Problem: Let's call two numbers similar if their binary representations contain the same number of digits equal to 1. For example:

  * 2 and 4 are similar (binary representations are 10 and 100); 
  * 1337 and 4213 are similar (binary representations are 10100111001 and 1000001110101); 
  * 3 and 2 are not similar (binary representations are 11 and 10); 
  * 42 and 13 are similar (binary representations are 101010 and 1101). 



You are given an array of n integers a_1, a_2, ..., a_n. You may choose a non-negative integer x, and then get another array of n integers b_1, b_2, ..., b_n, where b_i = a_i ⊕ x (⊕ denotes bitwise XOR).

Is it possible to obtain an array b where all numbers are similar to each other?

Input

The first line contains one integer n (2 ≤ n ≤ 100).

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 2^{30} - 1).

Output

If it is impossible to choose x so that all elements in the resulting array are similar to each other, print one integer -1.

Otherwise, print any non-negative integer not exceeding 2^{30} - 1 that can be used as x so that all elements in the resulting array are similar.

Examples

Input


2
7 2


Output


1


Input


4
3 17 6 0


Output


5


Input


3
1 2 3


Output


-1


Input


3
43 12 12


Output


1073709057

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main{
	static int n,in[];
	static int mod=(int)1e9+9,prime=31;
	static class array implements Comparable<array>{
		int[]arr;
		int hash;
		array(int[]a){
			arr=a;
			long p=1;
			long ans=0;
			for(int i=0;i<n;i++) {
				long add=(p*arr[i])%mod;
				ans=(ans+add)%mod;
				p=(p*prime)%mod;
			}
			hash=(int)ans;
		}
		@Override
		public int compareTo(array o) {
			for(int i=0;i<n;i++) {
				if(arr[i]>o.arr[i]) {
					return 1;
				}
				if(arr[i]<o.arr[i]) {
					return -1;
				}
			}
			return 0;
		}
		
		@Override
		public boolean equals(Object obj) {
			for(int i=0;i<n;i++) {
				if(arr[i]!=((array)obj).arr[i]) {
					return false;
				}
				
			}
			return true;
		}
		@Override
		public int hashCode() {
			return hash;
		}
	}
	static int solve() {
		int first15bits=(1<<15)-1;
		int last15bits=first15bits<<15;
		HashMap<array, Integer>map=new HashMap<array, Integer>();
		for(int msk=0;msk<(1<<15);msk++) {
			int[]cur=new int[n];
			int min=77;
			for(int i=0;i<n;i++) {
				int res=msk^(in[i]&first15bits);
				cur[i]=Integer.bitCount(res);
				min=Math.min(min, cur[i]);
			}
			for(int i=0;i<n;i++) {
				cur[i]-=min;
			}
			array x=new array(cur);
			
			if(!map.containsKey(x)) {
				map.put(x, msk);
			}
		}
		for(int msk=0;msk<(1<<15);msk++) {
			int curMsk=msk<<15;
			int[]wanted=new int[n];
			int max=0;
			for(int i=0;i<n;i++) {
				int res=curMsk^(in[i]&last15bits);
				wanted[i]=Integer.bitCount(res);
				max=Math.max(max, wanted[i]);
			}
			for(int i=0;i<n;i++) {
				wanted[i]=max-wanted[i];
			}
			array x=new array(wanted);
			if(map.containsKey(x)) {
				int ans=map.get(x)|curMsk;
				return ans;
			}
		}
		return -1;
	}
	static void main() throws Exception{
		n=sc.nextInt();
		in=sc.intArr(n);
		boolean same=true;
		for(int i=1;i<n && same;i++) {
			same&=(in[i]==in[i-1]);
		}
		if(same) {
			pw.println(0);
			return;
		}
//		int ans=solve();
//		System.out.println(ans);
//		for(int i=0;i<n;i++) {
//			System.out.println(Integer.bitCount(in[i]^ans)+" "+(in[i]^ans));
//		}
		pw.println(solve());
	}
	public static void main(String[] args) throws Exception{
		sc=new MScanner(System.in);
		pw = new PrintWriter(System.out);
		main();
		pw.flush();
	}
	static PrintWriter pw;
	static MScanner  sc;
	static class MScanner {
		StringTokenizer st;
		BufferedReader br;
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int[] intArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public long[] longArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public int[] intSortedArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public long[] longSortedArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public Integer[] IntegerArr(int n) throws IOException {
	        Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public Long[] LongArr(int n) throws IOException {
	        Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
	static void shuffle(int[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*(i+1));
			int tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
	static void shuffle(long[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*(i+1));
			long tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
}