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.*;
public class equal {
public static int[] turn(int x , int[]y) {
	for(int i=0;i<y.length;i++) {
		if(y[i]==x)
			y[i]=-1;
	}
return y;
}
public static int[] different (int []x) {
	int []y=new int[3];
	int []f= {-1,-1};
	int g=0;
	for(int i=0;i<x.length;i++) {
		for(int j=0;j<x.length;j++) {
			if(x[i]!=x[j]&x[i]!=-1) {
				if(g<3) {
				y[g]=x[i];
				turn(x[i],x);
				}
				g++;
			}
			if(g>3)
				return f;	
		}
	}
Arrays.sort(y);
return y;
}
public static int[] onlytwo(int[]x) {
	int g[]=new int [2];
	Arrays.sort(x);
	if(x[0]==0) {
		g[0]=x[1];
		g[1]=x[2];
		return g;
	}
	else
		return x;
		
}
public static String ToString (int []x) {
	String s="";
	for(int i=0;i<x.length;i++) {
		s=s+x[i]+" ";
	}
return s;
}
public static void main (String []args) {
	Scanner a=new Scanner(System.in);
	Scanner b=new Scanner(System.in);
	int g=0;
	int[]f= {-1,-1};
	int[]y=new int [1];
	y[0]=a.nextInt();
	int []x=new int[y[0]]; 
	int r=0;
	for(int i=0;i<y[0];i++) {
		x[i]=a.nextInt();
	}
x=onlytwo(different(x));
//System.out.println(ToString(x));
if((x[0]==f[0])) 
	System.out.println(-1);
else {
if(x.length==3) {
	r=(x[2]-x[0])/2;
	if(x[0]+r==x[1]&x[2]-r==x[1])
		System.out.println(r);
	else
		System.out.println(-1);
}
	else {
	g=(x[1]-x[0])/2;
	r=(x[1]-x[0]);
	if(x[0]+g==x[1]-g)
		System.out.println(g);
	else
		System.out.println(r);
	}
}
}
}
