#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimize("179")
#pragma GCC optimize("unroll-loops")
using namespace std;
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr), cout.tie(nullptr);
  int n;
  cin >> n;
  vector<vector<bool>> a(5001, vector<bool>(10000, false));
  vector<vector<int>> b(5001);
  for (int i = 0; i <= 5000; ++i) {
    a[i][0] = 1, b[i].push_back(0);
  }
  vector<int> ans;
  ans.push_back(0);
  for (int i = 0; i < n; ++i) {
    int x;
    cin >> x;
    for (auto j : b[x]) {
      ans.push_back(j ^ x);
      for (int k = x + 1; k <= 5000; ++k) {
        if (a[k][j ^ x]) break;
        b[k].push_back(j ^ x), a[k][j ^ x] = 1;
      }
    }
    b[x].clear();
  }
  sort(ans.begin(), ans.end());
  ans.erase(unique(ans.begin(), ans.end()), ans.end());
  cout << ans.size() << '\n';
  for (auto i : ans) cout << i << " ";
}

### Prompt

In CPP, your task is to solve the following problem:

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] 

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimize("179")
#pragma GCC optimize("unroll-loops")
using namespace std;
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr), cout.tie(nullptr);
  int n;
  cin >> n;
  vector<vector<bool>> a(5001, vector<bool>(10000, false));
  vector<vector<int>> b(5001);
  for (int i = 0; i <= 5000; ++i) {
    a[i][0] = 1, b[i].push_back(0);
  }
  vector<int> ans;
  ans.push_back(0);
  for (int i = 0; i < n; ++i) {
    int x;
    cin >> x;
    for (auto j : b[x]) {
      ans.push_back(j ^ x);
      for (int k = x + 1; k <= 5000; ++k) {
        if (a[k][j ^ x]) break;
        b[k].push_back(j ^ x), a[k][j ^ x] = 1;
      }
    }
    b[x].clear();
  }
  sort(ans.begin(), ans.end());
  ans.erase(unique(ans.begin(), ans.end()), ans.end());
  cout << ans.size() << '\n';
  for (auto i : ans) cout << i << " ";
}

```