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
#include <bits/stdc++.h>
using namespace std;
const int inf = numeric_limits<int>::max();
const long long int linf = numeric_limits<long long int>::max();
const long long int MOD = (long long int)1e9 + 7;
long long int fast_mod(long long int abcd, int expp) {
  long long int res = 1;
  while (expp > 0) {
    if (expp % 2 == 1) res = (res * abcd) % MOD;
    abcd = (abcd * abcd) % MOD;
    expp /= 2;
  }
  return res % MOD;
}
long long int gcd(long long int a, long long int b) {
  long long int temppp = max(a, b);
  b = min(a, b);
  a = temppp;
  if (b == 0) return a;
  return gcd(b, a % b);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  clock_t begin123 = clock();
  map<int, int> m;
  int n, temp;
  cin >> n;
  for (int i = 0; i < (n); ++i) {
    cin >> temp;
    m[temp]++;
  }
  if (m.size() > 3) {
    cout << "-1";
  } else if (m.size() == 2) {
    auto it = m.begin();
    auto it1 = it;
    it1++;
    int teemp = it1->first - it->first;
    if (teemp & 1)
      cout << teemp << "\n";
    else
      cout << teemp / 2 << "\n";
  } else if (m.size() == 1) {
    cout << "0"
         << "\n";
  } else if (m.size() == 3) {
    auto it = m.begin();
    auto it1 = it;
    it1++;
    auto it2 = it1;
    it2++;
    if (it2->first - it1->first == it1->first - it->first)
      cout << it1->first - it->first << "\n";
    else
      cout << "-1"
           << "\n";
  }
  return 0;
}
