#include <bits/stdc++.h>
using namespace std;
const long long INF = 1e9 + 7, maxn = 1e5 + 7;
const double Pi = 3.1415926535;
long long n, i, j, k1, k2, l, m, ans, a, t, w[maxn];
string s, s1;
vector<long long> te, pos;
set<long long> q;
map<long long, long long> g;
bool b;
long long bin_p(long long a, long long b) {
  long long res = 1;
  while (n) {
    if (n & 1) res *= a;
    a *= a;
    n >>= 1;
  }
  return res;
}
long long gcd(long long a, long long b) {
  while (b) {
    a %= b;
    swap(a, b);
  }
  return a;
}
int main() {
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> w[i];
  }
  sort(w, w + i);
  if (n == 1) {
    cout << -1;
    return 0;
  }
  for (i = 1; i < n; i++) {
    g[w[i] - w[i - 1]]++;
    if (g[w[i] - w[i - 1]] > ans) {
      ans = g[w[i] - w[i - 1]];
      l = i;
    }
    if (g[w[i] - w[i - 1]] == 1) {
      t++;
      te.push_back(w[i] - w[i - 1]);
      pos.push_back(i);
      if (t > 2) {
        cout << 0;
        return 0;
      }
    }
  }
  if (t == 2) {
    if (g[te[0]] > 1 && g[te[1]] >= 2 || te[0] == 0 || te[1] == 0) {
      cout << 0;
      return 0;
    }
    if (n == 3) {
      if (w[1] + g[l] == w[2] - g[l]) {
        q.insert(w[1] + g[l]);
        b = 1;
      }
      if (w[1] - g[l] == w[0] + g[l]) {
        q.insert(w[1] - g[l]);
        b = 1;
      }
      if (w[1] + min(g[te[0]], g[te[1]]) == w[2] - min(g[te[0]], g[te[1]])) {
        q.insert(w[1] + min(g[te[0]], g[te[1]]));
        b = 1;
      }
      if (w[1] - min(g[te[0]], g[te[1]]) == w[0] + min(g[te[0]], g[te[1]])) {
        q.insert(w[1] - min(g[te[0]], g[te[1]]));
        b = 1;
      }
      if (!b) {
        cout << 0;
        return 0;
      }
      cout << 1 << endl;
      for (auto t = q.begin(); t != q.end(); t++) cout << *t;
      return 0;
    } else {
      if (g[w[pos[0]] - w[pos[0] - 1]] > g[w[pos[1]] - w[pos[1] - 1]]) {
        j = pos[1];
        if (w[j - 1] + w[pos[0]] - w[pos[0] - 1] ==
            w[j] - w[pos[0]] + w[pos[0] - 1]) {
          q.insert(w[j - 1] + w[pos[0]] - w[pos[0] - 1]);
        } else {
          cout << 0;
          return 0;
        }
      } else {
        j = pos[0];
        if (w[j - 1] + w[pos[1]] - w[pos[1] - 1] ==
            w[j] - w[pos[1]] + w[pos[1] - 1]) {
          q.insert(w[j - 1] + w[pos[1]] - w[pos[1] - 1]);
        } else {
          cout << 0;
          return 0;
        }
      }
      cout << 1 << endl;
      for (auto t = q.begin(); t != q.end(); t++) cout << *t;
      return 0;
    }
  }
  q.insert(w[0] - w[l] + w[l - 1]);
  q.insert(w[n - 1] + w[l] - w[l - 1]);
  if (n == 2) {
    if ((w[1] - w[0]) % 2 == 0) q.insert(w[0] + (w[1] - w[0]) / 2);
  }
  cout << q.size() << endl;
  for (auto t = q.begin(); t != q.end(); t++) cout << *t << " ";
  return 0;
}
