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
//package que_c;

import java.io.*;
import java.util.*;
import java.math.*;

public class utkarsh {

    InputStream is;
    PrintWriter out;
    
    long mod = (long)(1e9 + 7), inf = (long)(3e18);
    
    void solve() {
        //SZ = sieve(); //SZ = 1000001;
        int n = ni();
        TreeSet <Integer> h = new TreeSet<>();
        for(int i = 0; i < n; i++)  h.add(ni());
        if(h.size() == 1)   out.println(0);
        else if(h.size() == 2) {
            int a[] = new int[2];
            int z = 0;
            for(int x : h)  a[z++] = x;
            int ans = a[1] - a[0];
            if(ans%2 == 0)  ans /= 2;
            out.println(ans);
        } else if(h.size() == 3) {
            int a[] = new int[h.size()];
            int z = 0;
            for(int x : h)  a[z++] = x;
            int ans = a[1] - a[0];
            for(int i = 1; i < z; i++)  if(a[i] - a[i-1] != ans) {
                out.println(-1);   return;
            }
            out.println(ans);
        } else {
            out.println(-1);
        }
    }
    
    //--------- Extra Template -----------
    
    int P[], S[], SZ, NP = 15485900;
    boolean isP[];
    
    int sieve() {
        int i, j, n = NP; 
        isP = new boolean[n]; 
        S = new int[n];
        for(i = 3; i < n; i += 2) {
            isP[i] = true;
            S[i-1] = 2;
            S[i] = i;
        }
        isP[2] = true;
        S[1] = 1;   //(UD)
        for(i = 3; i * i <= n; i += 2) {
            if( !isP[i] )   continue;
            for(j = i * i; j < n; j += i) {
                isP[j] = false;
                if(S[j] == j)   S[j] = i;
            }
        }

        P = new int[n];
        P[0] = 2;
        j = 1;
        for(i = 3; i < n; i += 2) {
            if ( isP[i] )   P[j++] = i;
        }
        P = Arrays.copyOf(P, j);
        return j;
    }

    long mp(long b, long e, long mod) {
        b %= mod;
        long r = 1;
        while(e > 0) {
            if((e & 1) == 1) {
                r *= b; r %= mod;
            }
            b *= b; b %= mod;
            e >>= 1;
        }
        return r;
    }

    //---------- I/O Template ----------
    
    public static void main(String[] args) { new utkarsh().run(); }
    void run() { 
        is = System.in; 
        out = new PrintWriter(System.out);
        solve();
        out.flush();
    }
    
    byte input[] = new byte[1024];
    int len = 0, ptr = 0;
    
    int readByte() { 
        if(ptr >= len) { ptr = 0; 
            try { len = is.read(input); } 
            catch(IOException e) { throw new InputMismatchException(); } 
            if(len <= 0) { return -1; } 
        } return input[ptr++];
    }
    boolean isSpaceChar(int c) { return !( c >= 33 && c <= 126 ); }
    int skip() { 
        int b = readByte(); 
        while(b != -1 && isSpaceChar(b)) { b = readByte(); } 
        return b;
    }
    
    char nc() { return (char)skip(); }
    String ns() { 
        int b = skip(); 
        StringBuilder sb = new StringBuilder(); 
        while(!isSpaceChar(b)) { sb.appendCodePoint(b); b = readByte(); } 
        return sb.toString();
    }
    String nLine() { 
        int b = skip(); 
        StringBuilder sb = new StringBuilder(); 
        while( !(isSpaceChar(b) && b != ' ') ) { sb.appendCodePoint(b); b = readByte(); } 
        return sb.toString();
    }
    int ni() { 
        int n = 0, b = readByte(); 
        boolean minus = false; 
        while(b != -1 && !( (b >= '0' && b <= '9') || b == '-')) { b = readByte(); } 
        if(b == '-') { minus = true; b = readByte(); } 
        if(b == -1) { return -1; }  //no input 
        while(b >= '0' && b <= '9') { n = n * 10 + (b - '0'); b = readByte(); } 
        return minus ? -n : n;
    }
    long nl() { 
        long n = 0L;    int b = readByte(); 
        boolean minus = false; 
        while(b != -1 && !( (b >= '0' && b <= '9') || b == '-')) { b = readByte(); } 
        if(b == '-') { minus = true; b = readByte(); } 
        while(b >= '0' && b <= '9') { n = n * 10 + (b - '0'); b = readByte(); } 
        return minus ? -n : n;
    }

    double nd() { return Double.parseDouble(ns()); }
    float nf() { return Float.parseFloat(ns()); }
    int[] na(int n) { 
        int a[] = new int[n]; 
        for(int i = 0; i < n; i++) { a[i] = ni(); } 
        return a;
    }
    char[] ns(int n) { 
        char c[] = new char[n]; 
        int i, b = skip(); 
        for(i = 0; i < n; i++) { 
            if(isSpaceChar(b)) { break; } 
            c[i] = (char)b; b = readByte(); 
        } return i == n ? c : Arrays.copyOf(c,i);
    }
}