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 double esp = 1e-7;
const double pi = acos(-1.0);
const int maxx = 1101000;
const int mod = int(1e9 + 7);
namespace fastIO {
bool IOerror = 0;
inline char nc() {
  static char buf[100000], *p1 = buf + 100000, *pend = buf + 100000;
  if (p1 == pend) {
    p1 = buf;
    pend = buf + fread(buf, 1, 100000, stdin);
    if (pend == p1) {
      IOerror = 1;
      return -1;
    }
  }
  return *p1++;
}
inline bool blank(char ch) {
  return ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t';
}
inline void read(int &x) {
  char ch;
  while (blank(ch = nc()))
    ;
  if (IOerror) return;
  for (x = ch - '0'; (ch = nc()) >= '0' && ch <= '9'; x = x * 10 + ch - '0')
    ;
}
inline void readll(long long int &x) {
  char ch;
  while (blank(ch = nc()))
    ;
  if (IOerror) return;
  for (x = ch - '0'; (ch = nc()) >= '0' && ch <= '9'; x = x * 10 + ch - '0')
    ;
}
inline void reads(char *s) {
  char ch;
  while (blank(ch = nc()))
    ;
  if (IOerror) return;
  s[0] = ch;
  for (int i = 1; (!blank(ch = nc())); ++i) {
    s[i] = ch;
  }
}
};  // namespace fastIO
int a[110];
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  sort(a, a + n);
  int cnt = 0;
  int minn = a[0];
  int maxn = a[n - 1];
  bool yes = false;
  for (int i = 0; i < 101; ++i) {
    int ye = true;
    for (int j = 0; j < n; ++j) {
      if (a[j] == a[0] || a[j] - i == a[0] + i || a[j] == a[0] + i) {
        continue;
      } else {
        ye = false;
        break;
      }
    }
    if (ye) {
      yes = true;
      cnt = i;
      break;
    }
  }
  if (!yes)
    cout << -1 << endl;
  else
    cout << cnt << endl;
  return 0;
}
