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 io, sys, atexit, os

import math as ma
from sys import exit
from decimal import Decimal as dec
from itertools import permutations


def li ():
	return list (map (int, input ().split ()))


def num ():
	return map (int, input ().split ())


def nu ():
	return int (input ())


def find_gcd ( x, y ):
	while (y):
		x, y = y, x % y
	return x


mm = 1000000007


def solve ():
	t = 1
	for tt in range (t):
		n=nu()
		a=li()
		a.sort()
		bf=-1
		for i in range(0,1001):
			x1=a[0]+i
			x2=a[0]-i
			x3=a[0]
			zp=[0]*n
			for ii in range(n):
				zp[ii]=a[ii]
			for ii in range(n):
				if(zp[ii]==x1):
					continue
				if(zp[ii]>x1):
					zp[ii]-=i
					continue
				if(zp[ii]<=x1):
					zp[ii]+=i
					continue
			fl=True
			for ii in range(n):
				if(zp[ii]!=zp[0]):
					fl=False
					break
			if(fl):
				bf=i
				break
			zp = [ 0 ] * n
			for ii in range (n):
				zp [ ii ] = a [ ii ]
			for ii in range (n):
				if (zp [ ii ] == x2):
					continue
				if (zp [ ii ] > x2):
					zp [ ii ] -= i
					continue
				if (zp [ ii ] <= x2):
					zp [ ii ] += i
					continue
			fl = True
			for ii in range (n):
				if (zp [ ii ] != zp [ 0 ]):
					fl = False
					break
			if (fl):
				bf=i
				break
			zp = [ 0 ] * n
			for ii in range (n):
				zp [ ii ] = a [ ii ]
			for ii in range (n):
				if (zp [ ii ] == x3):
					continue
				if (zp [ ii ] > x3):
					zp [ ii ] -= i
					continue
				if (zp [ ii ] <= x3):
					zp [ ii ] += i
					continue
			fl = True
			for ii in range (n):
				if (zp [ ii ] != zp [ 0 ]):
					fl = False
					break
			if (fl):
				bf=i
				break
		print(bf)





if __name__ == "__main__":
	solve ()