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.*;
import java.math.BigInteger;
import java.util.*;

//Mann Shah [ DAIICT ].
//fast io

public class Main {
	public static int mod = (int) (1e9 + 7);
	public static long inf = (long) 1e15 + 42;
	static InputReader in;
	static PrintWriter out;

	public static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}

	public static void main(String args[]) {

		in = new InputReader(System.in);
		out = new PrintWriter(System.out);
		int n = in.nextInt();
		int[] a = new int[n];
		for(int i=0;i<n;i++) {
			a[i]=in.nextInt();
		}
		

		ArrayList<Integer> hs = new ArrayList();
		
		for(int i=0;i<n;i++) {
			if(!hs.contains(a[i])) {
				hs.add(a[i]);
			}
		}
		
		if(hs.size()>3) {
			out.println("-1");
		}
		else {
			Collections.sort(hs);
			if(hs.size()==1) {
				out.println("0");
			}
			else if(hs.size()==2) {
				int vv = hs.get(1)-hs.get(0);
				
				if(vv%2==0) {
					out.println(vv/2);
				}
				else {
					out.println(vv);
				}
				
			}
			else {
				if(hs.get(1)-hs.get(0) == hs.get(2)-hs.get(1)) {
					out.println(hs.get(1)-hs.get(0));
				}
				else {
					out.println("-1");
				}
			}
		}
		
		
		
		out.close();
	}

	static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

		public long[] nextLongArray(int n) {
			long a[] = new long[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextLong();
			}
			return a;
		}

		public String readString() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}

	}

}

// For Pair sorting

// Arrays.sort(arr,new Comparator<Pair>() {
// @Override public int compare(Pair p1, Pair p2)
// {
// return p1.x - p2.x;
// }
// });

// Pair arr[] = new Pair[n];
// arr[0] = new Pair(10, 20);
class Pair {
	int x;
	int y;

	// Constructor
	public Pair(int x, int y) {
		this.x = x;
		this.y = y;
	}
}

// // Comparator to sort the pair according to first element.
// Arrays.sort(arr, new Comparator<Pair>() {
// @Override public int compare(Pair p1, Pair p2){
//  return p1.x - p2.x;
// }
// });

class couple implements Comparable<couple> {
	int x, y;

	public couple(int m, int f) {
		x = m;
		y = f;
	}

	public int compareTo(couple o) {

		return x - o.x;
	}
}