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
# Program in python 2.x to find an element X
# that can be used to operate on an array and
# get equal elements

# Prints "YES" and an element x if we can
# equalize array using x. Else prints "NO"
def canEqualise(array):

	# We all the unique elements (using set
	# function). Then we sort unique elements.
	uniques = sorted(set(array))

	# if there are only 1 or 2 unique elements,
	# then we can add or subtract x from one of them
	# to get the other element
	if len(uniques) == 1:
		print(0)
	elif len(uniques) == 2:
		if (uniques[1] - uniques[0])%2 == 0:
			print(int((uniques[1] - uniques[0])/2))
		else:
			print(uniques[1] - uniques[0])

	# If count of unique elements is three, then
	# difference between the middle and minimum
	# should be same as difference between maximum
	# and middle
	elif len(uniques) == 3:
		if uniques[2] - uniques[1] == uniques[1] - uniques[0]:
			X = uniques[2] - uniques[1]
			print(X)
		else:
			print(-1)

	# if there are more than three unique elements, then
	# we cannot add or subtract the same value from all
	# the elements.
	else:
		print(-1)

# Driver code
#array = [55, 52, 52, 49, 52]
#array = []
n = int(input())
str = input().split(' ')
array = [int(x) for x in str]
#print(array)
canEqualise(array)
