You are given a sequence a_1, a_2, ..., a_n consisting of n integers.

You can choose any non-negative integer D (i.e. D ≥ 0), and for each a_i you can:

  * add D (only once), i. e. perform a_i := a_i + D, or 
  * subtract D (only once), i. e. perform a_i := a_i - D, or 
  * leave the value of a_i unchanged. 



It is possible that after an operation the value a_i becomes negative.

Your goal is to choose such minimum non-negative integer D and perform changes in such a way, that all a_i are equal (i.e. a_1=a_2=...=a_n).

Print the required D or, if it is impossible to choose such value D, print -1.

For example, for array [2, 8] the value D=3 is minimum possible because you can obtain the array [5, 5] if you will add D to 2 and subtract D from 8. And for array [1, 4, 7, 7] the value D=3 is also minimum possible. You can add it to 1 and subtract it from 7 and obtain the array [4, 4, 4, 4].

Input

The first line of the input contains one integer n (1 ≤ n ≤ 100) — the number of elements in a.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 100) — the sequence a.

Output

Print one integer — the minimum non-negative integer value D such that if you add this value to some a_i, subtract this value from some a_i and leave some a_i without changes, all obtained values become equal.

If it is impossible to choose such value D, print -1.

Examples

Input


6
1 4 4 7 4 1


Output


3


Input


5
2 2 5 2 5


Output


3


Input


4
1 3 3 7


Output


-1


Input


2
2 8


Output


3
import java.util.*;
import java.io.*;
public class A  {
    static FastReader in=new FastReader();
    static final Random random=new Random();
    static long mod=1000000007L;
    static HashMap<Integer,Integer>map=new HashMap<>();

    public static void main(String args[]) throws IOException {
        int t=1;//in.nextInt();
        StringBuilder res=new StringBuilder();
        loop:
        while(t-->0)
        {
        	int n=in.nextInt();
        	int a[]=in.readintarray(n);
        	Arrays.sort(a);
        	HashSet<Integer>set=new HashSet<>();
        	for(int x: a)
        		set.add(x);
        	if(set.size()>3)
        	{
        		res.append(-1);
        		break;
        	}
        	if(set.size()==1)
        	{
        		res.append(0);
        		break;
        	}
        	if(set.size()==2)
        	{
        		ArrayList<Integer>list=new ArrayList<>();
        		for(int x: set)
        			list.add(x);
        		Collections.sort(list);
        		if((list.get(1)-list.get(0))%2==0)
        		{
        			res.append((list.get(1)-list.get(0))/2);
        		}
        		else
        		{
        			res.append(list.get(1)-list.get(0));
        		}
        	}
        	if(set.size()==3)
        	{
        		ArrayList<Integer>list=new ArrayList<>();
        		for(int x: set)
        			list.add(x);
        		Collections.sort(list);
        		if((list.get(2)-list.get(0))%2==0&&list.get(0)+(list.get(2)-list.get(0))/2==list.get(1))
        		{
        			res.append((list.get(2)-list.get(0))/2);
        		}
        		else
        		{
        			res.append(-1);
        		}
        	}
        }
        print(res);
        
    }
    
    
    
    
    static long min(long a, long b)
    {
        if(a<b)
        	return a;
        return b;
    }
    
    

   
     
    static void ruffleSort(int[] a) {
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static < E > void print(E res)
    {
        System.out.println(res);
    }


    static  int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }
    
    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }

    
    static int abs(int a)
    {
        if(a<0)
            return -1*a;
        return a;
    }

    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;
        }

        int [] readintarray(int n) {
            int res [] = new int [n];
            for(int i = 0; i<n; i++)res[i] = nextInt();
            return res;
        }
        long [] readlongarray(int n) {
            long res [] = new long [n];
            for(int i = 0; i<n; i++)res[i] = nextLong();
            return res;
        }
    }

}




