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{
  	//見なくていいよ　ここから------------------------------------------
  	static class InputIterator{
  		ArrayList<String> inputLine = new ArrayList<>(buf);
  		int index = 0; int max; String read;
  		InputIterator(){
  			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  			try{
  				while((read = br.readLine()) != null){
  					inputLine.addAll(Arrays.asList(read.split(" ")));
  				}
  			}catch(IOException e){}
  			max = inputLine.size();
  		}
  		boolean hasNext(){return (index < max);}
  		String next(){
  			if(hasNext()){
  				return inputLine.get(index++);
  			}else{
  				throw new IndexOutOfBoundsException("There is no more input");
  			}
  		}
  	}
  	//入力バッファサイズのつもり。入力点数（スペース区切りでの要素数）が100万を超える場合はバッファサイズを100万にすること
  	static int buf = 1024 * 1024;
  	static HashMap<Integer, String> CONVSTR = new HashMap<>();
  	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
  	static PrintWriter out = new PrintWriter(System.out);
  	static void flush(){out.flush();}
  	static void myout(Object t){out.println(t);}
  	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
  	static String next(){return ii.next();}
  	static boolean hasNext(){return ii.hasNext();}
  	static int nextInt(){return Integer.parseInt(next());}
  	static long nextLong(){return Long.parseLong(next());}
  	static double nextDouble(){return Double.parseDouble(next());}
  	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
  	static ArrayList<String> nextStrArray(int size){
  		ArrayList<String> ret = new ArrayList<>(size);
  		for(int i = 0; i < size; i++){
  			ret.add(next());
  		}
  		return ret;
  	}
  	static ArrayList<Integer> nextIntArray(int size){
  		ArrayList<Integer> ret = new ArrayList<>(size);
  		for(int i = 0; i < size; i++){
  			ret.add(Integer.parseInt(next()));
  		}
  		return ret;
  	}
  	static ArrayList<Long> nextLongArray(int size){
  		ArrayList<Long> ret = new ArrayList<>(size);
  		for(int i = 0; i < size; i++){
  			ret.add(Long.parseLong(next()));
  		}
  		return ret;
  	}
  	@SuppressWarnings("unchecked")
  	static String myconv(Object list, int no){//only join
  		StringBuilder sb = new StringBuilder("");
  		String joinString = CONVSTR.get(no);
  		if(list instanceof String[]){
  			return String.join(joinString, (String[])list);
  		}else if(list instanceof long[]){
  			long[] tmp = (long[])list;
  			if(tmp.length == 0){
  				return "";
  			}
  			sb.append(String.valueOf(tmp[0]));
  			for(int i = 1; i < tmp.length; i++){
  				sb.append(joinString).append(String.valueOf(tmp[i]));
  			}
  			return sb.toString();
  		}else if(list instanceof int[]){
  			int[] tmp = (int[])list;
  			if(tmp.length == 0){
  				return "";
  			}
  			sb.append(String.valueOf(tmp[0]));
  			for(int i = 1; i < tmp.length; i++){
  				sb.append(joinString).append(String.valueOf(tmp[i]));
  			}
  			return sb.toString();
  		}else if(list instanceof ArrayList){
  			ArrayList tmp = (ArrayList)list;
  			if(tmp.size() == 0){
  				return "";
  			}
  			sb.append(tmp.get(0));
  			for(int i = 1; i < tmp.size(); i++){
  				sb.append(joinString).append(tmp.get(i));
  			}
  			return sb.toString();
  		}else{
  			throw new ClassCastException("Don't join");
  		}
  	}
  	static ArrayList<String> myconv(String str, int no){//only split
  		String splitString = CONVSTR.get(no);
  		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
  	}
  	static ArrayList<String> myconv(String str, String no){
  		return new ArrayList<String>(Arrays.asList(str.split(no)));
  	}
  	public static void main(String[] args){
  		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
  		solve();flush();
  	}
  	//見なくていいよ　ここまで------------------------------------------
  	//このコードをコンパイルするときは、「-encoding UTF-8」を指定すること
  	static void solve(){//ここがメイン関数
  		int t = nextInt();
  		while(hasNext()){
  			int N = nextInt();
  			ArrayList<Long> list = nextLongArray(N);
  			
  			long max = 0;
  			long g1 = list.get(0);
  			long g2 = list.get(1);
  			for(int i = 0; i < N; i++){
  				if(i % 2 == 0){
  					g1 = gcd(g1, list.get(i));
  				}else{
  					g2 = gcd(g2, list.get(i));
  				}
  			}
  			HashSet<Long> gs = new HashSet<>();
  			gs.add(g1);
  			gs.add(g2);
  			gs.remove(1l);
  			for(long v : gs){
  				boolean ok = true;
  				for(int i = 0; i < N - 1; i++){
  					if((list.get(i) % v == 0 && list.get(i + 1) % v == 0) || (list.get(i) % v != 0 && list.get(i + 1) % v != 0)){
  						ok = false;
  						break;
  					}
  				}
  				if(ok){
  					max = Math.max(max, v);
  				}
  			}
  			myout(max);
  		}
  	}
  	//メソッド追加エリア　ここから
  
  static long gcd(long m, long n) {return n != 0 ? gcd(n, m % n) : m;}
  
  	//メソッド追加エリア　ここまで
  }
  