {
              return gcd(b % a, a);
          }
      }
  
      public static long gcdArray(long value[]) {
  
          long nilai = 0;
  
          for (long i : value) {
              nilai = gcd(i, nilai);
              if (nilai == 1) {
                  return nilai;
              }
          }
  
          return nilai;
  
      }
  
      public static void solve() throws Exception {
  
          long hasilAkhir = 0;
          int nilai = sc.nextInt();
          long value[] = new long[(nilai + 1) / 2];
          long value1[] = new long[(nilai) / 2];
  
          ArrayList<Long> nilaihasil = new ArrayList<Long>();
  
          int indx = 0, indx1 = 0;
  
          for (int i = 1; i <= nilai; i++) {
              if (i % 2 == 0) {
                  value1[indx] = sc.nextLong();
                  nilaihasil.add(value1[indx]);
                  indx++;
              } else {
                  value[indx1] = sc.nextLong();
                  nilaihasil.add(value[indx1]);
                  indx1++;
              }
          }
  
          long hasil1 = gcdArray(value);
  
          String temp = "kosong";
  
          boolean cek = true;
  
          for (Long integer : nilaihasil) {
              if (integer % hasil1 == 0) {
  
                  if (temp.equals("blue") || temp.equals("kosong")) {
                      temp = "red";
                  } else {
                      cek = false;
                      break;
                  }
  
              } else {
                  if (temp.equals("red") || temp.equals("kosong")) {
                      temp = "blue";
                  } else {
                      cek = false;
                      break;
                  }
              }
          }
  
          if (cek) {
              hasilAkhir = hasil1;
              System.out.println(hasilAkhir);
          } else {
              long hasil2 = gcdArray(value1);
  
              String temp2 = "kosong";
  
              boolean cek2 = true;
  
              for (Long integer : nilaihasil) {
                  if (integer % hasil2 == 0) {
  
                      if (temp2.equals("blue") || temp2.equals("kosong")) {
                          temp2 = "red";
                      } else {
                          cek2 = false;
                          break;
                      }
  
                  } else {
                      if (temp2.equals("red") || temp2.equals("kosong")) {
                          temp2 = "blue";
                      } else {
                          cek2 = false;
                          break;
                      }
                  }
              }
  
              if (cek2) {
                  hasilAkhir = hasil2;
                  System.out.println(hasilAkhir);
              } else {
                  System.out.println(hasilAkhir);
              }
          }
  
      }
  
      static class Reader {
          BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
          StringTokenizer st = new StringTokenizer("");
  
          public String next() {
              while (!st.hasMoreTokens()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (Exception e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          public int nextInt() {
              return Integer.parseInt(next());
          }
  
          public long nextLong() {
              return Long.parseLong(next());
          }
  
          public double nextDouble() {
              return Double.parseDouble(next());
          }
  
          public String nextLine() {
              try {
                  return br.readLine();
              } catch (Exception e) {
                  e.printStackTrace();
              }
              return null;
          }
  
          public boolean hasNext() {
              String next = null;
              try {
                  next = br.readLine();
              } catch (Exception e) {
              }
              if (next == null) {
                  return false;
              }
              st = new StringTokenizer(next);
              return true;
          }
      }
  }