#include <bits/stdc++.h>
using namespace std;
bool prog(vector<long long> &a, long long d) {
  int n = a.size();
  for (int i = 0; i < n; i++)
    if (a[i] != a[0] + d * i) return false;
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<long long> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a.begin(), a.end());
  long long d = 1e9;
  set<long long> diff;
  for (int i = 1; i < n; i++) {
    long long x = a[i] - a[i - 1];
    diff.insert(x);
    d = min(d, x);
  }
  if (prog(a, d)) {
    if (n == 1) {
      cout << -1 << endl;
      return 0;
    } else if (n == 2) {
      if (d % 2) {
        cout << 2 << endl;
        cout << a[0] - d << " " << a[n - 1] + d << endl;
      } else {
        if (d == 0) {
          cout << 1 << endl;
          cout << a[0] << endl;
          return 0;
        } else {
          cout << 3 << endl;
          cout << a[0] - d << " " << a[0] + d / 2 << " " << a[n - 1] + d
               << endl;
        }
      }
      return 0;
    } else if (n >= 3) {
      if (d == 0) {
        cout << 1 << endl;
        cout << a[0] << endl;
        return 0;
      }
      cout << 2 << endl;
      cout << a[0] - d << " " << a[n - 1] + d << endl;
      return 0;
    }
  } else {
    if (diff.size() >= 3) {
      cout << 0 << endl;
      return 0;
    } else if (diff.size() == 2) {
      if (diff.find(0) != diff.end()) {
        cout << 0 << endl;
        return 0;
      } else {
        set<long long> ret;
        for (int i = 0;; i++) {
          long long cur = a[0] + d * i;
          if (cur > a[n - 1]) break;
          ret.insert(cur);
        }
        for (int i = 0; i < n; i++) ret.erase(a[i]);
        if (ret.size() > 1) {
          cout << 0 << endl;
          return 0;
        }
        set<long long>::iterator it = ret.begin();
        cout << 1 << endl;
        cout << (*it) << endl;
      }
    }
  }
  return 0;
}
