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.HashSet;
  import java.io.BufferedReader;
  import java.io.FileReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.util.StringTokenizer;
  import java.util.Arrays;
  import java.util.Random;
  import java.io.FileWriter;
  import java.io.PrintWriter;
  /*
      Solution Created: 17:01:25 14/12/2021
      Custom Competitive programming helper.
  */
  
  public class Main {
  	
  	public static void solve() {
  		int n = in.nextInt();
  		long[] a = in.nl(n);
  		long gcdA = 0, gcdB = 0;
  		for(int i = 0; i<n; i++) {
  			if(i%2==0) {
  				gcdA = Util.gcd(a[i], gcdA);
  			}else {
  				gcdB = Util.gcd(a[i], gcdB);
  			}
  		}
  		boolean can1 = true, can2 = true;
  		{
  			for(int i = 1; i<n; i+=2) {
  				if(a[i]%gcdA==0) {
  					can1 = false;
  				}
  			}
  			if(can1) {
  				out.println(gcdA);
  				return;
  			}
  		}
  		{
  			for(int i = 0; i<n; i+=2) {
  				if(a[i]%gcdB==0) {
  					can2 = false;
  				}
  			}
  			if(can2) {
  				out.println(gcdB);
  				return;
  			}
  		}
  		out.println(0);
  	}
  	
  	public static void main(String[] args) {
  		in = new Reader();
  		out = new Writer();
  		int t = in.nextInt();
  		while(t-->0) solve();
  		out.exit();
  	}
  	static Reader in; static Writer out;
  
  static class Reader {
  	static BufferedReader br;
  	static StringTokenizer st;
  	
  	public Reader() {
  		this.br = new BufferedReader(new InputStreamReader(System.in));
  	}
  	
  	public Reader(String f){
  		try {
  			this.br = new BufferedReader(new FileReader(f));
  		} catch (IOException e) {
  			e.printStackTrace();
  		}
  	}
  	
  	public int[] na(int n) {
  		int[] a = new int[n];
  		for (int i = 0; i < n; i++) a[i] = nextInt();
  		return a;
  	}
  
  	public double[] nd(int n) {
  		double[] a = new double[n];
  		for (int i = 0; i < n; i++) a[i] = nextDouble();
  		return a;
  	}
  	
  	public long[] nl(int n) {
  		long[] a = new long[n];
  		for (int i = 0; i < n; i++) a[i] = nextLong();
  		return a;
  	}
  
  	public char[] nca() {
  		return next().toCharArray();
  	}
  
  	public String[] ns(int n) {
  		String[] a = new String[n];
  		for (int i = 0; i < n; i++) a[i] = next();
  		return a;
  	}
  
  	public int nextInt() {
  		ensureNext();
  		return Integer.parseInt(st.nextToken());
  	}
  
  	public double nextDouble() {
  		ensureNext();
  		return Double.parseDouble(st.nextToken());
  	}
  
  	public Long nextLong() {
  		ensureNext();
  		return Long.parseLong(st.nextToken());
  	}
  
  	public String next() {
  		ensureNext();
  		return st.nextToken();
  	}
  	
  	public String nextLine() {
  		try {
  			return br.readLine();
  		} catch (Exception e) {
  			e.printStackTrace();
  			return null;
  		}
  	}
  	
  	private void ensureNext() {
  		if (st == null || !st.hasMoreTokens()) {
  			try {
  				st = new StringTokenizer(br.readLine());
  			} catch (IOException e) {
  				e.printStackTrace();
  			}
  		}
  	}
  }
  
  static class Util{
  		private static Random random = new Random();
  		static long[] fact;
  		
  		public static void initFactorial(int n, long mod) {
  			fact = new long[n+1];
  			fact[0] = 1;
  			for (int i = 1; i < n+1; i++) fact[i] = (fact[i - 1] * i) % mod;
  		}
  		
  		public static long modInverse(long a, long MOD) {
  			long[] gcdE = gcdExtended(a, MOD);
  			if (gcdE[0] != 1) return -1; // Inverted doesn't exist
  			long x = gcdE[1];
  			return (x % MOD + MOD) % MOD;
  		}
  		
  		public static long[] gcdExtended(long p, long q) {
  			if (q == 0) return new long[] { p, 1, 0 };
  			long[] vals = gcdExtended(q, p % q);
  			long tmp = vals[2];
  			vals[2] = vals[1] - (p / q) * vals[2];
  			vals[1] = tmp;
  			return vals;
  		}
  		
  		public static long nCr(int n, int r, long MOD) {
  			if (r == 0) return 1;
  			return (fact[n] * modInverse(fact[r], MOD) % MOD * modInverse(fact[n - r], MOD) % MOD) % MOD;
  		}
  		
  		public static long nCr(int n, int r) {
  			return (fact[n]/fact[r])/fact[n-r];
  		}
  		
  		public static long nPr(int n, int r, long MOD) {
  			if (r == 0) return 1;
  			return (fact[n] * modInverse(fact[n - r], MOD) % MOD) % MOD;
  		}
  		public static long nPr(int n, int r) {
  			return fact[n]/fact[n-r];
  		}
  		
  		public static boolean isPrime(int 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 boolean[] getSieve(int n) {
  	        boolean[] isPrime = new boolean[n+1];
  	        for (int i = 2; i <= n; i++) isPrime[i] = true;
  	        for (int i = 2; i*i <= n; i++) if (isPrime[i]) 
  	                for (int j = i; i*j <= n; j++) isPrime[i*j] = false;
  	        return isPrime;
  	    }
  	    
  	    static long pow(long x, long pow, long mod){
  	    	long res = 1;
  	    	x = x % mod;
  	    	if (x == 0) return 0;
  	    	while (pow > 0){
  	    		if ((pow & 1) != 0) res = (res * x) % mod;
  	        	pow >>= 1;
  	        	x = (x * x) % mod;
  	    	}
  	    	return res;
  	    }
  	    
  	    public static int gcd(int a, int b) { 
  	    	int tmp = 0;
  	    	while(b != 0) {
  	    		tmp = b;
  	    		b = a%b;
  	    		a = tmp;
  	    	}
  	    	return a;
  	    }
  	    
  	    public static long gcd(long a, long b) { 
  	    	long tmp = 0;
  	    	while(b != 0) {
  	    		tmp = b;
  	    		b = a%b;
  	    		a = tmp;
  	    	}
  	    	return a;
  	    }
  	    
  	    public static int random(int min, int max) {
  	    	return random.nextInt(max-min+1)+min;
  	    }
  	    
  		public static void dbg(Object... o) { 
  			System.out.println(Arrays.deepToString(o)); 
  		}
  		
  		public static void reverse(int[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				int tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static void reverse(int[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static void reverse(long[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				long tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static void reverse(long[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static void reverse(float[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				float tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static void reverse(float[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static void reverse(double[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				double tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static void reverse(double[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static void reverse(char[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				char tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static void reverse(char[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static <T> void reverse(T[] s, int l , int r) {
  			for(int i = l; i<=(l+r)/2; i++) {
  				T tmp = s[i];
  				s[i] = s[r+l-i];
  				s[r+l-i] = tmp;
  			}
  	    }
  		
  		public static <T> void reverse(T[] s) {
  			reverse(s, 0, s.length-1);
  	    }
  		
  		public static void shuffle(int[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            int t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  		
  	    public static void shuffle(long[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            long t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  	    
  	    public static void shuffle(float[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            float t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  	    
  	    public static void shuffle(double[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            double t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  	    
  	    public static void shuffle(char[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            char t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  	    
  	    public static <T> void shuffle(T[] s) {
  	        for (int i = 0; i < s.length; ++i) {
  	            int j = random.nextInt(i + 1);
  	            T t = s[i];
  	            s[i] = s[j];
  	            s[j] = t;
  	        }
  	    }
  	    
  		public static void sortArray(int[] a) {
  	        shuffle(a);
  	        Arrays.sort(a);
  	    }
  		
  		public static void sortArray(long[] a) {
  			shuffle(a);
  	        Arrays.sort(a);
  	    }
  		
  		public static void sortArray(float[] a) {
  			shuffle(a);
  	        Arrays.sort(a);
  	    }
  		
  		public static void sortArray(double[] a) {
  			shuffle(a);
  	        Arrays.sort(a);
  	    }
  		
  		public static void sortArray(char[] a) {
  			shuffle(a);
  	        Arrays.sort(a);
  	    }
  		
  		public static <T extends Comparable<T>> void sortArray(T[] a) {
  	        Arrays.sort(a);
  	    }
  		
  		public static int[][] rotate90(int[][] a){
  			int n = a.length, m = a[0].length;
  			int[][] ans = new int[m][n];
  			for(int i = 0; i<n; i++) for(int j = 0; j<m; j++) ans[m-j-1][i] = a[i][j];
  			return ans;
  		}
  		
  		public static char[][] rotate90(char[][] a){
  			int n = a.length, m = a[0].length;
  			char[][] ans = new char[m][n];
  			for(int i = 0; i<n; i++) for(int j = 0; j<m; j++) ans[m-j-1][i] = a[i][j];
  			return ans;
  		}
  	}
  
  static class Writer {
  	private PrintWriter pw;
  	public Writer(){
  		pw = new PrintWriter(System.out);
  	}
  	
  	public Writer(String f){
  		try {
  			pw = new PrintWriter(new FileWriter(f));
  		} catch (IOException e) {
  			e.printStackTrace();
  		}
  	}
  	
  	public void yesNo(boolean condition) {
  		println(condition?"YES":"NO");
  	}
  	
  	public void printArray(int[] a) {
  		for(int i = 0; i<a.length; i++) print(a[i]+" ");
  	}
  	
  	public void printlnArray(int[] a) {
  		for(int i = 0; i<a.length; i++) print(a[i]+" ");
  		pw.println();
  	}
  	
  	public void printArray(long[] a) {
  		for(int i = 0; i<a.length; i++) print(a[i]+" ");
  	}
  	
  	public void printlnArray(long[] a) {
  		for(int i = 0; i<a.length; i++) print(a[i]+" ");
  		pw.println();
  	}
  	
  	public void print(Object o) {
  		pw.print(o.toString());
  	}
  	
  	public void println(Object o) {
  		pw.println(o.toString());
  	}
  	
  	public void println() {
  		pw.println();
  	}
  	
  	public void flush() {
  		pw.flush();
  	}
  	public void exit() {
  		pw.close();
  	}
  }
  }
  