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;
int dr[] = {1, 0, -1, 0};
int dc[] = {0, 1, 0, -1};
const int RT = 201110;
vector<int> prime;
bitset<202019> status;
void sieve() {
  int rt = sqrt(RT);
  for (int i = 3; i <= rt; i += 2)
    if (!status[i])
      for (int j = i * i; j < RT; j += (i << 1)) status[j] = true;
  prime.push_back(2);
  for (int i = 3; i <= RT; i += 2)
    if (!status[i]) prime.push_back(i);
}
void solve() {
  int n, moves = 0, num;
  cin >> n;
  vector<int> v(n);
  for (auto &it : v) cin >> it;
  sort(v.begin(), v.end());
  if (n == 1) {
    cout << 0 << endl;
    return;
  }
  for (int i = 0; i < n - 1; i++) {
    if (v[i + 1] - v[i] != 0) {
      if (moves == 0) {
        num = v[i + 1] - v[i];
        moves = 1;
      } else if (num != v[i + 1] - v[i]) {
        cout << -1 << endl;
        return;
      } else
        moves++;
    }
  }
  if (moves == 0) {
    cout << 0 << endl;
  } else if (moves == 1 && num % 2 == 0) {
    cout << num / 2 << endl;
  } else if (moves == 1 && num % 2 != 0) {
    cout << num << endl;
  } else if (moves == 2) {
    cout << num << endl;
  } else
    cout << -1 << endl;
}
void kick_ass() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  solve();
}
int main() { kick_ass(); }
