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.*;
  
  public class Main {
  	static InputReader in = new InputReader(System.in);
  	static OutputWriter out = new OutputWriter(System.out);
  
  	public static void main(String[] args) throws IOException {
  //		int t = 1;
  		int t = i();
  		int c = 1;
  		sb = new StringBuilder();
  		while (t-- > 0) {
  //			sb.append("Case #" + c + ": ");
  			solve();
  			c++;
  		}
  		out.println(sb.toString());
  		out.close();
  
  	}
  
  	static int mod = 1000000007;
  	static StringBuilder sb;
  
  	private static void solve() {
  		int n = i();
  		long[] arr = readArray(n * 1L);
  		long gcde = arr[0];
  		long gcdo = arr[1];
  		for (int i = 2; i < n; i++) {
  			if (i % 2 == 0) {
  				gcde = gcd(arr[i], gcde);
  			} else {
  				gcdo = gcd(arr[i], gcdo);
  			}
  		}
  		long res = 0;
  		if (gcde == gcdo) {
  			res = 0;
  		} else {
  			long v1=0;
  			boolean can=true;
  			for(int i=0;i<n;i+=2) {
  				if(arr[i]%gcdo==0) {
  					can=false;
  					break;
  				}
  			}
  			if(can) {
  				v1=gcdo;
  			}
  			long v2=0;
  			boolean can2 = true;
  			for(int i=1;i<n;i+=2) {
  				if(arr[i]%gcde==0) {
  					can2=false;
  					break;
  				}
  			}
  			if(can2) {
  				v2=gcde;
  			}
  			res=Math.max(v1, v2);
  		}
  		sb.append(res).append("\n");
  	}
  
  	private static boolean isPossible(int n, int[][] edges, int k, int[] idxs, int val) {
  		ArrayList<ArrayList<Integer>> graph = new ArrayList<>();
  		for (int i = 0; i < n; i++) {
  			graph.add(new ArrayList<>());
  		}
  		for (int[] e : edges) {
  			if (idxs[e[0]] >= val && idxs[e[1]] >= val) {
  				graph.get(e[0]).add(e[1]);
  			}
  		}
  		// Step-1 dfs while filling the stack
  		boolean[] visited = new boolean[n];
  		Stack<Integer> stack = new Stack<>();
  		for (int i = 0; i < n; i++) {
  			if (visited[i]) {
  				continue;
  			}
  			dfs1(graph, i, visited, stack);
  		}
  
  		// Step-2 make a reverse graph
  		ArrayList<ArrayList<Integer>> revgraph = new ArrayList<>();
  		for (int i = 0; i < n; i++) {
  			revgraph.add(new ArrayList<>());
  		}
  		for (int i = 0; i < n; i++) {
  			ArrayList<Integer> nbrs = graph.get(i);
  			for (int nbr : nbrs) {
  				revgraph.get(nbr).add(i);
  			}
  		}
  		// Step-3 Traverse rev graph in order of popping of stack
  		boolean[] visited2 = new boolean[n];
  		while (!stack.isEmpty()) {
  			int top = stack.pop();
  			if (visited2[top]) {
  				continue;
  			}
  			if (dfs2(revgraph, top, visited2) >= k) {
  				return true;
  			}
  
  		}
  		return false;
  	}
  
  	private static void dfs1(ArrayList<ArrayList<Integer>> graph, int src, boolean[] visited, Stack<Integer> stack) {
  		visited[src] = true;
  		for (int nbr : graph.get(src)) {
  			if (!visited[nbr]) {
  				visited[nbr] = true;
  				dfs1(graph, nbr, visited, stack);
  			}
  		}
  		stack.push(src);
  	}
  
  	private static int dfs2(ArrayList<ArrayList<Integer>> revgraph, int src, boolean[] visited) {
  		visited[src] = true;
  		int res = 1;
  		for (int nbr : revgraph.get(src)) {
  			if (!visited[nbr]) {
  				res += dfs2(revgraph, nbr, visited);
  			}
  		}
  		return res;
  	}
  
  	// Fenwick Tree
  	static class fenwickTree {
  		int n;
  		long[] farr;
  
  		fenwickTree(int n, long[] a) {
  			this.n = n;
  			farr = new long[n + 1];
  			for (int i = 0; i < n; i++) {
  				update(i + 1, a[i]);
  			}
  		}
  
  		void update(int i, long val) {
  			while (i < farr.length) {
  				farr[i] += val;
  				i += (i & -i);
  			}
  		}
  
  		long sum(int i) {
  			long sum = 0L;
  			while (i > 0) {
  				sum += farr[i];
  				i -= (i & -i);
  			}
  			return sum;
  		}
  	}
  
  // ****CLASS PAIR ************************************************
  //	static class Pair implements Comparable<Pair> {
  //		int sp;
  //		int ep;
  //
  //		Pair(int sp, int ep) {
  //			this.sp = sp;
  //			this.ep = ep;
  //		}
  //
  //		public int compareTo(Pair o) {
  //			return this.sp - o.sp;
  //		}
  //
  //	}
  
  	static class Pair implements Comparable<Pair> {
  		char ch;
  		ArrayList<Integer> idxs;
  
  		Pair(char ch, ArrayList<Integer> idxs) {
  			this.ch = ch;
  			this.idxs = idxs;
  		}
  
  		public int compareTo(Pair o) {
  			return o.idxs.size() - this.idxs.size();
  		}
  
  	}
  
  	static class Edge implements Comparable<Edge> {
  		int u;
  		int v;
  		int wt;
  
  		Edge(int u, int v, int wt) {
  			this.u = u;
  			this.v = v;
  			this.wt = wt;
  		}
  
  		public int compareTo(Edge o) {
  			return this.wt - o.wt;
  		}
  	}
  
  // *************Disjoint Set Union*********//
  	static class dsu {
  		int[] par;
  		int[] rank;
  
  		dsu(int n) {
  			par = new int[n + 1];
  			rank = new int[n + 1];
  			for (int i = 0; i <= n; i++) {
  				par[i] = i;
  				rank[i] = 1;
  			}
  		}
  
  		int find(int a) {
  			if (par[a] == a) {
  				return a;
  			}
  			int x = find(par[a]);
  			par[a] = x;
  			return x;
  		}
  
  		boolean union(int a, int b) {
  			int pa = find(a);
  			int pb = find(b);
  			if (pa == pb) {
  				return false;
  			}
  			if (rank[pa] > rank[pb]) {
  				par[pb] = pa;
  			} else if (rank[pb] > rank[pa]) {
  				par[pa] = pb;
  			} else {
  				par[pa] = pb;
  				rank[pb]++;
  			}
  			return true;
  		}
  
  	}
  
  	// **************NCR%P******************
  	static long ncr(int n, int r) {
  		if (r > n)
  			return (long) 0;
  		long[] fact = new long[(int) 1e6 + 10];
  		fact[0] = fact[1] = 1;
  		for (int i = 2; i < fact.length; i++) {
  			fact[i] = ((long) (i % mod) * (long) (fact[i - 1] % mod)) % mod;
  		}
  		long res = fact[n] % mod;
  		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;
  		return res;
  	}
  
  	static ArrayList<Integer> divisors(int n) {
  		ArrayList<Integer> al = new ArrayList<>();
  		for (int i = 1; i * i <= n; i++) {
  			if (n % i == 0) {
  				if (n == i * i) {
  					al.add(i);
  				} else {
  					al.add(i);
  					al.add(n / i);
  				}
  			}
  		}
  		Collections.sort(al);
  		return al;
  	}
  
  	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 % mod;
  	}
  
  	private static boolean pow2(int i) {
  		return (i & (i - 1)) == 0;
  	}
  
  	private static void sort(int[] arr) {
  		int n = arr.length;
  		ArrayList<Integer> res = new ArrayList<>();
  		for (int a : arr) {
  			res.add(a);
  		}
  		Collections.sort(res);
  		for (int i = 0; i < n; i++) {
  			arr[i] = res.get(i);
  		}
  	}
  
  	private static void sort(long[] arr) {
  		int n = arr.length;
  		ArrayList<Long> res = new ArrayList<>();
  		for (long a : arr) {
  			res.add(a);
  		}
  		Collections.sort(res);
  		for (int i = 0; i < n; i++) {
  			arr[i] = res.get(i);
  		}
  	}
  
  	private static void revSort(int[] arr) {
  		int n = arr.length;
  		ArrayList<Integer> res = new ArrayList<>();
  		for (int a : arr) {
  			res.add(a);
  		}
  		Collections.sort(res, Collections.reverseOrder());
  		for (int i = 0; i < n; i++) {
  			arr[i] = res.get(i);
  		}
  	}
  
  	private static ArrayList<Integer> sieveOfEratosthenes(int n) {
  		boolean[] arr = new boolean[n + 1];
  
  		arr[0] = arr[1] = true;
  		for (int i = 2; i * i <= n; i++) {
  			if (!arr[i]) {
  				for (int j = i * i; j <= n; j += i) {
  					arr[j] = true;
  				}
  			}
  		}
  		ArrayList<Integer> primes = new ArrayList<>();
  		for (int i = 2; i <= n; i++) {
  			if (!arr[i]) {
  				primes.add(i);
  			}
  		}
  		return primes;
  	}
  
  	private static ArrayList<Integer> segmentedSieve(int s, int e) {
  		int len = (int) (Math.sqrt(e) + 1);
  		ArrayList<Integer> primes = sieveOfEratosthenes(len);
  		boolean[] arr2 = new boolean[e - s + 1];
  		if (s == 1) {
  			arr2[0] = true;
  		}
  		ArrayList<Integer> res = new ArrayList<>();
  		for (int p : primes) {
  
  			int st = (int) (p * (Math.ceil((double) s / p)));
  			if (st < s) {
  				st += p;
  			}
  			if (st == p) {
  				st += p;
  			}
  			for (int i = st; i <= e; i += p) {
  				arr2[i - s] = true;
  			}
  		}
  		for (int i = 0; i < arr2.length; i++) {
  			if (!arr2[i]) {
  				res.add(i + s);
  			}
  		}
  		return res;
  	}
  
  	private static long pow(int n, int k) {
  		long res = 1;
  		long num = (long) n;
  		while (k > 0) {
  			if ((k & 1) == 1) {
  				res = (res * num) % mod;
  			}
  			k /= 2;
  			num = num * num % mod;
  		}
  		return res;
  	}
  
  	private static int countDigits(int n) {
  		int c = 0;
  		while (n != 0) {
  			c++;
  			n /= 10;
  		}
  		return c;
  	}
  
  	private static boolean palindrome(String str) {
  		int s = 0;
  		int e = str.length() - 1;
  		while (s < e) {
  			if (str.charAt(s) != str.charAt(e)) {
  				return false;
  			}
  			s++;
  			e--;
  		}
  		return true;
  	}
  
  	private static void reverse(int[] arr, int s, int e) {
  		while (s < e) {
  			int temp = arr[s];
  			arr[s++] = arr[e];
  			arr[e--] = temp;
  		}
  	}
  
  	private static int getMax(int[] arr, int s, int e) {
  		int maxi = s;
  		for (int i = s + 1; i <= e; i++) {
  			if (arr[i] > arr[maxi]) {
  				maxi = i;
  			}
  		}
  		return maxi;
  	}
  
  	private static int getMin(int[] arr, int s, int e) {
  		int mini = s;
  		for (int i = s + 1; i <= e; i++) {
  			if (arr[i] < arr[mini]) {
  				mini = i;
  			}
  		}
  		return mini;
  	}
  
  	// ******LOWEST COMMON MULTIPLE************************
  	private static long lcm(long n1, long n2) {
  		return (n1 * n2) / gcd(n1, n2);
  	}
  
  	private static int lcm(int n1, int n2) {
  		return (n1 * n2) / gcd(n1, n2);
  	}
  
  	// ***********GCD*****************
  	private static long gcd(long num1, long num2) {
  		if (num2 == 0) {
  			return num1;
  		}
  		return gcd(num2, num1 % num2);
  	}
  
  	private static int gcd(int num1, int num2) {
  		if (num2 == 0) {
  			return num1;
  		}
  		return gcd(num2, num1 % num2);
  	}
  
  	// **************PRIME FACTORIZE **********************************//
  	static TreeMap<Long, Long> prime(long n) {
  		TreeMap<Long, Long> h = new TreeMap<>();
  		long num = n;
  		for (int i = 2; i <= Math.sqrt(num); i++) {
  			if (n % i == 0) {
  				long nt = 0L;
  				while (n % i == 0) {
  					n = n / i;
  					nt++;
  				}
  				h.put(i * 1L, nt);
  			}
  		}
  		if (n != 1)
  			h.put(n, 1L);
  		return h;
  
  	}
  
  	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 println(Object... objects) {
  			print(objects);
  			writer.println();
  		}
  
  		public void close() {
  			writer.close();
  		}
  
  		public void flush() {
  			writer.flush();
  		}
  	}
  
  //*****************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[] readArray(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;
  	}
  
  }
  