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);
}
void solve() {}
int main() {
  FAST();
  int n;
  cin >> n;
  int arr[n + 7];
  for (int first = 0; first < n; ++first) cin >> arr[first];
  sort(arr, arr + n);
  int p = 0;
  if (arr[n - 1] == arr[0]) {
    cout << 0;
    return 0;
  }
  int ans = 107;
  for (int first = arr[0]; first <= arr[n - 1]; ++first) {
    int d = -1;
    p = 0;
    for (int second = 0; second < n; ++second) {
      int x;
      if (arr[second] == first) continue;
      if (arr[second] > first)
        x = arr[second] - first;
      else
        x = first - arr[second];
      if (d == -1)
        d = x;
      else if (d != x) {
        p = 1;
        break;
      }
    }
    if (p == 0) {
      ans = min(ans, d);
    }
  }
  if (ans == 107)
    cout << -1;
  else
    cout << ans;
  return 0;
}
