#include <bits/stdc++.h>
using namespace std;
const long double PI = acos(-1);
long long powm(long long a, long long b) {
  long long res = 1;
  while (b) {
    if (b & 1) res = (res * a) % 1000000007;
    a = (a * a) % 1000000007;
    b >>= 1;
  }
  return res;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
const long long maxn = 2 * 1e5 + 10;
map<long long, long long> dif;
void solve() {
  long long n;
  cin >> n;
  long long a[n + 2];
  for (long long i = 1; i <= n; i++) {
    cin >> a[i];
  }
  sort(a + 1, a + n + 1);
  for (long long i = 2; i <= n; i++) {
    long long cur = a[i] - a[i - 1];
    dif[cur]++;
  }
  if (dif.size() > 2) {
    cout << 0 << endl;
  } else if (n == 1) {
    cout << -1 << endl;
  } else if (n == 2) {
    if ((a[2] - a[1]) % 2 == 0 && a[2] != a[1]) {
      cout << 3 << endl;
      cout << a[1] - (a[2] - a[1]) << " " << a[1] + (a[2] - a[1]) / 2 << " "
           << a[2] + (a[2] - a[1]) << endl;
    } else if (a[1] == a[2]) {
      cout << 1 << endl;
      cout << a[1] << endl;
    } else {
      cout << 2 << endl;
      cout << a[1] - (a[2] - a[1]) << " " << a[2] + (a[2] - a[1]) << endl;
    }
  } else if (dif.size() == 2 && n > 1) {
    long long mx = 0, d = 1000000000, z = 0;
    vector<long long> s;
    for (auto i : dif) {
      if (i.first == 0) z = 1;
      if (mx <= i.second) {
        mx = i.second;
        d = min(d, i.first);
      }
      s.push_back(i.first);
    }
    if (z || dif[s[0]] < n - 2 || s[1] % 2 != 0 ||
        (s[1] % 2 == 0 && s[1] / 2 != s[0]))
      cout << 0 << endl;
    else {
      for (long long i = 2; i <= n; i++) {
        if (a[i] - a[i - 1] != d) {
          if ((a[i] - a[i - 1]) > d && (a[i] - a[i - 1]) % 2 == 0 &&
              (a[i] - a[i - 1]) / 2 == d) {
            cout << 1 << endl;
            cout << a[i - 1] + d << endl;
          } else {
            cout << 0 << endl;
            break;
          }
        }
      }
    }
  } else if (dif.size() == 1) {
    long long d = 0;
    for (auto i : dif) {
      d = i.first;
    }
    if (d) {
      cout << 2 << endl;
      cout << a[1] - (a[2] - a[1]) << " " << a[n] + (a[2] - a[1]) << endl;
    } else {
      cout << 1 << endl;
      cout << a[1] << endl;
    }
  } else
    cout << 0 << endl;
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long t = 1;
  for (long long i = 1; i <= t; i++) {
    solve();
  }
  return 0;
}
