description: This is a harder version of the problem with bigger constraints.
  
  Korney Korneevich dag up an array a of length n. Korney Korneevich has recently read about the operation [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR), so he wished to experiment with it. For this purpose, he decided to find all integers x ≥ 0 such that there exists an increasing subsequence of the array a, in which the bitwise XOR of numbers is equal to x.
  
  It didn't take a long time for Korney Korneevich to find all such x, and he wants to check his result. That's why he asked you to solve this problem!
  
  A sequence s is a subsequence of a sequence b if s can be obtained from b by deletion of several (possibly, zero or all) elements.
  
  A sequence s_1, s_2, … , s_m is called increasing if s_1 < s_2 < … < s_m.
  
  Input
  
  The first line contains a single integer n (1 ≤ n ≤ 10^6).
  
  The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 5000) — the elements of the array a.
  
  Output
  
  In the first line print a single integer k — the number of found x values.
  
  In the second line print k integers in increasing order x_1, x_2, … x_k (0 ≤ x_1 < … < x_k) — found x values.
  
  Examples
  
  Input
  
  
  4
  4 2 2 4
  
  
  Output
  
  
  4
  0 2 4 6 
  
  
  Input
  
  
  8
  1 0 1 7 12 5 3 2
  
  
  Output
  
  
  12
  0 1 2 3 4 5 6 7 10 11 12 13 
  
  Note
  
  In the first test case:
  
    * To get value x = 0 it is possible to choose and empty subsequence 
    * To get value x = 2 it is possible to choose a subsequence [2] 
    * To get value x = 4 it is possible to choose a subsequence [4] 
    * To get value x = 6 it is possible to choose a subsequence [2, 4] 
solution: #include <bits/stdc++.h>
  using namespace std;
  clock_t startTime;
  double getCurrentTime() {
    return (double)(clock() - startTime) / CLOCKS_PER_SEC;
  }
  template <typename T, typename U>
  inline ostream &operator<<(ostream &_out, const pair<T, U> &_p) {
    _out << _p.first << " " << _p.second;
    return _out;
  }
  template <typename T, typename U>
  inline istream &operator>>(istream &_in, pair<T, U> &_p) {
    _in >> _p.first >> _p.second;
    return _in;
  }
  template <typename T>
  inline ostream &operator<<(ostream &_out, const vector<T> &_v) {
    if (_v.empty()) return _out;
    _out << _v.front();
    for (auto _it = ++_v.begin(); _it != _v.end(); ++_it) _out << ' ' << *_it;
    return _out;
  }
  template <typename T>
  inline istream &operator>>(istream &_in, vector<T> &_v) {
    for (auto &_i : _v) _in >> _i;
    return _in;
  }
  template <typename T>
  inline ostream &operator<<(ostream &_out, const set<T> &_s) {
    if (_s.empty()) return _out;
    _out << *_s.begin();
    for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) _out << ' ' << *_it;
    return _out;
  }
  template <typename T>
  inline ostream &operator<<(ostream &_out, const multiset<T> &_s) {
    if (_s.empty()) return _out;
    _out << *_s.begin();
    for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) _out << ' ' << *_it;
    return _out;
  }
  template <typename T>
  inline ostream &operator<<(ostream &_out, const unordered_set<T> &_s) {
    if (_s.empty()) return _out;
    _out << *_s.begin();
    for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) _out << ' ' << *_it;
    return _out;
  }
  template <typename T>
  inline ostream &operator<<(ostream &_out, const unordered_multiset<T> &_s) {
    if (_s.empty()) return _out;
    _out << *_s.begin();
    for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) _out << ' ' << *_it;
    return _out;
  }
  template <typename T, typename U>
  inline ostream &operator<<(ostream &_out, const map<T, U> &_m) {
    if (_m.empty()) return _out;
    _out << "{\"" << _m.begin()->first << "\", \"" << _m.begin()->second << "\"}";
    for (auto _it = ++_m.begin(); _it != _m.end(); ++_it)
      _out << ", { \"" << _it->first << "\", \"" << _it->second << "\"}";
    return _out;
  }
  template <typename T, typename U>
  inline ostream &operator<<(ostream &_out, const unordered_map<T, U> &_m) {
    if (_m.empty()) return _out;
    _out << '(' << _m.begin()->first << ": " << _m.begin()->second << ')';
    for (auto _it = ++_m.begin(); _it != _m.end(); ++_it)
      _out << ", (" << _it->first << ": " << _it->second << ')';
    return _out;
  }
  template <typename T>
  void out(const vector<T> &a, int n) {
    for (int i = 1; i <= n; ++i) {
      cout << a[i] << ' ';
    }
    cout << "\n";
  }
  template <typename T>
  void out(const vector<vector<T>> &a, int n, int m) {
    for (int i = 1; i <= n; ++i) {
      for (int j = 1; j <= m; ++j) {
        cout << a[i][j] << ' ';
      }
      cout << '\n';
    }
  }
  template <typename T, typename U>
  int less_than_or_equal_to(T val, const vector<U> &a) {
    int n = a.size();
    int l = -1, r = n, mid;
    while (r > l + 1) {
      mid = (l + r) / 2;
      if (a[mid] <= val)
        l = mid;
      else
        r = mid;
    }
    return l;
  }
  template <typename T, typename U>
  int less_than(T val, const vector<U> &a) {
    int n = a.size();
    int l = -1, r = n, mid;
    while (r > l + 1) {
      mid = (l + r) / 2;
      if (a[mid] < val)
        l = mid;
      else
        r = mid;
    }
    return l;
  }
  template <typename T, typename U>
  int greater_than_or_equal_to(T val, const vector<U> &a) {
    int n = a.size();
    int l = -1, r = n, mid;
    while (r > l + 1) {
      mid = (l + r) / 2;
      if (a[mid] < val)
        l = mid;
      else
        r = mid;
    }
    return r;
  }
  template <typename T, typename U>
  int greater_than(T val, const vector<U> &a) {
    int n = a.size();
    int l = -1, r = n, mid;
    while (r > l + 1) {
      mid = (l + r) / 2;
      if (a[mid] <= val)
        l = mid;
      else
        r = mid;
    }
    return r;
  }
  const int N = 8200;
  const int INF = 1e7;
  void solve() {
    int n;
    cin >> n;
    vector<vector<int>> a(N);
    for (int i = 1; i <= n; ++i) {
      int x;
      cin >> x;
      a[x].push_back(i);
    }
    vector<int> dp(N, INF), ndp(N, INF);
    dp[0] = 0;
    for (int i = 1; i < N; ++i) {
      if (a[i].empty()) continue;
      ndp = dp;
      for (int j = 0; j < N; ++j) {
        if (dp[j] != INF) {
          int ind = greater_than(dp[j], a[i]);
          if (ind < (int)a[i].size()) ndp[i ^ j] = min(ndp[i ^ j], a[i][ind]);
        }
      }
      dp = ndp;
    }
    int ans = 0;
    for (int i = 0; i < N; ++i) ans += dp[i] != INF;
    cout << ans << "\n";
    for (int i = 0; i < N; ++i)
      if (dp[i] != INF) cout << i << ' ';
  }
  int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    startTime = clock();
    int T = 1;
    while (T--) {
      solve();
    }
    return 0;
  }
  