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 atexit, io, sys, collections, math, heapq, fractions, bisect,copy
buffer = io.BytesIO() 
sys.stdout = buffer
@atexit.register 
def write(): sys.__stdout__.write(buffer.getvalue())   
class SGT(object):

	def __init__(self, a):
		self.a = a[::]
		self.t = self.build(self.a)

	def build(self, a):
		t = [0 for _ in range(len(a)<< 1)]
		for i in range(len(a)): t[i+len(a)] = a[i]
		for i in range(len(a)-1, 0, -1):t[i] += t[2*i] + t[2*i +1]
		return t

	## a[i] = val
	def update(self,i,val):
		delta = val - self.a[i]
		self.a[i] += delta 
		i += len(self.a)
		while(i > 0):
			self.t[i] += delta
			i >>= 1
	## queries l and r included
	def query(self,l,r):
		l += len(self.t) // 2
		r += len(self.t) // 2
		ans = 0
		while(l <= r):
			if l % 2: 
				ans += self.t[l]
				l +=1
			if r % 2 == 0: 
				ans += self.t[r]
				r -=1
			l >>= 1
			r >>= 1
		return ans
####################################
n = int(raw_input())
ais = map(int, raw_input().split())
def f(ais):
	cc = collections.Counter(ais)
	keys= cc.keys()
	if len(cc) == 1:
		return 0
	if len(cc) == 2:

		return abs(keys[0] - keys[1]) / (2 if abs(keys[0] - keys[1]) % 2 == 0 else 1)
	if len(cc) == 3:
		
		a,b,c = sorted(keys)
		if c - b == b -a:
			return b-a


	return -1
print f(ais)
