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.util.*;
  import java.io.*;
  
  public class Main {
  
      static long startTime = System.currentTimeMillis();
  
      // for global initializations and methods starts here
  
      // global initialisations and methods end here
  
      static void run() {
          boolean tc = true;
          AdityaFastIO r = new AdityaFastIO();
          //FastReader r = new FastReader();
  
          try (OutputStream out = new BufferedOutputStream(System.out)) {
  
              //long startTime = System.currentTimeMillis();
  
              int testcases = tc ? r.ni() : 1;
              int tcCounter = 1;
              // Hold Here Sparky------------------->>>
              // Solution Starts Here
  
              start:
              while (testcases-- > 0) {
  
                  int n = r.ni();
                  List<Long> al = new ArrayList<>();
                  for (int i = 0; i < n; i++) al.add(r.nl());
  
                  long gcd1 = 0;
                  long gcd2 = 0;
                  for (int i = 0; i < n; i++) {
                      if ((i & 1) == 0)
                          gcd1 = gcd(gcd1, al.get(i));
                      else gcd2 = gcd(gcd2, al.get(i));
                  }
                  boolean ff = false;
                  if (gcd1 != 1) {
                      int i = 1;
                      while (i < n) {
                          if (al.get(i) < gcd1 || al.get(i) % gcd1 != 0) {
                              i += 2;
                          } else {
                              ff = true;
                              break;
                          }
                      }
                      if (!ff) {
                          out.write((gcd1 + " ").getBytes());
  //                    out.write(("lol" + " ").getBytes());
                          out.write(("\n").getBytes());
                          continue start;
                      }
                  }
  
  
  
                  ff = false;
                  if (gcd2 != 1) {
                      int i = 0;
                      while (i < n) {
                          if (al.get(i) < gcd2 || al.get(i) % gcd2 != 0) {
                              i += 2;
                          } else {
                              ff = true;
                              break;
                          }
                      }
                      if (!ff) {
                          out.write((gcd2 + " ").getBytes());
                          out.write(("\n").getBytes());
                          continue start;
                      }
                  }
  
  
                  out.write((0 + " ").getBytes());
                  out.write(("\n").getBytes());
              }
              // Solution Ends Here
          } catch (IOException e) {
              e.printStackTrace();
          }
      }
  
      static class AdityaFastIO {
          final private int BUFFER_SIZE = 1 << 16;
          private final DataInputStream din;
          private final byte[] buffer;
          private int bufferPointer, bytesRead;
          public BufferedReader br;
          public StringTokenizer st;
  
          public AdityaFastIO() {
              br = new BufferedReader(new InputStreamReader(System.in));
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public AdityaFastIO(String file_name) throws IOException {
              din = new DataInputStream(new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public String word() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          public String line() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
  
          public String readLine() throws IOException {
              byte[] buf = new byte[100000001]; // line length
              int cnt = 0, c;
              while ((c = read()) != -1) {
                  if (c == '\n') break;
                  buf[cnt++] = (byte) c;
              }
              return new String(buf, 0, cnt);
          }
  
          public int ni() 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 nl() 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 nd() 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();
          }
      }
  
      public static void main(String[] args) throws Exception {
          run();
      }
  
      static long mod = 998244353;
  
      static long modInv(long base, long e) {
          long result = 1;
          base %= mod;
          while (e > 0) {
              if ((e & 1) > 0) result = result * base % mod;
              base = base * base % mod;
              e >>= 1;
          }
          return result;
      }
  
      static class FastReader {
          BufferedReader br;
          StringTokenizer st;
  
          public FastReader() {
              br = new BufferedReader(new InputStreamReader(System.in));
          }
  
          String word() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          String line() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
  
          int ni() {
              return Integer.parseInt(word());
          }
  
          long nl() {
              return Long.parseLong(word());
          }
  
          double nd() {
              return Double.parseDouble(word());
          }
      }
  
      static int MOD = (int) (1e9 + 7);
  
      static long powerLL(long x, long n) {
          long result = 1;
          while (n > 0) {
              if (n % 2 == 1) result = result * x % MOD;
              n = n / 2;
              x = x * x % MOD;
          }
          return result;
      }
  
      static long powerStrings(int i1, int i2) {
          String sa = String.valueOf(i1);
          String sb = String.valueOf(i2);
          long a = 0, b = 0;
          for (int i = 0; i < sa.length(); i++) a = (a * 10 + (sa.charAt(i) - '0')) % MOD;
          for (int i = 0; i < sb.length(); i++) b = (b * 10 + (sb.charAt(i) - '0')) % (MOD - 1);
          return powerLL(a, b);
      }
  
      static long gcd(long a, long b) {
          if (a == 0) return b;
          else return gcd(b % a, a);
      }
  
      static long lcm(long a, long b) {
          return (a * b) / gcd(a, b);
      }
  
      static long lower_bound(int[] arr, int x) {
          int l = -1, r = arr.length;
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (arr[m] >= x) r = m;
              else l = m;
          }
          return r;
      }
  
      static int upper_bound(int[] arr, int x) {
          int l = -1, r = arr.length;
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (arr[m] <= x) l = m;
              else r = m;
          }
          return l + 1;
      }
  
      static void addEdge(ArrayList<ArrayList<Integer>> graph, int edge1, int edge2) {
          graph.get(edge1).add(edge2);
          graph.get(edge2).add(edge1);
      }
  
      public static class Pair implements Comparable<Pair> {
          int first;
          int second;
  
          public Pair(int first, int second) {
              this.first = first;
              this.second = second;
          }
  
          public String toString() {
              return "(" + first + "," + second + ")";
          }
  
          public int compareTo(Pair o) {
              // TODO Auto-generated method stub
              if (this.first != o.first)
                  return (int) (this.first - o.first);
              else return (int) (this.second - o.second);
          }
      }
  
      public static class PairC<X, Y> implements Comparable<PairC> {
          X first;
          Y second;
  
          public PairC(X first, Y second) {
              this.first = first;
              this.second = second;
          }
  
          public String toString() {
              return "(" + first + "," + second + ")";
          }
  
          public int compareTo(PairC o) {
              // TODO Auto-generated method stub
              return o.compareTo((PairC) first);
          }
      }
  
      static boolean isCollectionsSorted(List<Long> list) {
          if (list.size() == 0 || list.size() == 1) return true;
          for (int i = 1; i < list.size(); i++) if (list.get(i) <= list.get(i - 1)) return false;
          return true;
      }
  
      static boolean isCollectionsSortedReverseOrder(List<Long> list) {
          if (list.size() == 0 || list.size() == 1) return true;
          for (int i = 1; i < list.size(); i++) if (list.get(i) >= list.get(i - 1)) return false;
          return true;
      }
  
  }