#include <bits/stdc++.h>
using namespace std;
long long a[200000], kol1, kol2, s;
int main() {
  long long n, i, kol = 0, d, x, y;
  cin >> n;
  if (n == 1) {
    cout << -1;
    return 0;
  }
  for (i = 1; i <= n; i++) cin >> a[i];
  sort(a + 1, a + 1 + n);
  d = a[2] - a[1];
  if (n == 2) {
    if (d == 0) {
      cout << 1 << '\n' << a[1];
      return 0;
    }
    if (d % 2 == 0)
      cout << 3 << '\n' << a[1] - d << ' ' << a[1] + d / 2 << ' ' << a[2] + d;
    else
      cout << 2 << '\n' << a[1] - d << ' ' << a[2] + d;
    return 0;
  }
  s = -1;
  x = y = 100000000;
  for (i = 3; i <= n; i++)
    if (a[i] - a[i - 1] != a[i - 1] - a[i - 2]) {
      if (i != s + 1 || (y != a[i] - a[i - 1]))
        kol++, x = a[i] - a[i - 1], s = i, y = a[i - 1] - a[i - 2];
    }
  for (i = 2; i <= n; i++) {
    if (a[i] - a[i - 1] == x) kol1++;
    if (a[i] - a[i - 1] == y) kol2++;
  }
  if (kol > 1) {
    cout << 0;
    return 0;
  }
  if (kol == 0) {
    if (d == 0) {
      cout << 1 << '\n' << a[1];
      return 0;
    }
    cout << 2 << '\n' << a[1] - d << ' ' << a[n] + d;
    return 0;
  } else {
    if (kol1 == 1 && kol2 == 1) {
      if (x > y) {
        if (x % 2 == 0 && x / 2 == y) {
          cout << 1 << '\n' << a[s - 1] + y;
        } else
          cout << 0;
      } else {
        if (y % 2 == 0 && y / 2 == x) {
          cout << 1 << '\n' << a[s - 2] + x;
        } else
          cout << 0;
      }
    } else if (kol1 == 1) {
      if (x % 2 == 0 && x / 2 == y) {
        cout << 1 << '\n' << a[s - 1] + y;
      } else
        cout << 0;
    } else if (kol2 == 1) {
      if (y % 2 == 0 && y / 2 == x) {
        cout << 1 << '\n' << a[s - 2] + x;
      } else
        cout << 0;
    } else {
      cout << 0;
    }
  }
}
