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;
  const long long INF = 1e+16;
  const int SMALL_INF = 1998244353;
  const int NSIZE = 4 * 1e+5 + 1000;
  const long long MOD = 998244353;
  const long double EPS = 1e-12;
  const int MAX = 1e+6 + 1000;
  const long double PI = atan(1) * 4;
  const long long HZ = -1692281337;
  int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int n;
    cin >> n;
    vector<int> xpos(10001, SMALL_INF);
    xpos[0] = -1;
    vector<vector<int> > apos(5001);
    for (int i = 0; i < n; i++) {
      int a;
      cin >> a;
      apos[a].push_back(i);
    }
    for (int i = 0; i <= 5000; i++) {
      if (apos[i].empty()) continue;
      for (int j = 0; j <= 10000; j++) {
        if ((i ^ j) <= 10000 && xpos[i ^ j] < apos[i].back()) {
          xpos[j] = min(
              xpos[j], *upper_bound(apos[i].begin(), apos[i].end(), xpos[i ^ j]));
        }
      }
    }
    vector<int> ans;
    for (int i = 0; i <= 10000; i++) {
      if (xpos[i] != SMALL_INF) ans.push_back(i);
    }
    cout << ans.size() << '\n';
    for (auto i : ans) cout << i << " ";
  }
  