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 StringBuilder sb;
  	static dsu dsu;
  	static long fact[];
  	static int mod = (int) (1e9 + 7);
  static boolean check(long[]arr,long g,int r){
      
  	for(int i=0;i<arr.length;i++){
  	    if(i%2==r){
  	        if(arr[i]%g==0)return false;
  	    }
  	    
  	}
      return true;
      
      
      
  }
  	static void solve() {
  		int n=i();
  		long[]arr=new long[n];
  		for(int i=0;i<n;i++)arr[i]=l();
  		long g=arr[0];
  		for(int i=2;i<n;i+=2){
  		    g=gcd(g,arr[i]);
  		    
  		}
  		boolean b=check(arr,g,1);
  		if(b){
  		    sb.append(g+"\n");
  		    return;
  		}
  			 g=arr[1];
  		for(int i=3;i<n;i+=2){
  		    g=gcd(g,arr[i]);
  		    
  		}
  			 b=check(arr,g,0);
  		if(b){
  		    sb.append(g+"\n");
  		    return;
  		}
  		else sb.append(0+"\n");
  	}
  
  	public static void main(String[] args) {
  		sb = new StringBuilder();
  		int test = i();
  		while (test-- > 0) {
  			solve();
  		}
  		System.out.println(sb);
  
  	}
  
  	/*
  	 * fact=new long[(int)1e6+10]; fact[0]=fact[1]=1; for(int i=2;i<fact.length;i++)
  	 * { fact[i]=((long)(i%mod)1L(long)(fact[i-1]%mod))%mod; }
  	 */
  //**************NCR%P******************	 
  	static long ncr(int n, int r) {
  		if (r > n)
  			return (long) 0;
  
  		long res = fact[n] % mod;
  		// System.out.println(res);
  		res = ((long) (res % mod) * (long) (p(fact[r], mod - 2) % mod)) % mod;
  		res = ((long) (res % mod) * (long) (p(fact[n - r], mod - 2) % mod)) % mod;
  		// System.out.println(res);
  		return res;
  
  	}
  
  	static long p(long x, long y)// POWER FXN //
  	{
  		if (y == 0)
  			return 1;
  
  		long res = 1;
  		while (y > 0) {
  			if (y % 2 == 1) {
  				res = (res * x) % mod;
  				y--;
  			}
  
  			x = (x * x) % mod;
  			y = y / 2;
  
  		}
  		return res;
  	}
  
  //**************END******************
  
  	// *************Disjoint set
  	// union*********//
  	static class dsu {
  		int parent[];
  
  		dsu(int n) {
  			parent = new int[n];
  			for (int i = 0; i < n; i++)
  				parent[i] = -1;
  		}
  
  		int find(int a) {
  			if (parent[a] < 0)
  				return a;
  			else {
  				int x = find(parent[a]);
  				parent[a] = x;
  				return x;
  			}
  		}
  
  		void merge(int a, int b) {
  			a = find(a);
  			b = find(b);
  			if (a == b)
  				return;
  			parent[b] = a;
  		}
  	}
  
  //**************PRIME FACTORIZE **********************************//
  	static TreeMap<Integer, Integer> prime(long n) {
  		TreeMap<Integer, Integer> h = new TreeMap<>();
  		long num = n;
  		for (int i = 2; i <= Math.sqrt(num); i++) {
  			if (n % i == 0) {
  				int nt = 0;
  				while (n % i == 0) {
  					n = n / i;
  					nt++;
  				}
  				h.put(i, nt);
  			}
  		}
  		if (n != 1)
  			h.put((int) n, 1);
  		return h;
  
  	}
  
  //****CLASS PAIR ************************************************
  	static class Pair implements Comparable<Pair> {
  		int x;
  		long y;
  
  		Pair(int x, long y) {
  			this.x = x;
  			this.y = y;
  		}
  
  		public int compareTo(Pair o) {
  			return (int) (this.y - o.y);
  
  		}
  
  	}
  //****CLASS PAIR **************************************************
  
  	static class InputReader {
  		private InputStream stream;
  		private byte[] buf = new byte[1024];
  		private int curChar;
  		private int numChars;
  		private SpaceCharFilter filter;
  
  		public InputReader(InputStream stream) {
  			this.stream = stream;
  		}
  
  		public int read() {
  			if (numChars == -1)
  				throw new InputMismatchException();
  			if (curChar >= numChars) {
  				curChar = 0;
  				try {
  					numChars = stream.read(buf);
  				} catch (IOException e) {
  					throw new InputMismatchException();
  				}
  				if (numChars <= 0)
  					return -1;
  			}
  			return buf[curChar++];
  		}
  
  		public int Int() {
  			int c = read();
  			while (isSpaceChar(c))
  				c = read();
  			int sgn = 1;
  			if (c == '-') {
  				sgn = -1;
  				c = read();
  			}
  			int res = 0;
  			do {
  				if (c < '0' || c > '9')
  					throw new InputMismatchException();
  				res *= 10;
  				res += c - '0';
  				c = read();
  			} while (!isSpaceChar(c));
  			return res * sgn;
  		}
  
  		public String String() {
  			int c = read();
  			while (isSpaceChar(c))
  				c = read();
  			StringBuilder res = new StringBuilder();
  			do {
  				res.appendCodePoint(c);
  				c = read();
  			} while (!isSpaceChar(c));
  			return res.toString();
  		}
  
  		public boolean isSpaceChar(int c) {
  			if (filter != null)
  				return filter.isSpaceChar(c);
  			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
  		}
  
  		public String next() {
  			return String();
  		}
  
  		public interface SpaceCharFilter {
  			public boolean isSpaceChar(int ch);
  		}
  	}
  
  	static class OutputWriter {
  		private final PrintWriter writer;
  
  		public OutputWriter(OutputStream outputStream) {
  			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
  		}
  
  		public OutputWriter(Writer writer) {
  			this.writer = new PrintWriter(writer);
  		}
  
  		public void print(Object... objects) {
  			for (int i = 0; i < objects.length; i++) {
  				if (i != 0)
  					writer.print(' ');
  				writer.print(objects[i]);
  			}
  		}
  
  		public void printLine(Object... objects) {
  			print(objects);
  			writer.println();
  		}
  
  		public void close() {
  			writer.close();
  		}
  
  		public void flush() {
  			writer.flush();
  		}
  	}
  
  	static InputReader in = new InputReader(System.in);
  	static OutputWriter out = new OutputWriter(System.out);
  
  	public static long[] sort(long[] a2) {
  		int n = a2.length;
  		ArrayList<Long> l = new ArrayList<>();
  		for (long i : a2)
  			l.add(i);
  		Collections.sort(l);
  		for (int i = 0; i < l.size(); i++)
  			a2[i] = l.get(i);
  		return a2;
  	}
  
  	public static char[] sort(char[] a2) {
  		int n = a2.length;
  		ArrayList<Character> l = new ArrayList<>();
  		for (char i : a2)
  			l.add(i);
  		Collections.sort(l);
  		for (int i = 0; i < l.size(); i++)
  			a2[i] = l.get(i);
  		return a2;
  	}
  
  	public static long pow(long x, long y) {
  		long res = 1;
  		while (y > 0) {
  			if (y % 2 != 0) {
  				res = (res * x);// % modulus;
  				y--;
  
  			}
  			x = (x * x);// % modulus;
  			y = y / 2;
  		}
  		return res;
  	}
  
  //GCD___+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  	public static long gcd(long x, long y) {
  		if (x == 0)
  			return y;
  		else
  			return gcd(y % x, x);
  	}
  	// ******LOWEST COMMON MULTIPLE
  	// *********************************************
  
  	public static long lcm(long x, long y) {
  		return (x * (y / gcd(x, y)));
  	}
  
  //INPUT PATTERN********************************************************
  	public static int i() {
  		return in.Int();
  	}
  
  	public static long l() {
  		String s = in.String();
  		return Long.parseLong(s);
  	}
  
  	public static String s() {
  		return in.String();
  	}
  
  	public static int[] readArrayi(int n) {
  		int A[] = new int[n];
  		for (int i = 0; i < n; i++) {
  			A[i] = i();
  		}
  		return A;
  	}
  
  	public static long[] readArray(long n) {
  		long A[] = new long[(int) n];
  		for (int i = 0; i < n; i++) {
  			A[i] = l();
  		}
  		return A;
  	}
  
  }