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.IOException;
  import java.io.InputStream;
  import java.util.*;
  
  public class C {
  
    /**
     * Template @author William Fiset, william.alexandre.fiset@gmail.com
     *
     */
    static InputReader in = new InputReader(System.in);
    private static StringBuilder sb;
  
    static ArrayList<Long> getDivisors(long n) {
      ArrayList<Long> res = new ArrayList();
      // Note that this loop runs till square root
      for (long i = 1; i * i <= n; i++) {
        if (n % i == 0) {
          // If divisors are equal, print only one
          if (n / i == i) {
            res.add(i);
          } else // Otherwise print both
          {
            res.add(i);
            res.add(n / i);
          }
        }
      }
      Collections.sort(res);
      return res;
    }
  
    private static Long getD(long gcde, long gcdo, ArrayList<Long> even, ArrayList<Long> odd) {
      boolean flag = true;
      for (Long i : even) {
        if (i % gcdo == 0) {
          flag = false;
          break;
        }
      }
      if (flag) {
        return gcdo; 
      }
      flag = true;
      for (Long i : odd) {
        if (i % gcde == 0) {
          flag = false;
          break;
        }
      }
      if (flag) {
        return gcde; 
      }
      return 0l;
    }
  
    static class InputReader {
  
      private static final int DEFAULT_BUFFER_SIZE = 1 << 16;
      private static final InputStream DEFAULT_STREAM = System.in;
      private static final int MAX_DECIMAL_PRECISION = 21;
      private int c;
      private byte[] buf;
      private int bufferSize, bufIndex, numBytesRead;
  
      private InputStream stream;
  
      private static final byte EOF = -1;
      private static final byte NEW_LINE = 10;
      private static final byte SPACE = 32;
      private static final byte DASH = 45;
      private static final byte DOT = 46;
  
      private char[] charBuffer;
  
      private static byte[] bytes = new byte[58];
      private static int[] ints = new int[58];
      private static char[] chars = new char[128];
  
      static {
        char ch = ' ';
        int value = 0;
        byte _byte = 0;
        for (int i = 48; i < 58; i++) {
          bytes[i] = _byte++;
        }
        for (int i = 48; i < 58; i++) {
          ints[i] = value++;
        }
        for (int i = 32; i < 128; i++) {
          chars[i] = ch++;
        }
      }
  
      private static final double[][] doubles = {
        {0.0d, 0.00d, 0.000d, 0.0000d, 0.00000d, 0.000000d, 0.0000000d, 0.00000000d, 0.000000000d,
          0.0000000000d, 0.00000000000d, 0.000000000000d,
          0.0000000000000d, 0.00000000000000d, 0.000000000000000d, 0.0000000000000000d,
          0.00000000000000000d, 0.000000000000000000d,
          0.0000000000000000000d, 0.00000000000000000000d, 0.000000000000000000000d},
        {0.1d, 0.01d, 0.001d, 0.0001d, 0.00001d, 0.000001d, 0.0000001d, 0.00000001d, 0.000000001d,
          0.0000000001d, 0.00000000001d, 0.000000000001d,
          0.0000000000001d, 0.00000000000001d, 0.000000000000001d, 0.0000000000000001d,
          0.00000000000000001d, 0.000000000000000001d,
          0.0000000000000000001d, 0.00000000000000000001d, 0.000000000000000000001d},
        {0.2d, 0.02d, 0.002d, 0.0002d, 0.00002d, 0.000002d, 0.0000002d, 0.00000002d, 0.000000002d,
          0.0000000002d, 0.00000000002d, 0.000000000002d,
          0.0000000000002d, 0.00000000000002d, 0.000000000000002d, 0.0000000000000002d,
          0.00000000000000002d, 0.000000000000000002d,
          0.0000000000000000002d, 0.00000000000000000002d, 0.000000000000000000002d},
        {0.3d, 0.03d, 0.003d, 0.0003d, 0.00003d, 0.000003d, 0.0000003d, 0.00000003d, 0.000000003d,
          0.0000000003d, 0.00000000003d, 0.000000000003d,
          0.0000000000003d, 0.00000000000003d, 0.000000000000003d, 0.0000000000000003d,
          0.00000000000000003d, 0.000000000000000003d,
          0.0000000000000000003d, 0.00000000000000000003d, 0.000000000000000000003d},
        {0.4d, 0.04d, 0.004d, 0.0004d, 0.00004d, 0.000004d, 0.0000004d, 0.00000004d, 0.000000004d,
          0.0000000004d, 0.00000000004d, 0.000000000004d,
          0.0000000000004d, 0.00000000000004d, 0.000000000000004d, 0.0000000000000004d,
          0.00000000000000004d, 0.000000000000000004d,
          0.0000000000000000004d, 0.00000000000000000004d, 0.000000000000000000004d},
        {0.5d, 0.05d, 0.005d, 0.0005d, 0.00005d, 0.000005d, 0.0000005d, 0.00000005d, 0.000000005d,
          0.0000000005d, 0.00000000005d, 0.000000000005d,
          0.0000000000005d, 0.00000000000005d, 0.000000000000005d, 0.0000000000000005d,
          0.00000000000000005d, 0.000000000000000005d,
          0.0000000000000000005d, 0.00000000000000000005d, 0.000000000000000000005d},
        {0.6d, 0.06d, 0.006d, 0.0006d, 0.00006d, 0.000006d, 0.0000006d, 0.00000006d, 0.000000006d,
          0.0000000006d, 0.00000000006d, 0.000000000006d,
          0.0000000000006d, 0.00000000000006d, 0.000000000000006d, 0.0000000000000006d,
          0.00000000000000006d, 0.000000000000000006d,
          0.0000000000000000006d, 0.00000000000000000006d, 0.000000000000000000006d},
        {0.7d, 0.07d, 0.007d, 0.0007d, 0.00007d, 0.000007d, 0.0000007d, 0.00000007d, 0.000000007d,
          0.0000000007d, 0.00000000007d, 0.000000000007d,
          0.0000000000007d, 0.00000000000007d, 0.000000000000007d, 0.0000000000000007d,
          0.00000000000000007d, 0.000000000000000007d,
          0.0000000000000000007d, 0.00000000000000000007d, 0.000000000000000000007d},
        {0.8d, 0.08d, 0.008d, 0.0008d, 0.00008d, 0.000008d, 0.0000008d, 0.00000008d, 0.000000008d,
          0.0000000008d, 0.00000000008d, 0.000000000008d,
          0.0000000000008d, 0.00000000000008d, 0.000000000000008d, 0.0000000000000008d,
          0.00000000000000008d, 0.000000000000000008d,
          0.0000000000000000008d, 0.00000000000000000008d, 0.000000000000000000008d},
        {0.9d, 0.09d, 0.009d, 0.0009d, 0.00009d, 0.000009d, 0.0000009d, 0.00000009d, 0.000000009d,
          0.0000000009d, 0.00000000009d, 0.000000000009d,
          0.0000000000009d, 0.00000000000009d, 0.000000000000009d, 0.0000000000000009d,
          0.00000000000000009d, 0.000000000000000009d,
          0.0000000000000000009d, 0.00000000000000000009d, 0.000000000000000000009d}
      };
  
      public InputReader() {
        this(DEFAULT_STREAM, DEFAULT_BUFFER_SIZE);
      }
  
      public InputReader(int bufferSize) {
        this(DEFAULT_STREAM, bufferSize);
      }
  
      public InputReader(InputStream stream) {
        this(stream, DEFAULT_BUFFER_SIZE);
      }
  
      public InputReader(InputStream stream, int bufferSize) {
        if (stream == null || bufferSize <= 0) {
          throw new IllegalArgumentException();
        }
        buf = new byte[bufferSize];
        charBuffer = new char[128];
        this.bufferSize = bufferSize;
        this.stream = stream;
      }
  
      private byte read() throws IOException {
  
        if (numBytesRead == EOF) {
          throw new IOException();
        }
  
        if (bufIndex >= numBytesRead) {
          bufIndex = 0;
          numBytesRead = stream.read(buf);
          if (numBytesRead == EOF) {
            return EOF;
          }
        }
  
        return buf[bufIndex++];
      }
  
      private void doubleCharBufferSize() {
        char[] newBuffer = new char[charBuffer.length << 1];
        for (int i = 0; i < charBuffer.length; i++) {
          newBuffer[i] = charBuffer[i];
        }
        charBuffer = newBuffer;
      }
  
      private int readJunk(int token) throws IOException {
  
        if (numBytesRead == EOF) {
          return EOF;
        }
  
        do {
  
          while (bufIndex < numBytesRead) {
            if (buf[bufIndex] > token) {
              return 0;
            }
            bufIndex++;
          }
  
          numBytesRead = stream.read(buf);
          if (numBytesRead == EOF) {
            return EOF;
          }
          bufIndex = 0;
  
        } while (true);
  
      }
  
      public byte nextByte() throws IOException {
        return (byte) nextInt();
      }
  
      public int nextInt() throws IOException {
  
        if (readJunk(DASH - 1) == EOF) {
          throw new IOException();
        }
        int sgn = 1, res = 0;
  
        c = buf[bufIndex];
        if (c == DASH) {
          sgn = -1;
          bufIndex++;
        }
  
        do {
  
          while (bufIndex < numBytesRead) {
            if (buf[bufIndex] > SPACE) {
              res = (res << 3) + (res << 1);
              res += ints[buf[bufIndex++]];
            } else {
              bufIndex++;
              return res * sgn;
            }
          }
  
          numBytesRead = stream.read(buf);
          if (numBytesRead == EOF) {
            return res * sgn;
          }
          bufIndex = 0;
  
        } while (true);
  
      }
  
      public int[] nextIntArray(int n) throws IOException {
        int[] ar = new int[n];
        for (int i = 0; i < n; i++) {
          ar[i] = nextInt();
        }
        return ar;
      }
  
      public void close() throws IOException {
        stream.close();
      }
  
      public long nextLong() throws IOException {
        if (readJunk(DASH - 1) == EOF) {
          throw new IOException();
        }
        int sgn = 1;
        long res = 0L;
        c = buf[bufIndex];
        if (c == DASH) {
          sgn = -1;
          bufIndex++;
        }
        do {
          while (bufIndex < numBytesRead) {
            if (buf[bufIndex] > SPACE) {
              res = (res << 3) + (res << 1);
              res += ints[buf[bufIndex++]];
            } else {
              bufIndex++;
              return res * sgn;
            }
          }
          numBytesRead = stream.read(buf);
          if (numBytesRead == EOF) {
            return res * sgn;
          }
          bufIndex = 0;
        } while (true);
      }
  
      public String nextString() throws IOException {
        if (numBytesRead == EOF) {
          return null;
        }
        if (readJunk(SPACE) == EOF) {
          return null;
        }
  
        for (int i = 0;;) {
          while (bufIndex < numBytesRead) {
            if (buf[bufIndex] > SPACE) {
              if (i == charBuffer.length) {
                doubleCharBufferSize();
              }
              charBuffer[i++] = (char) buf[bufIndex++];
            } else {
              bufIndex++;
              return new String(charBuffer, 0, i);
            }
          }
  
          // Reload buffer
          numBytesRead = stream.read(buf);
          if (numBytesRead == EOF) {
            return new String(charBuffer, 0, i);
          }
          bufIndex = 0;
        }
      }
    }
  
    public static void main(String args[]) throws Exception {
      int t = in.nextInt();
      sb = new StringBuilder();
      while (t-- != 0) {
        solve();
      }
      System.out.print(sb.toString());
    }
  
    static void solve() throws IOException {
      int n;
      n = in.nextInt();
      ArrayList<Long> odd = new ArrayList();
      ArrayList<Long> even = new ArrayList();
      for (int i = 0; i < n; i++) {
        long x = in.nextLong();
        if (i % 2 == 0) {
          odd.add(x);
        } else {
          even.add(x);
        }
      }
      long gcde = findGCD(even, even.size());
      long gcdo = findGCD(odd, odd.size());
  //    Set<Long> evenset = new HashSet();
  //    Set<Long> oddset = new HashSet();
  //    calculateFactors(evenset, even);
  //    calculateFactors(oddset, odd);
      System.out.println(getD(gcde, gcdo, even, odd));
    }
  
    static long gcd(long a, long b) {
      if (a == 0) {
        return b;
      }
      return gcd(b % a, a);
    }
  
    static long findGCD(ArrayList<Long> arr, long n) {
      long result = 0;
      for (long element : arr) {
        result = gcd(result, element);
  
        if (result == 1) {
          return 1;
        }
      }
      return result;
    }
  }
  