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.*;
  import java.math.*;
  
  public class Main {
      // ArrayList<Integer> al = new ArrayList<>();
      // ArrayList<Pair<Integer, Integer>> al = new ArrayList<>();
      // Set<Integer> set = new TreeSet<>();
      // Pair<Integer, Integer> pair;
      // Map<Integer, Integer> map = new HashMap<>();
      // LinkedList<Integer> ll = new LinkedList<>();
      // for(Map.Entry<Integer,Integer> e:map.entrySet())pn(e.getKey()+"
      // "+e.getValue());
      // map.put(key,map.getOrDefault(key,0)+1);
  
      // *********************** Code Begins From Here*************************
  
      public static void solve() {
          int n = c.i(), fg1 = 0, fg2 = 0;
          long a[] = c.longArray(n), g1 = 0, g2 = 0;
          for (int i = 0; i < n; i += 2)
              g1 = gcd(g1, a[i]);
          for (int i = 1; i < n; i += 2)
              g2 = gcd(g2, a[i]);
          // pn(g1 + " " + g2);
          for (int i = 0; i < n; i += 2)
              if (a[i] % g2 == 0) {
                  fg1 = 1;
                  break;
              }
          for (int i = 1; i < n; i += 2)
              if (a[i] % g1 == 0) {
                  fg2 = 1;
                  break;
              }
          if (fg1 == 1 && fg2 == 1)
              pn(0);
          else if (fg1 == 1)
              pn(g1);
          else
              pn(g2);
      }
  
      public static void main(String[] args) throws FileNotFoundException {
          c = new FastScanner();
          pw = new PrintWriter(System.out);
          int tc = 1;
          tc = c.i();
          long start = System.currentTimeMillis();
          for (int t = 0; t < tc; t++) {
              // p("Case #" + (t + 1) + ": ");
              solve();
          }
          long end = System.currentTimeMillis();
          if (System.getProperty("os.name").equals("Mac OS X")) {
              pn("The Program takes " + (end - start) + "ms");
          }
          pw.close();
      }
  
      // math util
      private static int lower(int a[], int x) {
          int l = 0, r = a.length - 1, mid, ans = -1;
          while (l <= r) {
              mid = l + ((r - l) >> 1);
              if (a[mid] <= x) {
                  ans = max(ans, mid);
                  l = mid + 1;
              } else
                  r = mid - 1;
          }
          return ans;
      }
  
      private static int upper(int a[], int x) {
          int l = 0, r = a.length - 1, mid, ans = -1;
          while (l <= r) {
              mid = l + ((r - l) >> 1);
              if (a[mid] >= x) {
                  ans = mid;
                  r = mid - 1;
              } else
                  l = mid + 1;
              // pn(l + " " + mid + " " + r);
          }
          return ans;
      }
  
      private static int cei(double d) {
          return (int) Math.ceil(d);
      }
  
      private static long ceil(double d) {
          return (long) Math.ceil(d);
      }
  
      private static int gcd(int a, int b) {
          return b == 0 ? a : gcd(b, a % b);
      }
  
      private static long gcd(long a, long b) {
          return b == 0 ? a : gcd(b, a % b);
      }
  
      private static int abs(int a, int b) {
          return (int) Math.abs(a - b);
      }
  
      private static int abs(int a) {
          return (int) Math.abs(a);
      }
  
      private static long abs(long a) {
          return (long) Math.abs(a);
      }
  
      private static long abs(long a, long b) {
          return (long) Math.abs(a - b);
      }
  
      private static int max(int a, int b) {
          if (a > b) {
              return a;
          } else {
              return b;
          }
      }
  
      private static int min(int a, int b) {
          if (a > b) {
              return b;
          } else {
              return a;
          }
      }
  
      private static long max(long a, long b) {
          if (a > b) {
              return a;
          } else {
              return b;
          }
      }
  
      private static long min(long a, long b) {
          if (a > b) {
              return b;
          } else {
              return a;
          }
      }
  
      private static int pow(int base, int exp) {
          int result = 1;
          while (exp != 0) {
              if ((exp & 1) == 1)
                  result *= base;
              exp >>= 1;
              base *= base;
          }
          return result;
      }
  
      private static long powerMod(long base, long exp, long mod) {
          long result = 1;
          base %= mod;
          while (exp > 0) {
              if ((exp & 1) != 0)
                  result = (result * base) % mod;
              exp >>= 1;
              base = base * base % mod;
          }
          return result < 0 ? result + mod : result;
      }
  
      private static long addMod(long a, long b, long mod) {
          return (a % mod + b % mod) % mod;
      }
  
      private static long subMod(long a, long b, long mod) {
          return (a % mod - b % mod) % mod;
      }
  
      private static long mulMod(long a, long b, long mod) {
          return ((a % mod) * (b % mod)) % mod;
      }
  
      private static long pow(long base, long exp) {
          long result = 1;
          while (exp != 0) {
              if ((exp & 1) == 1)
                  result = result * base;
              exp >>= 1;
              base *= base;
          }
          return result;
      }
  
      // array util
      private static void sortList(ArrayList<Integer> al) {
          Collections.sort(al);
      }
  
      private static void sortListP(ArrayList<Pair<Integer, Integer>> al) {
          Collections.sort(al);
      }
  
      private static void sort(int[] a) {
          ArrayList<Integer> al = new ArrayList<>();
          for (int e : a)
              al.add(e);
          sortList(al);
          int i = 0;
          for (int e : al)
              a[i++] = e;
      }
  
      private static void sort(double[] a) {
          ArrayList<Double> al = new ArrayList<>();
          for (double e : a)
              al.add(e);
          Collections.sort(al);
          int i = 0;
          for (double e : al)
              a[i++] = e;
      }
  
      private static void sort(char[] a) {
          ArrayList<Character> al = new ArrayList<>();
          for (char e : a)
              al.add(e);
          Collections.sort(al);
          int i = 0;
          for (char e : al)
              a[i++] = e;
      }
  
      private static void sort(long[] a) {
          ArrayList<Long> al = new ArrayList<>();
          for (long e : a)
              al.add(e);
          Collections.sort(al);
          int i = 0;
          for (long e : al)
              a[i++] = e;
      }
  
      private static int[] copy(int[] a) {
          int[] ans = new int[a.length];
          for (int i = 0; i < a.length; ++i)
              ans[i] = a[i];
          return ans;
      }
  
      private static char[] copy(char[] a) {
          char[] ans = new char[a.length];
          for (int i = 0; i < a.length; ++i)
              ans[i] = a[i];
          return ans;
      }
  
      private static long[] copy(long[] a) {
          long[] ans = new long[a.length];
          for (int i = 0; i < a.length; ++i)
              ans[i] = a[i];
          return ans;
      }
      // output
  
      private static void pn(Object o) {
          pw.println(o);
      }
  
      private static void p(Object o) {
          pw.print(o);
      }
  
      private static void pry() {
          pn("Yes");
      }
  
      private static void pY() {
          pn("YES");
      }
  
      private static void prn() {
          pn("No");
      }
  
      private static void pN() {
          pn("NO");
      }
  
      private static void flush() {
          pw.flush();
      }
  
      private static void watch(int[] a) {
          for (int e : a)
              p(e + " ");
          pn("");
      }
  
      private static void watch(long[] a) {
          for (long e : a)
              p(e + " ");
          pn("");
      }
  
      private static void watch(char[] a) {
          for (char e : a)
              p(e);
          pn("");
      }
  
      private static void watchList(ArrayList<Integer> al) {
          for (int e : al)
              p(e + " ");
          pn("");
      }
  
      private static Set<Integer> putSet(int[] a) {
          Set<Integer> set = new TreeSet<>();
          for (int e : a)
              set.add(e);
          return set;
      }
  
      private static boolean[] sieve(int n) {
          boolean[] isPrime = new boolean[n + 1];
          Arrays.fill(isPrime, true);
          isPrime[0] = false;
          isPrime[1] = false;
          for (int i = 2; i * i <= n; i++) {
              for (int j = i * i; j <= n; j += i) {
                  isPrime[j] = false;
              }
          }
          return isPrime;
      }
  
      private static class Pair<U, V> implements Comparable<Pair<U, V>> {
          public final U first;
          public V second;
  
          public <U, V> Pair<U, V> makePair(U first, V second) {
              return new Pair<U, V>(first, second);
          }
  
          public Pair(U first, V second) {
              this.first = first;
              this.second = second;
          }
  
          @Override
          public boolean equals(Object o) {
              if (this == o) {
                  return true;
              }
              if (o == null || getClass() != o.getClass()) {
                  return false;
              }
  
              Pair pair = (Pair) o;
  
              return !(first != null ? !first.equals(pair.first) : pair.first != null)
                      && !(second != null ? !second.equals(pair.second) : pair.second != null);
          }
  
          @Override
          public int hashCode() {
              int result = first != null ? first.hashCode() : 0;
              result = 31 * result + (second != null ? second.hashCode() : 0);
              return result;
          }
  
          public Pair<V, U> swap() {
              return makePair(second, first);
          }
  
          @Override
          public String toString() {
              return "(" + first + "," + second + ")";
          }
  
          @SuppressWarnings({ "unchecked" })
          public int compareTo(Pair<U, V> o) {
              int value = ((Comparable<U>) first).compareTo(o.first);
              if (value != 0) {
                  return value;
              }
              return ((Comparable<V>) second).compareTo(o.second);
          }
      }
  
      private static class FastScanner {
          BufferedReader br;
          StringTokenizer st;
  
          public FastScanner() throws FileNotFoundException {
  
              if (System.getProperty("os.name").equals("Mac OS X")) {
                  // Input is a file
                  br = new BufferedReader(new FileReader("input.txt"));
  
                  // PrintWriter class prints formatted representations
                  // of objects to a text-output stream.
                  PrintStream pw = new PrintStream(new FileOutputStream("output.txt"));
                  System.setOut(pw);
              } else {
                  // Input is System.in
                  br = new BufferedReader(new InputStreamReader(System.in), 32768);
                  st = null;
              }
  
          }
  
          String next() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          int i() {
              return Integer.parseInt(next());
          }
  
          int[] intArray(int n) {
              int[] ret = new int[n];
              for (int i = 0; i < n; i++)
                  ret[i] = i();
              return ret;
          }
  
          ArrayList<Integer> intList(int n) {
              ArrayList<Integer> al = new ArrayList<>();
              for (int i = 0; i < n; i++)
                  al.add(i());
              return al;
          }
  
          long l() {
              return Long.parseLong(next());
          }
  
          long[] longArray(int n) {
              long[] ret = new long[n];
              for (int i = 0; i < n; i++)
                  ret[i] = l();
              return ret;
          }
  
          double[] doubleArray(int n) {
              double[] ret = new double[n];
              for (int i = 0; i < n; i++)
                  ret[i] = l();
              return ret;
          }
  
          ArrayList<Long> longList(int n) {
              ArrayList<Long> al = new ArrayList<>();
              for (int i = 0; i < n; i++)
                  al.add(l());
              return al;
          }
  
          double d() {
              return Double.parseDouble(next());
          }
  
          String nextLine() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
      }
  
      private static boolean arr[] = sieve(1000001);
      private static ArrayList<Long> primes = new ArrayList<>();
      private static int freq[] = new int[200005];
      private static int mod = (int) (1e9 + 7);
      private static final int IMAX = 2147483647;
      private static final int IMIN = -2147483648;
      private static final long LMAX = 9223372036854775807L;
      private static final long LMIN = -9223372036854775808L;
      private static FastScanner c;
      private static PrintWriter pw;
  }