#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int n, i, j, k;
  cin >> n;
  long long int a[n + 1];
  for (i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  if (n == 1) {
    cout << -1 << endl;
    return 0;
  }
  set<long long int> s;
  for (i = 0; i < n - 1; i++) {
    s.insert(a[i + 1] - a[i]);
  }
  if (s.size() > 2) {
    cout << 0 << endl;
    return 0;
  }
  if (a[0] == a[n - 1]) {
    cout << 1 << endl;
    cout << a[0] << endl;
    return 0;
  }
  if (s.size() == 1) {
    if (n == 2) {
      if ((a[1] - a[0]) % 2 == 0) {
        cout << 3 << endl;
        cout << a[0] - (a[1] - a[0]) << " " << a[0] + (a[1] - a[0]) / 2 << " "
             << a[n - 1] + a[1] - a[0] << endl;
        return 0;
      } else {
        cout << 2 << endl;
        cout << a[0] - (a[1] - a[0]) << " " << a[n - 1] + a[1] - a[0] << endl;
        return 0;
      }
    } else {
      cout << 2 << endl;
      cout << a[0] - (a[1] - a[0]) << " " << a[n - 1] + a[1] - a[0] << endl;
      return 0;
    }
  }
  set<long long int>::iterator it;
  it = s.begin();
  long long int d1 = *it;
  it++;
  long long int d2 = *it;
  long long int ct1 = 0, ct2 = 0, x1, x2;
  for (i = 0; i < n - 1; i++) {
    if (a[i + 1] - a[i] == d1) {
      ct1++;
      x1 = i;
    } else if (a[i + 1] - a[i] == d2) {
      ct2++;
      x2 = i;
    }
  }
  if (ct1 == 1) {
    if (d1 == 2 * d2) {
      cout << 1 << endl;
      cout << a[x1] + (d2) << endl;
      return 0;
    }
  }
  if (ct2 == 1) {
    if (d2 == 2 * d1) {
      cout << 1 << endl;
      cout << a[x2] + (d1) << endl;
      return 0;
    }
  }
  cout << 0 << endl;
}
