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;
bool comp(pair<long long, long long> a, pair<long long, long long> b) {
  if (a.first - a.second < b.first - b.second == 0) return a.first < b.first;
  return a.first - a.second < b.first - b.second;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  unsigned long long L = 1;
  for (unsigned long long T = 1; T <= L; T++) {
    long long n;
    cin >> n;
    vector<long long> v;
    set<long long> P;
    for (long long i = 0; i < n; i++) {
      long long x;
      cin >> x;
      v.push_back(x);
      P.insert(x);
    }
    if (P.size() > 3) {
      cout << -1 << "\n";
      return 0;
    }
    sort(v.begin(), v.end());
    set<long long> dif;
    for (long long i = 1; i < n; i++) {
      dif.insert(abs(v[i] - v[i - 1]));
    }
    if (dif.size() > 2)
      cout << -1 << "\n";
    else {
      if (dif.size() == 2 && dif.find(0) == dif.end()) {
        cout << -1 << "\n";
      } else {
        vector<long long> B;
        for (auto i : P) {
          B.push_back(i);
        }
        if (B.size() == 1) {
          cout << 0 << "\n";
        } else if (B.size() == 3)
          cout << B[2] - B[1] << "\n";
        else {
          if ((B[1] - B[0]) % 2 == 0)
            cout << (B[1] - B[0]) / 2;
          else
            cout << B[1] - B[0] << "\n";
        }
      }
    }
  }
  return 0;
}
