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 Main {
    public static void main(String[] args) throws IOException{
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new PrintStream(System.out));
        int n=Integer.parseInt(f.readLine());
        StringTokenizer st=new StringTokenizer(f.readLine());
        int[]arr=new int[n];
        for(int i=0;i<n;i++){
            arr[i]=Integer.parseInt(st.nextToken());
        }
        boolean printed=true;
        for(int i=0;i<n;i++){
            if(arr[i]!=arr[0]){
                printed=false;
            }
        }
        if(printed){
            System.out.println(0);
        }
        a:
        for(int i=1;i<=100;i++){
            if(printed)break;
            HashMap<Integer,Integer>hm=new HashMap<>();

            for(int j=0;j<n;j++){
                if(hm.containsKey(arr[j]+i)){
                   hm.put(arr[j]+i,hm.get(arr[j]+i)+1);
                }
                else{
                    hm.put(arr[j]+i,1);
                }
                if(hm.containsKey(arr[j]-i)){
                    hm.put(arr[j]-i,hm.get(arr[j]-i)+1);
                }
                else{
                    hm.put(arr[j]-i,1);
                }
                if(hm.containsKey(arr[j])){
                    hm.put(arr[j],hm.get(arr[j])+1);
                }
                else{
                    hm.put(arr[j],1);
                }
            }

            for (Integer key : hm.keySet()) {
                if(hm.get(key)==n){
                    printed=true;
                    System.out.println(i);
                    break a;
                }
            }
        }
        if(!printed){
            System.out.println(-1);
        }
        f.close();
        out.close();
    }
}
//import java.util.*;
//import java.io.*;
//
//public class Main {
//    public static void main(String[] args) throws IOException{
//        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
//        PrintWriter out = new PrintWriter(new PrintStream(System.out));
//        int n=Integer.parseInt(f.readLine());
//        StringTokenizer st=new StringTokenizer(f.readLine());
//        int []arr=new int[n];
//        for(int i=0;i<n;i++){
//            arr[i]=Integer.parseInt(st.nextToken());
//        }
//        HashSet<Integer>has=new HashSet<>();
//        has.add(1);
//        boolean a=has.contains(1);
//        boolean bool=true;
//        po:
//        for(int i=0;i<=100;i++){
//            HashMap<Integer>hs=new HashSet<>();
//            p:
//            for(int j=0;j<n;j++){
//                if(hs.contains(arr[j]+i)|| hs.contains(arr[j]-i) || hs.contains(arr[j])){
//                    hs.add(arr[j]+i);
//                    hs.add(arr[j]-i);
//                    hs.add(arr[j]);
//                }
//                else{
//                   if(j==0){
//                       hs.add(arr[j]+i);
//                       hs.add(arr[j]-i);hs.add(arr[j]);
//
//                       continue p;
//                   }
//                   else{
//                       continue po;
//                   }
//
//                }
//            }
//            Iterator<Integer> it = hs.iterator();
//            int dif=0;
//            op:
//            while(it.hasNext()){
//                int o=it.next();
//                for(int j=0;j<n;j++){
//                    if((Math.abs(arr[j]-o)!=dif && o-arr[j]!=0) && j!=0){
//                        continue op;
//                    }
//                    if(o-arr[j]!=0){
//                        dif=arr[j]-o;
//                        dif= Math.abs(dif);
//                    }
//                }
//                bool=false;
//                System.out.println(dif);
//                break po;
//            }
//
//        }
//        if(bool){
//            out.println(-1);
//        }
//        f.close();
//        out.close();
//    }
//}