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;
#pragma GCC optimize("O2")
vector<long long int> ar[1000001];
long long int vis[1000001], dis[1000001], level[1000001];
const int MAX_SIZE = 1000001;
const int N = 2000010;
const int mod = 1e9 + 7;
vector<int> isprime(MAX_SIZE, true);
vector<int> prime;
vector<int> SPF(MAX_SIZE);
long long int fact[N];
void manipulated_seive(int N) {
  isprime[0] = isprime[1] = false;
  for (int i = 2; i < N; ++i) {
    if (isprime[i]) {
      prime.push_back(i);
      SPF[i] = i;
    }
    for (int j = 0;
         j < (int)prime.size() && i * prime[j] < N && prime[j] <= SPF[i]; ++j) {
      isprime[i * prime[j]] = false;
      SPF[i * prime[j]] = prime[j];
    }
  }
}
bool sortbysec(const pair<int, int> &a, const pair<int, int> &b) {
  return (a.second < b.second);
}
unordered_map<long long int, long long int> myp;
void primeFactors(long long int n) {
  while (n % 2 == 0) {
    myp[2]++;
    n = n / 2;
  }
  for (long long int i = 3; i <= sqrt(n); i = i + 2) {
    while (n % i == 0) {
      myp[i]++;
      n = n / i;
    }
  }
  if (n > 2) myp[n]++;
}
long long int gcd(long long int a, long long int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long int findlcm(long long int a, long long int b) {
  return a * b / gcd(a, b);
}
long long int power(long long int a, long long int b) {
  long long int res = 1;
  while (b) {
    if (b % 2) res *= a;
    a *= a;
    b /= 2;
  }
  return res;
}
long long int power_mod(long long int a, long long int b, long long int p) {
  long long int res = 1;
  while (b) {
    if (b % 2) {
      res *= a;
      res %= p;
    }
    a *= a;
    a %= p;
    b /= 2;
  }
  return res;
}
long long int mod_inverse(long long int x) {
  return power_mod(x, mod - 2, mod);
}
long long int nCr(long long int n, long long int r) {
  if (r == 0) return 1;
  long long int a = fact[n];
  long long int b = mod_inverse(fact[n - r]);
  long long int c = mod_inverse(fact[r]);
  return (((a * b) % mod) * c) % mod;
}
void fun() {
  long long int n;
  cin >> n;
  long long int arr[n];
  unordered_set<long long int> s;
  for (long long int i = 0; i < n; i++) {
    cin >> arr[i];
    s.insert(arr[i]);
  }
  vector<long long int> v;
  for (auto it = s.begin(); it != s.end(); it++) {
    v.push_back(*it);
  }
  sort(v.begin(), v.end());
  if (v.size() > 3) {
    cout << -1 << '\n';
    return;
  }
  if (v.size() == 3) {
    if (v[2] - v[1] == v[1] - v[0]) {
      cout << v[1] - v[0] << '\n';
      return;
    } else {
      cout << -1 << '\n';
      return;
    }
  }
  if (v.size() == 2) {
    if ((v[1] - v[0]) % 2 == 0) {
      cout << (v[1] - v[0]) / 2 << '\n';
      return;
    } else {
      cout << (v[1] - v[0]) << '\n';
      return;
    }
  }
  cout << 0 << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  unsigned long long int t;
  t = 1;
  while (t--) {
    cout << fixed;
    cout << setprecision(10);
    fun();
  }
  return 0;
}
