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 math
n = int(input())
a = list(map(int,input().split()))
a = list(set(a))
a.sort()
if len(a) == 1:
	print(0)
else:
	for i in range(1,101):
		flag= True
		su = a[0]+i 
		prin = False
		# dif = abs(a[0]-i)
		# print(i,' ',su,' ',dif,'\n')
		for j in range(1,len(a)):
				# 	if a[j]+i != su and abs(a[j] - i)!=dif and a[j]+i != dif and abs(a[j] - i)!=su and a[j]!=su and a[j]!=dif:
				# flag = False
				# if i==3:
				# 	print(a[j],' ',i)
				# break
			if a[j]+i != su and (a[j] - i)!=su and a[j]!=su:
				# print(a[j],' ',i,' ',su)
				flag = False
				break

		if flag:
			print(i)
			prin = True
			break
	if not prin:
		print(-1)



# mid = a[n//2]
# mid = math.ceil(sum(a)//n)
# m = -1
# flag = True
# for x in a:
# 	if m==-1 or m==0:
# 		m = abs(mid-x)
# 	elif abs(mid-x) == m or abs(mid-x) == 0:
# 		pass 
# 	else:
# 		flag = False
# 		break
# if flag:
# 	print(m)
# else:
# 	print(-1)


