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


import java.math.*;
import java.math.BigInteger;


public final class A
{    
	static PrintWriter out = new PrintWriter(System.out); 
	static StringBuilder ans=new StringBuilder();
	static FastReader in=new FastReader();
	static ArrayList<Integer> g[];
	static long mod=(long)998244353,INF=Long.MAX_VALUE;
	//	static boolean set[]; 
	static int par[],partial[];
	static int Days[],P[][];
	static int sum=0,size[];
	static int seg[],col[];
	//	static ArrayList<Long> A;
	static char X[][];
	static boolean set[][];
	static int D[],min[],A[];
	static long dp[][];
	//	static HashSet<Integer> visited,imposters;
	//	static HashSet<Integer> set;
	//	static node1 seg[];
	//static pair moves[]= {new pair(-1,0),new pair(1,0), new pair(0,-1), new pair(0,1)};
	public static void main(String args[])throws IOException
	{	
		/*
		 * star,rope,
		 * BS,LST
		 */		

		int T=i();
		outer:while(T-->0)
		{
			int N=i();
			long A[]=inputLong(N);
			long g1=0L,g2=0L;
			for(int i=0; i<N; i++)
			{
				if(i%2==0)
				{
					g1=GCD(g1,A[i]);
				}
				else  g2=GCD(g2,A[i]);
			}
			boolean a=true,b=true;
			for(int i=0; i<N; i++)
			{
				if(i%2==0)
				{
					if(A[i]%g2==0)b=false;
				}
				else 
				{
					if(A[i]%g1==0)a=false;
				}
			}
			if(a)ans.append(g1+"\n");
			else if(b)ans.append(g2+"\n");
			else ans.append(0+"\n");
		}
		out.println(ans);
		out.close();
	}
	
	static boolean can_loose(Trie root,boolean t)
	{
		if(root==null)return true; //never hits
		int cnt=0;
		for(Trie x:root.A)
		{
			if(x!=null)
			{
				cnt++;
				if(!can_loose(x,t^true)) 
				{
					//System.out.println("TRUE FOR--> "+x.ch+" "+t);
					return true;
				}
			}
		}
		if(cnt==0)return true;
		return false;
	}
	static boolean f(Trie root)
	{
		if(root==null)return false;		
//		int cnt=0;
		for(Trie x:root.A)
		{
			if(x!=null)
			{
//				cnt++;
				if(!f(x))
				{
					
					return true;
				}
			}
		}	
		return false;
	}
	static void insert(String X,Trie head)
	{
		Trie root=head;
        for(char x:X.toCharArray())
        {
        	int a=x-'a';
        	if(root.A[a]==null)root.A[a]=new Trie();
        	root=root.A[a];
        	root.ch=x;
        }
        root.ends=true;        
	}
	static boolean search(String X,Trie head)
	{
		Trie root=head;
		for(char x:X.toCharArray()) {
			int a=x-'a';
			if(root.A[a]==null)return false;
			root=root.A[a];
		}
		return root.ends;
				
	}
	static boolean starts_with(String X,Trie head)
	{
		Trie root=head;
		for(char x:X.toCharArray()) {
			int a=x-'a';
			if(root.A[a]==null)return false;
			root=root.A[a];
		}
		return true;
	}
	static int lower(ArrayList<Integer>A,int i)
	{
		int l=-1,r=A.size();
		while(r-l>1)
		{
			int m=(l+r)/2;
			if(A.get(m)>i)r=m;
			else l=m;
		}		
		return r;
	}
	static int upper(ArrayList<Integer>A,int i)
	{
		int l=-1,r=A.size();
		while(r-l>1)
		{
			int m=(l+r)/2;
			if(A.get(m)<i)l=m;
			else l=m;
		}		
		return l;
	}
	static String f()
	{
		StringBuilder X=new StringBuilder(i()+"");int p=i();
		while(p-->0)X.append("0");
		return X.toString();
	}
	static long f(int i,int g,int x,int left)
	{
		if(x<=1)return left;
		if(i<0 || g==1)return left;
		//		System.out.println(i+" "+g);
		if(dp[i][g]==0)
		{
			int next=min[i];
			int new_gcd=(int)GCD(g,x);
			//System.out.println(" factor--> "+x+" gcd--> "+g+" new-->  "+new_gcd);
			long s=0;
			int c=0;
			for(int j=next+1; j<=i; j++)
			{
				if(A[i]%new_gcd==0)
				{
					s+=new_gcd;
					c--;
				}
			}
			long a=0,b=0;
			a=f(i,g,x-1,left);
			b=s+f(next,new_gcd,x-1,left-c);
			dp[i][g]=Math.max(a, b);
		}
		return dp[i][g];
	}
	static boolean f(int A[],int B[],int x)
	{
		int c=0;
		int N=A.length;
		int l=0,r=x-1;
		for(int i=0; i<N; i++)
		{
			if(A[i]>=r && B[i]>=l)
			{
				r--;
				l++;
				c++;				
			}
			if(c>=x)return true;
		}
		return false;
	}
	static boolean isPalindrome(int A[])
	{
		int i=0,j=A.length-1;
		while(i<j)
		{
			if(A[i]!=A[j])return false;
			i++;
			j--;
		}
		return true;
	}
	static boolean isPalindrome(int A[],int x)
	{
		int i=0,j=A.length-1;
		while(i<j)
		{
			if(A[i]!=A[j])
			{
				if(A[i]==x)i++;
				else if(A[j]==x)j--;
				else return false;
			}
			else
			{
				i++;
				j--;
			}
		}
		return true;
	}
	static long fact[];
	static double nCr(int a,int b)
	{
		double x=fact[a], y=fact[b]*fact[a-b];
		return x/y;
	}
	static int f(ArrayList<Integer> A,int x)
	{
		int l=-1,r=A.size();
		while(r-l>1)
		{
			int m=(l+r)/2;
			if(A.get(m)<x)l=m;
			else r=m;
		}
		return r;
	}
	static boolean f(long a,long b,long x)
	{
		if(b==0)
		{
			return (x==a || x==b);
		}
		if(a<x)return false;
		else
		{
			if(a%b==x%b)return true;
			return f(b,a%b,x);
		}
	}

	static void dfs(int n,int p)
	{
		if(p!=-1)D[n]=D[p]+1;
		for(int c:g[n])
		{
			if(c!=p)
				dfs(c,n);
		}
	}
	static long f(long a,long A[])
	{
		int l=-1,r=A.length;
		while(r-l>1)
		{
			int m=(l+r)/2;
			if(A[m]<=a)l=m;
			else r=m;
		}
		return A[l];
	}
	static void build(int v,int tl,int tr,int A[])
	{
		if(tl==tr)
		{
			seg[v]=A[tl];
			return;
		}
		int tm=(tl+tr)/2;
		build(v*2,tl,tm,A);
		build(v*2+1,tm+1,tr,A);
		seg[v]=Math.min(seg[v*2], seg[v*2+1]);
	}
	static void update(int v,int tl,int tr,int index,int x)
	{
		if(tl==tr && tl==index)
		{
			seg[v]=x;
			return;
		}		
		int tm=(tl+tr)/2;
		if(index<=tm)update(v*2,tl,tm,index,x);
		else update(v*2+1,tm+1,tr,index,x);
		seg[v]=Math.min(seg[v*2], seg[v*2+1]);
	}
	static int ask(int v,int tl,int tr,int l,int r)
	{
		//		System.out.println(v);
		//		if(v>100)return 0;
		if(l>r)return Integer.MAX_VALUE;
		if(tl==l && tr==r)return seg[v];
		int tm=(tl+tr)/2;
		int a=ask(v*2,tl,tm,l,Math.min(tm, r));
		//		System.out.println("for--> "+(v)+" tm--> "+(tm+1)+" tr--> "+tr+" l--> "+Math.max(l, tm+1)+" r--> "+r);
		int b=ask(v*2+1,tm+1,tr,Math.max(l, tm+1),r);
		return Math.min(a, b);
	}
	static int find(int a)
	{
		if(par[a]<0)return a;
		return par[a]=find(par[a]);
	}
	static void union(int a,int b)
	{
		a=find(a);
		b=find(b);
		if(a!=b)
		{
			par[a]+=par[b];
			par[b]=a;
		}
	}
	static int ask(int a,int b)
	{
		System.out.println("? "+a+" "+b);
		return i();
	}




	static long and(int i,int j)
	{
		System.out.println("and "+i+" "+j);
		return l();
	}
	static long or(int i,int j)
	{
		System.out.println("or "+i+" "+j);
		return l();
	}
	static boolean is_Sorted(int A[])
	{
		int N=A.length;
		for(int i=1; i<=N; i++)if(A[i-1]!=i)return false;
		return true;
	}
	static boolean f(StringBuilder sb,String Y,String order)
	{
		StringBuilder res=new StringBuilder(sb.toString());
		HashSet<Character> set=new HashSet<>();
		for(char ch:order.toCharArray())
		{
			set.add(ch);
			for(int i=0; i<sb.length(); i++)
			{
				char x=sb.charAt(i);
				if(set.contains(x))continue;
				res.append(x);
			}
		}

		String str=res.toString();
		return str.equals(Y);
	}
	static boolean all_Zero(int f[])
	{
		for(int a:f)if(a!=0)return false;
		return true;
	}
	static long form(int a,int l)
	{
		long x=0;
		while(l-->0)
		{
			x*=10;
			x+=a;
		}
		return x;
	}
	static int count(String X)
	{
		HashSet<Integer> set=new HashSet<>();
		for(char x:X.toCharArray())set.add(x-'0');
		return set.size();
	}


	//	static void build(int v,int tl,int tr,long A[])
	//	{
	//		if(tl==tr)
	//		{
	//			seg[v]=A[tl];
	//		}
	//		else
	//		{
	//			int tm=(tl+tr)/2;
	//			build(v*2,tl,tm,A);
	//			build(v*2+1,tm+1,tr,A);
	//			seg[v]=Math.min(seg[v*2], seg[v*2+1]);
	//		}
	//	}

	static int [] sub(int A[],int B[])
	{
		int N=A.length;
		int f[]=new int[N];
		for(int i=N-1; i>=0; i--)
		{
			if(B[i]<A[i])
			{
				B[i]+=26;
				B[i-1]-=1;
			}
			f[i]=B[i]-A[i];
		}
		for(int i=0; i<N; i++)
		{
			if(f[i]%2!=0)f[i+1]+=26;
			f[i]/=2;
		}
		return f;
	}





	static int max(int a ,int b,int c,int d)
	{
		a=Math.max(a, b);
		c=Math.max(c,d);
		return Math.max(a, c);
	}
	static int min(int a ,int b,int c,int d)
	{
		a=Math.min(a, b);
		c=Math.min(c,d);
		return Math.min(a, c);
	}



	static HashMap<Integer,Integer> Hash(int A[])
	{
		HashMap<Integer,Integer> mp=new HashMap<>();
		for(int a:A)
		{
			int f=mp.getOrDefault(a,0)+1;
			mp.put(a, f);
		}
		return mp;
	}
	static long mul(long a, long b)
	{
		return ( a %mod * 1L * b%mod )%mod;
	}
	static void swap(int A[],int a,int b)
	{
		int t=A[a];
		A[a]=A[b];
		A[b]=t;
	}



	static boolean isSorted(int A[])
	{
		for(int i=1; i<A.length; i++)
		{
			if(A[i]<A[i-1])return false;
		}
		return true;
	}

	static boolean isDivisible(StringBuilder X,int i,long num)
	{
		long r=0;
		for(; i<X.length(); i++)
		{
			r=r*10+(X.charAt(i)-'0');
			r=r%num;
		}
		return r==0;
	}    



	static int lower_Bound(int A[],int low,int high, int x) 
	{ 
		if (low > high) 
			if (x >= A[high]) 
				return A[high]; 

		int mid = (low + high) / 2; 

		if (A[mid] == x) 
			return A[mid]; 

		if (mid > 0 && A[mid - 1] <= x && x < A[mid]) 
			return A[mid - 1]; 

		if (x < A[mid]) 
			return lower_Bound( A, low, mid - 1, x); 

		return lower_Bound(A, mid + 1, high, x); 
	} 

	static String f(String A)
	{
		String X="";
		for(int i=A.length()-1; i>=0; i--)
		{
			int c=A.charAt(i)-'0';
			X+=(c+1)%2;
		}
		return X;
	}

	static void sort(long[] a) //check for long
	{
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

	static String swap(String X,int i,int j)
	{
		char ch[]=X.toCharArray();
		char a=ch[i];
		ch[i]=ch[j];
		ch[j]=a;
		return new String(ch);
	}

	static int sD(long n)  
	{  

		if (n % 2 == 0 )  
			return 2;  

		for (int i = 3; i * i <= n; i += 2) {  
			if (n % i == 0 )  
				return i;  
		}  

		return (int)n;  
	}  

	static void setGraph(int N)
	{
		//		tot=new int[N+1];
		partial=new int[N+1];
		Days=new int[N+1];
		P=new int[N+1][(int)(Math.log(N)+10)];
		//		set=new boolean[N+1];
		g=new ArrayList[N+1];
		D=new int[N+1];
		for(int i=0; i<=N; i++)
		{

			g[i]=new ArrayList<>();		
			Days[i]=-1;
			D[i]=Integer.MAX_VALUE;
			//D2[i]=INF;
		}
	}



	static  long pow(long a,long b)
	{
		long pow=1;
		long x=a;
		while(b!=0)
		{
			if((b&1)!=0)pow=(pow*x)%mod;
			x=(x*x)%mod;
			b/=2;
		}
		return pow;
	}

	static long toggleBits(long x)//one's complement || Toggle bits
	{
		int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;

		return ((1<<n)-1)^x;
	}

	static int countBits(long a)
	{
		return (int)(Math.log(a)/Math.log(2)+1);
	}

	static long fact(long N)
	{ 
		long n=2; 
		if(N<=1)return 1;
		else
		{
			for(int i=3; i<=N; i++)n=(n*i)%mod;
		}
		return n;
	}

	static int kadane(int A[])
	{
		int lsum=A[0],gsum=A[0];
		for(int i=1; i<A.length; i++)
		{
			lsum=Math.max(lsum+A[i],A[i]);
			gsum=Math.max(gsum,lsum);
		}
		return gsum;
	}

	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

	static boolean isPrime(long 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; 
	}
	static void print(char A[])
	{
		for(char c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(boolean A[])
	{
		for(boolean c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(int A[])
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();	
	}
	static void print(long A[])
	{
		for(long i:A)System.out.print(i+ " ");
		System.out.println();

	}
	static void print(boolean A[][])
	{
		for(boolean a[]:A)print(a);
	}
	static void print(long A[][])
	{
		for(long a[]:A)print(a);
	}
	static void print(int A[][])
	{
		for(int a[]:A)print(a);
	}
	static void print(ArrayList<Integer> A)
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();
	}

	static int i()
	{
		return in.nextInt();
	}

	static long l()
	{
		return in.nextLong();
	}

	static int[] input(int N){
		int A[]=new int[N];
		for(int i=0; i<N; i++)
		{
			A[i]=in.nextInt();
		}
		return A;
	}

	static long[] inputLong(int N)     {
		long A[]=new long[N];
		for(int i=0; i<A.length; i++)A[i]=in.nextLong();
		return A;
	}

	static long GCD(long a,long b) 
	{
		if(b==0)
		{
			return a;
		}
		else return GCD(b,a%b);
	}

}
class Trie
{
	char ch;
	Trie A[];
	boolean ends;
	Trie()
	{
		ch='*';
		A=new Trie[26];
		ends=false;
	}
}
class pair1 implements Comparable<pair1>
{
	int a, index;
	pair1(int b,int i)
	{
		a=b;
		index=i;
	}
	public int compareTo(pair1 x)
	{
		return x.a-this.a;
	}
}

//Code For FastReader
//Code For FastReader
//Code For FastReader
//Code For FastReader
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;
	}

}