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;
void fast() {
  std::ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
const long long MOD = 1e9 + 7;
int main() {
  long long t = 1;
  while (t--) {
    long long n;
    cin >> n;
    long long a[n];
    map<long long, long long> mp;
    long long val;
    long long mx = -1;
    vector<long long> vc;
    for (long long i = 0; i < n; ++i) {
      cin >> a[i];
      if (mp[a[i]] == 0) {
        mp[a[i]]++;
        vc.push_back(a[i]);
      }
    }
    if (vc.size() > 3) {
      cout << -1 << '\n';
      return 0;
    }
    map<long long, long long>::iterator it;
    it = mp.begin();
    if (vc.size() == 2) {
      long long fs = vc[0];
      long long sss = vc[1];
      if (abs(fs - sss) % 2 == 1)
        cout << abs(fs - sss);
      else
        cout << abs(fs - sss) / 2;
      return 0;
    }
    if (vc.size() == 1) {
      cout << 0 << '\n';
      return 0;
    } else {
      sort((vc).begin(), (vc).end());
      if (vc[1] - vc[0] == vc[2] - vc[1]) {
        cout << vc[1] - vc[0] << '\n';
      } else
        cout << -1 << '\n';
    }
  }
}
