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 sys, bisect, heapq, math
sys.setrecursionlimit(10**9+7)
def fi(): return int(sys.stdin.readline())
def fi2(): return map(int, sys.stdin.readline().split())
def fi3(): return sys.stdin.readline().rstrip()
def fo(*args):
    for s in args: sys.stdout.write(str(s)+' ')
    sys.stdout.write('\n')
##    sys.stdout.flush()
def puts(*args):
    for s in args: sys.stdout.write(str(s))
OUT = []
def bfo(*args):
    for s in args: OUT.append(str(s)+' ')
    OUT.append('\n')
def bputs(*args):
    for s in args: OUT.append(str(s))        
def flush():
    sto = ''.join(OUT); fo(sto)
##
alpha = 'abcdefghijklmnopqrstuvwxyz'; mod = 10**9+7; inf = int(2e18+5) ; nax = 201010
##

n = fi()
a = fi2()

d = [0 for i in range(n)]
check =  set(a)
if(len(check) == 1):
    print 0
    exit(0)

res = []
for i in range(0, 101):
    D = i
    for j in range(n):
        d[j] = abs(D-a[j])
    
    K = set(d)
    if(len(K) == 1 or (len(K) == 2 and 0 in K)):
        for x in K:
            if x != 0:
                v = x
        res.append(v)


        
if(len(res) == 0): bfo(-1)
else:
    res.sort()
    bfo(res[0])

flush()
