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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.*;
 
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 void main(String[] args) {
        FastReader in = new FastReader();
        
        int n = in.nextInt();
        int a[] = new int[n];
        int i = 0;
        for(i=0;i<n;i++) {
            a[i] = in.nextInt();
        }
        
        Arrays.sort(a);
        int f = 1;
        
        
        int count = 1;
        for(i=0;i<n-1;i++) {
            if(a[i] != a[i+1]) {
                count++;
            }
        }
        
        int ans;
        if(count == 2) {
            ans = a[n-1] - a[0];
            if(ans%2 == 0) {
                ans = ans/2;
            }
        } else {
            int found = 0;
             ans = (a[0] + a[n-1])/2;
             for(i=0;i<n;i++) {
                 if(a[i] == ans) {
                     found = 1;
                     break;
                 }
             }
             if(found == 1) {
                 ans = ans - a[0];
             } else {
                 ans = -1;
             }
             
        }
       
        if((a[0] + a[n-1])%2!=0 && count ==3) {
            f = 0;
        }
        if(count>3) {
            f=0;
        }
        if(f==0) {
            System.out.println(-1);
        }else {
            System.out.println(ans);
        }
    }
}
 