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 final class Main {
  
      static PrintWriter out = new PrintWriter(System.out);
      static FastReader in = new FastReader();
      static Pair[] moves = new Pair[]{new Pair(-1, 0), new Pair(0, 1), new Pair(1, 0), new Pair(0, -1)};
      static int mod = (int) (1e9 + 7);
      static int mod2 = 998244353;
  
      public static void main(String[] args) {
          int tt = i();
          while (tt-- > 0) {
              solve();
          }
          out.flush();
      }
  
      public static void solve() {
          int n = i();
          long[] a = inputLong(n);
  
          long gcd = a[0];
          for (int i = 0; i < n; i += 2) {
              gcd = GCD(gcd, a[i]);
          }
          long gcd2 = a[1];
          for (int i = 1; i < n; i += 2) {
              gcd2 = GCD(gcd2, a[i]);
          }
  
          boolean check = true;
          for (int i = 1; i < n; i += 2) {
              if (a[i] % gcd == 0) {
                  check = false;
                  break;
              }
          }
  
          boolean check2 = true;
          for (int i = 0; i < n; i += 2) {
              if (a[i] % gcd2 == 0) {
                  check2 = false;
                  break;
              }
          }
  
          if (check) {
              out.println(gcd);
              return;
          }
          if (check2) {
              out.println(gcd2);
              return;
          }
          out.println(0);
  
      }
  
      static long[] pre(int[] a) {
          long[] pre = new long[a.length + 1];
          pre[0] = 0;
          for (int i = 0; i < a.length; i++) {
              pre[i + 1] = pre[i] + a[i];
          }
          return pre;
      }
  
      static long[] pre(long[] a) {
          long[] pre = new long[a.length + 1];
          pre[0] = 0;
          for (int i = 0; i < a.length; i++) {
              pre[i + 1] = pre[i] + a[i];
          }
          return pre;
      }
  
      static void print(char A[]) {
          for (char c : A) {
              out.print(c);
          }
          out.println();
      }
  
      static void print(boolean A[]) {
          for (boolean c : A) {
              out.print(c + " ");
          }
          out.println();
      }
  
      static void print(int A[]) {
          for (int c : A) {
              out.print(c + " ");
          }
          out.println();
      }
  
      static void print(long A[]) {
          for (long i : A) {
              out.print(i + " ");
          }
          out.println();
      }
  
      static void print(List<Integer> A) {
          for (int a : A) {
              out.print(a + " ");
          }
      }
  
      static int i() {
          return in.nextInt();
      }
  
      static long l() {
          return in.nextLong();
      }
  
      static double d() {
          return in.nextDouble();
      }
  
      static String s() {
          return in.nextLine();
      }
  
      static String c() {
          return in.next();
      }
  
      static int[][] inputWithIdx(int N) {
          int A[][] = new int[N][2];
          for (int i = 0; i < N; i++) {
              A[i] = new int[]{i, in.nextInt()};
          }
          return A;
      }
  
      static int[] input(int N) {
          int A[] = new int[N];
          for (int i = 0; i < N; i++) {
              A[i] = in.nextInt();
          }
          return A;
      }
  
      static long[] inputLong(int N) {
          long A[] = new long[N];
          for (int i = 0; i < A.length; i++) {
              A[i] = in.nextLong();
          }
          return A;
      }
  
      static int GCD(int a, int b) {
          if (b == 0) {
              return a;
          } else {
              return GCD(b, a % b);
          }
      }
  
      static long GCD(long a, long b) {
          if (b == 0) {
              return a;
          } else {
              return GCD(b, a % b);
          }
      }
  
      static long LCM(int a, int b) {
          return (long) a / GCD(a, b) * b;
      }
  
      static long LCM(long a, long b) {
          return a / GCD(a, b) * b;
      }
  
      static void shuffle(int[] arr) {
          for (int i = 0; i < arr.length; i++) {
              int rand = (int) (Math.random() * arr.length);
              int temp = arr[rand];
              arr[rand] = arr[i];
              arr[i] = temp;
          }
      }
  
      static void shuffleAndSort(int[] arr) {
          for (int i = 0; i < arr.length; i++) {
              int rand = (int) (Math.random() * arr.length);
              int temp = arr[rand];
              arr[rand] = arr[i];
              arr[i] = temp;
          }
          Arrays.sort(arr);
      }
  
      static void shuffleAndSort(int[][] arr, Comparator<? super int[]> comparator) {
          for (int i = 0; i < arr.length; i++) {
              int rand = (int) (Math.random() * arr.length);
              int[] temp = arr[rand];
              arr[rand] = arr[i];
              arr[i] = temp;
          }
          Arrays.sort(arr, comparator);
      }
  
      static void shuffleAndSort(long[] arr) {
          for (int i = 0; i < arr.length; i++) {
              int rand = (int) (Math.random() * arr.length);
              long temp = arr[rand];
              arr[rand] = arr[i];
              arr[i] = temp;
          }
          Arrays.sort(arr);
      }
  
      static boolean isPerfectSquare(double number) {
          double sqrt = Math.sqrt(number);
          return ((sqrt - Math.floor(sqrt)) == 0);
      }
  
      static void swap(int A[], int a, int b) {
          int t = A[a];
          A[a] = A[b];
          A[b] = t;
      }
  
      static void swap(char A[], int a, int b) {
          char t = A[a];
          A[a] = A[b];
          A[b] = t;
      }
  
      static long pow(long a, long b, int mod) {
          long pow = 1;
          long x = a;
          while (b != 0) {
              if ((b & 1) != 0) {
                  pow = (pow * x) % mod;
              }
              x = (x * x) % mod;
              b /= 2;
          }
          return pow;
      }
  
      static long pow(long a, long b) {
          long pow = 1;
          long x = a;
          while (b != 0) {
              if ((b & 1) != 0) {
                  pow *= x;
              }
              x = x * x;
              b /= 2;
          }
          return pow;
      }
  
      static long modInverse(long x, int mod) {
          return pow(x, mod - 2, mod);
      }
  
      static boolean isPrime(long N) {
          if (N <= 1) {
              return false;
          }
          if (N <= 3) {
              return true;
          }
          if (N % 2 == 0 || N % 3 == 0) {
              return false;
          }
          for (int i = 5; i * i <= N; i = i + 6) {
              if (N % i == 0 || N % (i + 2) == 0) {
                  return false;
              }
          }
          return true;
      }
  
      public static String reverse(String str) {
          if (str == null) {
              return null;
          }
          return new StringBuilder(str).reverse().toString();
      }
  
      public static void reverse(int[] arr) {
          for (int i = 0; i < arr.length / 2; i++) {
              int tmp = arr[i];
              arr[arr.length - 1 - i] = tmp;
              arr[i] = arr[arr.length - 1 - i];
          }
      }
  
      public static String repeat(char ch, int repeat) {
          if (repeat <= 0) {
              return "";
          }
          final char[] buf = new char[repeat];
          for (int i = repeat - 1; i >= 0; i--) {
              buf[i] = ch;
          }
          return new String(buf);
      }
  
      public static int[] manacher(String s) {
          char[] chars = s.toCharArray();
          int n = s.length();
          int[] d1 = new int[n];
          for (int i = 0, l = 0, r = -1; i < n; i++) {
              int k = (i > r) ? 1 : Math.min(d1[l + r - i], r - i + 1);
              while (0 <= i - k && i + k < n && chars[i - k] == chars[i + k]) {
                  k++;
              }
              d1[i] = k--;
              if (i + k > r) {
                  l = i - k;
                  r = i + k;
              }
          }
          return d1;
      }
  
      public static int[] kmp(String s) {
          int n = s.length();
          int[] res = new int[n];
          for (int i = 1; i < n; ++i) {
              int j = res[i - 1];
              while (j > 0 && s.charAt(i) != s.charAt(j)) {
                  j = res[j - 1];
              }
              if (s.charAt(i) == s.charAt(j)) {
                  ++j;
              }
              res[i] = j;
          }
          return res;
      }
  }
  
  class Pair {
  
      int i;
      int j;
  
      Pair(int i, int j) {
          this.i = i;
          this.j = j;
      }
  
      @Override
      public boolean equals(Object o) {
          if (this == o) {
              return true;
          }
          if (o == null || getClass() != o.getClass()) {
              return false;
          }
          Pair pair = (Pair) o;
          return i == pair.i && j == pair.j;
      }
  
      @Override
      public int hashCode() {
          return Objects.hash(i, j);
      }
  }
  
  class FastReader {
  
      BufferedReader br;
      StringTokenizer st;
  
      public FastReader() {
          br = new BufferedReader(new InputStreamReader(System.in));
      }
  
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
  
      int nextInt() {
          return Integer.parseInt(next());
      }
  
      long nextLong() {
          return Long.parseLong(next());
      }
  
      double nextDouble() {
          return Double.parseDouble(next());
      }
  
      String nextLine() {
          String str = "";
          try {
              str = br.readLine();
          } catch (IOException e) {
              e.printStackTrace();
          }
          return str;
      }
  }
  
  class Node {
  
      int val;
  
      public Node(int val) {
          this.val = val;
      }
  }
  
  
  class ST {
  
      int n;
      Node[] st;
  
      ST(int n) {
          this.n = n;
          st = new Node[4 * Integer.highestOneBit(n)];
      }
  
      void build(Node[] nodes) {
          build(0, 0, n - 1, nodes);
      }
  
      private void build(int id, int l, int r, Node[] nodes) {
          if (l == r) {
              st[id] = nodes[l];
              return;
          }
          int mid = (l + r) >> 1;
          build((id << 1) + 1, l, mid, nodes);
          build((id << 1) + 2, mid + 1, r, nodes);
          st[id] = comb(st[(id << 1) + 1], st[(id << 1) + 2]);
      }
  
      void update(int i, Node node) {
          update(0, 0, n - 1, i, node);
      }
  
      private void update(int id, int l, int r, int i, Node node) {
          if (i < l || r < i) {
              return;
          }
          if (l == r) {
              st[id] = node;
              return;
          }
          int mid = (l + r) >> 1;
          update((id << 1) + 1, l, mid, i, node);
          update((id << 1) + 2, mid + 1, r, i, node);
          st[id] = comb(st[(id << 1) + 1], st[(id << 1) + 2]);
      }
  
      Node get(int x, int y) {
          return get(0, 0, n - 1, x, y);
      }
  
      private Node get(int id, int l, int r, int x, int y) {
          if (x > r || y < l) {
              return new Node(0);
          }
          if (x <= l && r <= y) {
              return st[id];
          }
          int mid = (l + r) >> 1;
          return comb(get((id << 1) + 1, l, mid, x, y), get((id << 1) + 2, mid + 1, r, x, y));
      }
  
      Node comb(Node a, Node b) {
          if (a == null) {
              return b;
          }
          if (b == null) {
              return a;
          }
          return new Node(a.val | b.val);
      }
  }