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
1
5
6 5 12 5 16
 1
5
3 5 6 11 2

2
 0

import java.util.*;
import java.lang.*;
import java.io.*;

public class CodeForces {

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	public static int gcd(int a, int b) {
		if (b == 0)
			return a;
		else
			return gcd(b, a % b);
	}

//	public static void leftRotate(int arr[],int l,int r, int d)
//    {
//		int n = r-l+1;
//        int i, j, k, temp;
//        int g_c_d = gcd(d, n);
//        for (i = 0; i < g_c_d; i++) {
//            /* move i-th values of blocks */
//            temp = arr[i];
//            j = i;
//            while (true) {
//                k = j + d;
//                if (k >= n)
//                    k = k - n;
//                if (k == i)
//                    break;
//                arr[j] = arr[k];
//                j = k;
//            }
//            arr[j] = temp;
//        }
//    }

	public static void leftRotate(int arr[], int l, int r, int d) {
		for (int i = 0; i < d; i++)
			leftRotatebyOne(arr, l, r);
	}

	public static void leftRotatebyOne(int arr[], int l, int r) {
		int i, temp;
		temp = arr[l];
		for (i = l; i < r; i++)
			arr[i] = arr[i + 1];
		arr[r] = temp;
	}

	public static String last(String s) {
		int n = s.length();
		return s.substring(n - 2, n);
	}
	
	 static long __gcd(long a, long b) 
	    { 
	        return b == 0? a:__gcd(b, a % b);    
	    }
	
	static long GcdOfArray(long[] arr, int idx)
	{
	    if (idx == arr.length - 1) {
	        return arr[idx];
	    }
	    long a = arr[idx];
	    long b = GcdOfArray(arr, idx + 1);
	    return __gcd(a, b); // __gcd(a,b) is inbuilt library function
	}

	public static void main(String[] args) {
		FastReader sc = new FastReader();

		int t = sc.nextInt();

		while (t-- > 0) {
			int n = sc.nextInt();
			long[] arr = new long[n];
			long d=0;
			ArrayList<Long> odd = new ArrayList<>();
			ArrayList<Long> even = new ArrayList<>();
			
			
			for(int i=0;i<n;i++) {
				arr[i]=sc.nextLong();
				if(i%2==0) {
					even.add(arr[i]);
				}else {
					odd.add(arr[i]);
				}
			}
			
			long[] o = new long[odd.size()];
			long[] e = new long[even.size()];
			
			int i=0;
			for(Long x:odd) {
				o[i]=x;
				i++;
			}

			i=0;
			for(Long x:even) {
				e[i]=x;
				i++;
			}
			i=0;
			
			
			long go = GcdOfArray(o, 0);
			long ge = GcdOfArray(e, 0);
			int flag=0;
			long ans=0;
			
			if(go!=1) {
				for(Long x:even) {
					flag=1;
					if(x%go==0) {
						flag=-1;
						break;
					}
				}
			}
			if(flag==1) {
				ans=go;
			}
			
			if(flag==-1 && ge!=1) {
				for(Long x:odd) {
					flag=1;
					if(x%ge==0) {
						flag=-1;
						break;
					}
				}
			}
			if(flag==1 && ans==0) {
				ans=ge;
			}
			
			
			System.out.println(ans);
		}
	}

}

