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.*;
import java.math.*;
import java.util.BitSet;
public class population
{


     static int MAXN=5*1000001; static int arr[]=new int[MAXN];
    static int spf[] = new int[MAXN]; 
   
    static long power(long x, long y) 
    { 
     
    long res = 1;  
  x=x%1000000007L;
    while (y > 0)  
    { 
       
        if ((y & 1) == 1) 
            res = ((res) * (x))%1000000007L; 
  
        
        y = y >> 1;
        x = ((x)) *((x))%1000000007L;
    } 
    return res%1000000007L; 
    } 


    static void sieveOfEratosthenes(boolean prime[],int n) 
    { 
        for(int i=0;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) 
        { 
            
            if(prime[p] == true) 
            { 
        
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
    }
    
     
    static int gcd(int a, int b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 


     private static void union(int[] parent,int src,int dest)
    {
        int a = find(parent,src);
        int b = find(parent,dest);
        if(a!=b)
        parent[a]=b;
        return;
    }
    private static int find(int[] parent, int source) 
    {
        if(parent[source]==-1)
        return source;
        return find(parent,parent[source]);
    }
    
 
  
  
    public static void main(String ag[])
    {
       FastReader sc=new FastReader();
        /*ArrayList<Integer> al=new ArrayList<Integer>();*/ 
        /*String s=sc.nextLine();*/
        //hm.containsKey(); hm.get(k); hm.put(k,v); HashMap<Integer,Integer> hm=new HashMap<>();
        /*String[] arrOfStr = s.split(" "); */
        /*boolean visited[]=new boolean[arrOfStr.length];*/
     int i,j;
     int n=sc.nextInt();
      int arr[]=new int[n];
        

        HashSet hs=new HashSet();
        for(i=0;i<n;i++)
        {
        arr[i]=sc.nextInt();
        hs.add(arr[i]);
        }
       
        Arrays.sort(arr);
        Iterator itr=hs.iterator();
        ArrayList<Integer> an=new ArrayList();
                        while(itr.hasNext())
                        {
                            an.add((Integer)itr.next());
                        }
        


        Collections.sort(an);
        if(hs.size()==1)
        System.out.println(0);
        
        else if(hs.size()==2)
        {
        if((an.get(1)-an.get(0))%2==0)
        System.out.println((an.get(1)-an.get(0))/2);
        else
        System.out.println(an.get(1)-an.get(0));
        }
        
        else if(hs.size()==3)
        {
            if(an.get(2)-an.get(1)==an.get(1)-an.get(0))
            {
             System.out.println(an.get(2)-an.get(1));
            }
            else
            System.out.println(-1);
        }
        
        else
        System.out.println(-1);
        
  
    } 

  
   
  
   static long gcd(long a, long b) 
    { 
        if (a == 0) 
            return b; 
        return gcd(b % a, a); 
    } 
   public static void sieves() 
    { 
        spf[1] = 1; 
        for (int i=2; i<MAXN; i++) 
            spf[i] = i; 
        for (int i=4; i<MAXN; i+=2) 
            spf[i] = 2; 
        for (long i=3; i*i<MAXN; i++) 
        { 
            if (spf[(int)i] == i) 
            { 
                for (long j=i*i; j<MAXN; j+=i) 
                    if (spf[(int)j]==j) 
                        spf[(int)j] = (int)i; 
            } 
        } 
    } 
    static void getFactorizations(int x) 
    { 
        int num=x;
        while (x != 1) 
        { 
            arr[num]++;
            x = x / spf[x]; 
        }
    } 
}

class Edge
{
    int v,w;
    Edge(int v,int w)
    {
        this.v=v;
        this.w=w;
    }
}

class Graph
{
    int V;
    int E;
    boolean visited[];
    ArrayList<Edge> adjLists[];
    BitSet bs;
    HashSet<Integer> hs[];
 
    Graph(int V,int E)
    {
        this.V=V;
        this.E=E;
        visited=new boolean[V+1];
        adjLists=new ArrayList[V+1];
        bs=new BitSet(V+1); 
        hs=new HashSet[V+1];      
        for (int i = 0; i <=V; i++)
        {
            adjLists[i]=new ArrayList<Edge>();
            hs[i]=new HashSet<Integer>();
        }
        
    }
 

    public void addEdge(int s,int d)
    {
        
        Edge e=new Edge(d,0);
        adjLists[s].add(e);
        Edge e1=new Edge(s,0);
        adjLists[d].add(e1);
       
    }


    public void DFS(int v) 
    { 
    Iterator<Edge> i = adjLists[v].listIterator(); 
    while (i.hasNext()) 
    { 
        Edge e=i.next();
        int n = e.v; 
       
        if (bs.get(n)==false) 
        {
          hs[v].add(n);
          bs.set(n);
          DFS(n);    
        }
       
    } 
    }
    
    public boolean isEulerCircuit()
    {
       for(int i=1;i<=V;i++)
       {
           if(bs.get(i)==false||adjLists[i].size()%2!=0)
           return false;
       } 
       return true;
    }
    public void BFS()
    {
        Queue<Edge> q=new LinkedList<>();
        int price[]=new int[V+1];
        Arrays.fill(price,Integer.MAX_VALUE);
        q.add(new Edge(1,0));
        price[1]=0;
        while(!q.isEmpty())
        {
            Edge e=q.poll();
            int cost=e.w;
            if(e.v!=V)
            {
             for(Edge s:adjLists[e.v])
            {
            if(cost+s.w<price[s.v])
            {
                price[s.v]=cost+s.w;
                q.add(new Edge(s.v,cost+s.w));
            }    
            }   
            }
            
        }
        if(price[V]==Integer.MAX_VALUE)
        System.out.println(-1);
        else
        System.out.println(price[V]);
    } 
  
}


class Tcomp implements Comparator<Node>
{
    @Override
    public int compare(Node e1, Node e2) {
        if(e1.e<e2.e)
        {
        return 1;
        }
        else if(e1.e>e2.e)
        {
            return -1;
        }
        if(e1.d<e2.d)
        {
            return 1;
        }
        else if(e1.d>e2.d)
        {
            return -1;
        }

       if(e1.b<e2.b)
        {
            return 1;
        }
        else if(e1.b>e2.b)
        {
            return -1;
        }

        if(e1.a<e2.a)
        {
            return 1;
        }
       else
       {
           return -1;
       }
    }
    
}


class Node
{
    int a;
    int b;
    int c;
    int d;
    int e;
    Node(int a,int b,int c,int d,int e)
    {
        this.a=a;
        this.b=b;
        this.c=c;
        this.d=d;
        this.e=e;
       
        
    }
}


class FastReader {

    BufferedReader bf;
    StringTokenizer st;

    public FastReader() {
        bf = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(bf.readLine());
            } catch (Exception e) {
                System.out.println(e);
            }
        }
        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 = bf.readLine();
        } catch (Exception e) {
            System.out.println(e);
        }
        return str;
    }
}






