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.*;
  
  import static java.lang.Math.*;
  import static java.lang.Math.ceil;
  import static java.util.Arrays.*;
  
  public class Codeforces {
      static int mod = 1000000007;
      static int ar[] = new int[10];
  
      public static void main(String[] args) throws IOException {
          int t = ri();
          while (t-- > 0) {
              int n = ri();
              long a[] = rla(n);
              boolean done = true;
              long gcd = 0;
              for (int i = 0; i < n; i += 2) {
                  gcd = gcd(gcd, a[i]);
              }
              for (int i = 1; i < n; i += 2) {
                  if (a[i] % gcd == 0) {
                      done = false;
                      break;
                  }
              }
              if (done) {
                  prln(gcd);
              } else {
                  done = true;
                  gcd = 0;
                  for (int i = 1; i < n; i += 2) {
                      gcd = gcd(gcd, a[i]);
                  }
                  for (int i = 0 ; i < n ; i+=2){
                      if (a[i]%gcd == 0){
                          done =false;
                          break;
                      }
                  }
                  if (done){
                      prln(gcd);
                  }else{
                      prln(0);
                  }
              }
  
          }
  
  
          close();
      }
  
      static boolean check(int a, int b, int h, int m) {
          if (ar[a % 10] == -1 || ar[a / 10] == -1 || ar[b % 10] == -1 || ar[b / 10] == -1) {
              return false;
          }
          int x = ar[b % 10] * 10 + ar[b / 10];
          int y = ar[a % 10] * 10 + ar[a / 10];
          if (x < h && y < m) {
              return true;
          }
          return false;
      }
  
      static boolean isPalindrome(char[] c) {
          int low = 0, high = c.length - 1;
          while (low < high) {
              if (c[low] != c[high] || c[low] == '?' || c[high] == '?') return false;
              low++;
              high--;
          }
          return true;
      }
  
  
      static char get(int a) {
          return (char) (a + 'a');
      }
  
      static void addToPq(int n, PriorityQueue<Integer> p) {
          for (int i = 0; i < n; i++) {
              p.add(i);
          }
      }
  
      static boolean better(int a, int b, int[][] matrix) {
          int cnt = 0;
          for (int i = 0; i < 5; i++) {
              if (matrix[a][i] < matrix[b][i]) cnt++;
          }
          return cnt >= 3;
      }
  
      static BufferedReader __i = new BufferedReader(new InputStreamReader(System.in));
      static PrintWriter __o = new PrintWriter(new OutputStreamWriter(System.out));
      static StringTokenizer input;
      static Random __r = new Random();
  
      // references
      // IBIG = 1e9 + 7
      // IMAX ~= 2e9
      // LMAX ~= 9e18
  
      // constants
      static final int IBIG = 1000000007;
      static final int IMAX = 2147483647;
      static final long LMAX = 9223372036854775807L;
  
      // math util
      static int minof(int a, int b, int c) {
          return min(a, min(b, c));
      }
  
      static int minof(int... x) {
          if (x.length == 1) return x[0];
          if (x.length == 2) return min(x[0], x[1]);
          if (x.length == 3) return min(x[0], min(x[1], x[2]));
          int min = x[0];
          for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i];
          return min;
      }
  
      static long minof(long a, long b, long c) {
          return min(a, min(b, c));
      }
  
      static long minof(long... x) {
          if (x.length == 1) return x[0];
          if (x.length == 2) return min(x[0], x[1]);
          if (x.length == 3) return min(x[0], min(x[1], x[2]));
          long min = x[0];
          for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i];
          return min;
      }
  
      static int maxof(int a, int b, int c) {
          return max(a, max(b, c));
      }
  
      static int maxof(int... x) {
          if (x.length == 1) return x[0];
          if (x.length == 2) return max(x[0], x[1]);
          if (x.length == 3) return max(x[0], max(x[1], x[2]));
          int max = x[0];
          for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i];
          return max;
      }
  
      static long maxof(long a, long b, long c) {
          return max(a, max(b, c));
      }
  
      static long maxof(long... x) {
          if (x.length == 1) return x[0];
          if (x.length == 2) return max(x[0], x[1]);
          if (x.length == 3) return max(x[0], max(x[1], x[2]));
          long max = x[0];
          for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i];
          return max;
      }
  
      static int powi(int a, int b) {
          if (a == 0) return 0;
          int ans = 1;
          while (b > 0) {
              if ((b & 1) > 0) ans *= a;
              a *= a;
              b >>= 1;
          }
          return ans;
      }
  
      static long powl(long a, int b) {
          if (a == 0) return 0;
          long ans = 1;
          while (b > 0) {
              if ((b & 1) > 0) ans *= a;
              a *= a;
              b >>= 1;
          }
          return ans;
      }
  
      static int fli(double d) {
          return (int) d;
      }
  
      static int cei(double d) {
          return (int) ceil(d);
      }
  
      static long fll(double d) {
          return (long) d;
      }
  
      static long cel(double d) {
          return (long) ceil(d);
      }
  
      static int gcd(int a, int b) {
          return b == 0 ? a : gcd(b, a % b);
      }
  
      static long gcd(long a, long b) {
          return b == 0 ? a : gcd(b, a % b);
      }
  
      static int[] exgcd(int a, int b) {
          if (b == 0) return new int[]{1, 0};
          int[] y = exgcd(b, a % b);
          return new int[]{y[1], y[0] - y[1] * (a / b)};
      }
  
      static long[] exgcd(long a, long b) {
          if (b == 0) return new long[]{1, 0};
          long[] y = exgcd(b, a % b);
          return new long[]{y[1], y[0] - y[1] * (a / b)};
      }
  
      static int randInt(int min, int max) {
          return __r.nextInt(max - min + 1) + min;
      }
  
      static long mix(long x) {
          x += 0x9e3779b97f4a7c15L;
          x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L;
          x = (x ^ (x >> 27)) * 0x94d049bb133111ebL;
          return x ^ (x >> 31);
      }
  
      public static boolean[] findPrimes(int limit) {
          assert limit >= 2;
  
          final boolean[] nonPrimes = new boolean[limit];
          nonPrimes[0] = true;
          nonPrimes[1] = true;
  
          int sqrt = (int) Math.sqrt(limit);
          for (int i = 2; i <= sqrt; i++) {
              if (nonPrimes[i]) continue;
              for (int j = i; j < limit; j += i) {
                  if (!nonPrimes[j] && i != j) nonPrimes[j] = true;
              }
          }
  
          return nonPrimes;
      }
  
      // array util
      static void reverse(int[] a) {
          for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
              int swap = a[i];
              a[i] = a[n - i - 1];
              a[n - i - 1] = swap;
          }
      }
  
      static void reverse(long[] a) {
          for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
              long swap = a[i];
              a[i] = a[n - i - 1];
              a[n - i - 1] = swap;
          }
      }
  
      static void reverse(double[] a) {
          for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
              double swap = a[i];
              a[i] = a[n - i - 1];
              a[n - i - 1] = swap;
          }
      }
  
      static void reverse(char[] a) {
          for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
              char swap = a[i];
              a[i] = a[n - i - 1];
              a[n - i - 1] = swap;
          }
      }
  
      static void shuffle(int[] a) {
          int n = a.length - 1;
          for (int i = 0; i < n; ++i) {
              int ind = randInt(i, n);
              int swap = a[i];
              a[i] = a[ind];
              a[ind] = swap;
          }
      }
  
      static void shuffle(long[] a) {
          int n = a.length - 1;
          for (int i = 0; i < n; ++i) {
              int ind = randInt(i, n);
              long swap = a[i];
              a[i] = a[ind];
              a[ind] = swap;
          }
      }
  
      static void shuffle(double[] a) {
          int n = a.length - 1;
          for (int i = 0; i < n; ++i) {
              int ind = randInt(i, n);
              double swap = a[i];
              a[i] = a[ind];
              a[ind] = swap;
          }
      }
  
      static void rsort(int[] a) {
          shuffle(a);
          sort(a);
      }
  
      static void rsort(long[] a) {
          shuffle(a);
          sort(a);
      }
  
      static void rsort(double[] a) {
          shuffle(a);
          sort(a);
      }
  
      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;
      }
  
      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;
      }
  
      static double[] copy(double[] a) {
          double[] ans = new double[a.length];
          for (int i = 0; i < a.length; ++i) ans[i] = a[i];
          return ans;
      }
  
      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;
      }
  
      static void resetBoolean(boolean[] vis, int n) {
          for (int i = 0; i < n; i++) {
              vis[i] = false;
          }
      }
  
      static void setMinusOne(int[][] matrix) {
          int row = matrix.length;
          int col = matrix[0].length;
  
          for (int i = 0; i < row; i++) {
              for (int j = 0; j < col; j++) {
                  matrix[i][j] = -1;
              }
          }
  
      }
  
      // input
      static void r() throws IOException {
          input = new StringTokenizer(rline());
      }
  
      static int ri() throws IOException {
          return Integer.parseInt(rline().split(" ")[0]);
      }
  
      static long rl() throws IOException {
          return Long.parseLong(rline());
      }
  
      static double rd() throws IOException {
          return Double.parseDouble(rline());
      }
  
      static int[] ria(int n) throws IOException {
          int[] a = new int[n];
          r();
          for (int i = 0; i < n; ++i) a[i] = ni();
          return a;
      }
  
      static void ria(int[] a) throws IOException {
          int n = a.length;
          r();
          for (int i = 0; i < n; ++i) a[i] = ni();
      }
  
      static int[] riam1(int n) throws IOException {
          int[] a = new int[n];
          r();
          for (int i = 0; i < n; ++i) a[i] = ni() - 1;
          return a;
      }
  
      static void riam1(int[] a) throws IOException {
          int n = a.length;
          r();
          for (int i = 0; i < n; ++i) a[i] = ni() - 1;
      }
  
      static long[] rla(int n) throws IOException {
          long[] a = new long[n];
          r();
          for (int i = 0; i < n; ++i) a[i] = nl();
          return a;
      }
  
      static void rla(long[] a) throws IOException {
          int n = a.length;
          r();
          for (int i = 0; i < n; ++i) a[i] = nl();
      }
  
      static double[] rda(int n) throws IOException {
          double[] a = new double[n];
          r();
          for (int i = 0; i < n; ++i) a[i] = nd();
          return a;
      }
  
      static void rda(double[] a) throws IOException {
          int n = a.length;
          r();
          for (int i = 0; i < n; ++i) a[i] = nd();
      }
  
      static char[] rcha() throws IOException {
          return rline().toCharArray();
      }
  
      static void rcha(char[] a) throws IOException {
          int n = a.length, i = 0;
          for (char c : rline().toCharArray()) a[i++] = c;
      }
  
      static String rline() throws IOException {
          return __i.readLine();
      }
  
      static String n() {
          return input.nextToken();
      }
  
      static int rni() throws IOException {
          r();
          return ni();
      }
  
      static int ni() {
          return Integer.parseInt(n());
      }
  
      static long rnl() throws IOException {
          r();
          return nl();
      }
  
      static long nl() {
          return Long.parseLong(n());
      }
  
      static double rnd() throws IOException {
          r();
          return nd();
      }
  
      static double nd() {
          return Double.parseDouble(n());
      }
  
      // output
      static void pr(int i) {
          __o.print(i);
      }
  
      static void prln(int i) {
          __o.println(i);
      }
  
      static void pr(long l) {
          __o.print(l);
      }
  
      static void prln(long l) {
          __o.println(l);
      }
  
      static void pr(double d) {
          __o.print(d);
      }
  
      static void prln(double d) {
          __o.println(d);
      }
  
      static void pr(char c) {
          __o.print(c);
      }
  
      static void prln(char c) {
          __o.println(c);
      }
  
      static void pr(char[] s) {
          __o.print(new String(s));
      }
  
      static void prln(char[] s) {
          __o.println(new String(s));
      }
  
      static void pr(String s) {
          __o.print(s);
      }
  
      static void prln(String s) {
          __o.println(s);
      }
  
      static void pr(Object o) {
          __o.print(o);
      }
  
      static void prln(Object o) {
          __o.println(o);
      }
  
      static void prln() {
          __o.println();
      }
  
      static void pryes() {
          prln("yes");
      }
  
      static void pry() {
          prln("Yes");
      }
  
      static void prY() {
          prln("YES");
      }
  
      static void prno() {
          prln("no");
      }
  
      static void prn() {
          prln("No");
      }
  
      static void prN() {
          prln("NO");
      }
  
      static boolean pryesno(boolean b) {
          prln(b ? "yes" : "no");
          return b;
      }
  
      ;
  
      static boolean pryn(boolean b) {
          prln(b ? "Yes" : "No");
          return b;
      }
  
      static boolean prYN(boolean b) {
          prln(b ? "YES" : "NO");
          return b;
      }
  
      static void prln(int... a) {
          for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
          if (a.length > 0) prln(a[a.length - 1]);
          else prln();
      }
  
      static void prln(long... a) {
          for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
          if (a.length > 0) prln(a[a.length - 1]);
          else prln();
      }
  
      static void prln(double... a) {
          for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
          if (a.length > 0) prln(a[a.length - 1]);
          else prln();
      }
  
      static <T> void prln(Collection<T> c) {
          int n = c.size() - 1;
          Iterator<T> iter = c.iterator();
          for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i) ;
          if (n >= 0) prln(iter.next());
          else prln();
      }
  
      static void h() {
          prln("hlfd");
          flush();
      }
  
      static void flush() {
          __o.flush();
      }
  
      static void close() {
          __o.close();
      }
  
  }
  