#include <bits/stdc++.h>
using namespace std;
int n;
long long ar[100100];
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> ar[i];
  }
  sort(ar, ar + n);
  long long dif1 = ar[1] - ar[0], dif2 = -1;
  int cnt1 = 0, cnt2 = 0;
  if (n == 1) {
    cout << -1 << endl;
    return 0;
  } else if (n == 2) {
    if (ar[0] == ar[1]) {
      cout << 1 << endl << ar[0];
      return 0;
    } else {
      if ((ar[0] + ar[1]) % 2 == 0) {
        cout << 3 << endl
             << ar[0] - (ar[1] - ar[0]) << " " << (ar[1] + ar[0]) / 2 << " "
             << ar[1] + (ar[1] - ar[0]) << endl;
        return 0;
      } else {
        cout << 2 << endl
             << ar[0] - (ar[1] - ar[0]) << " " << ar[1] + (ar[1] - ar[0])
             << endl;
        return 0;
      }
    }
  } else {
    set<long long> nd;
    set<long long> ans;
    for (int i = 1; i < n; i++) {
      nd.insert(ar[i] - ar[i - 1]);
    }
    if (nd.size() > 2) {
      cout << 0 << endl;
    } else if (nd.size() == 1) {
      ans.insert(ar[0] - (ar[1] - ar[0]));
      ans.insert(ar[n - 1] + (ar[1] - ar[0]));
      cout << ans.size() << endl;
      for (auto it : ans) {
        cout << it << endl;
      }
    } else {
      int ls1 = -1, ls2 = -1;
      dif1 = *nd.begin();
      dif2 = *(++nd.begin());
      if (dif1 != 2 * dif2 && dif2 != 2 * dif1) {
        cout << 0 << endl;
        return 0;
      }
      for (int i = 1; i < n; i++) {
        if (ar[i] - ar[i - 1] == dif1) {
          cnt1++;
          ls1 = i;
        } else {
          cnt2++;
          ls2 = i;
        }
      }
      if (cnt1 == 1 && dif1 % 2 == 0 && dif1 > dif2) {
        cout << 1 << endl;
        cout << ar[ls1 - 1] + dif2 << endl;
        return 0;
      }
      if (cnt2 == 1 && dif2 % 2 == 0 && dif1 < dif2) {
        cout << 1 << endl;
        cout << ar[ls2 - 1] + dif1 << endl;
        return 0;
      }
      cout << 0 << endl;
    }
  }
  return 0;
}
