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;
inline void read(int &x) {
  x = 0;
  char ch = getchar();
  int pd = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') {
      pd = -pd;
    }
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  x *= pd;
}
inline void write(const int &x) {
  char ggg[10001];
  int s = 0;
  int tmp = x;
  if (tmp == 0) {
    putchar('0');
    return;
  }
  if (tmp < 0) {
    tmp = -tmp;
    putchar('-');
  }
  while (tmp > 0) {
    ggg[s++] = tmp % 10 + '0';
    tmp /= 10;
  }
  while (s > 0) {
    putchar(ggg[--s]);
  }
}
int a[10001];
int sz;
bool mp[10000001];
int main() {
  int n;
  read(n);
  for (register int i = 1; i <= n; ++i) {
    int xx;
    read(xx);
    if (!mp[xx]) {
      a[++sz] = xx;
      mp[xx] = 1;
    }
  }
  sort(a + 1, a + sz + 1);
  if (sz == 1) {
    puts("0");
    return 0;
  }
  if (sz == 2) {
    int now = (a[1] + a[2]);
    if (now & 1) {
      cout << a[2] - a[1];
    } else {
      cout << now / 2 - a[1];
    }
    return 0;
  }
  if (sz == 3) {
    if (a[2] - a[1] == a[3] - a[2]) {
      cout << a[2] - a[1];
      return 0;
    } else {
      puts("-1");
      return 0;
    }
  }
  puts("-1");
}
