#include <bits/stdc++.h>
using namespace std;
int r[8192];
vector<int> g[8192];
int ans[8192] = {
    0,
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  ans[0] = 1;
  for (int i = 0; i < 8192; i++) {
    g[i].push_back(0);
  }
  for (int i = 0; i < 8192; i++) {
    r[i] = 8192;
  }
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    for (const auto& key : g[x]) {
      int to = (key ^ x);
      ans[to] = 1;
      while (r[to] > x) {
        r[to]--;
        if (r[to] != x) g[r[to]].push_back(to);
      }
    }
    g[x].clear();
  }
  int cnt = 0;
  for (int i = 0; i < 8192; i++) {
    cnt += ans[i];
  }
  cout << cnt << "\n";
  for (int i = 0; i < 8192; i++) {
    if (ans[i]) cout << i << " ";
  }
  cout << "\n";
}

### Prompt

Develop a solution in CPP to the problem described below:

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>
using namespace std;
int r[8192];
vector<int> g[8192];
int ans[8192] = {
    0,
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  ans[0] = 1;
  for (int i = 0; i < 8192; i++) {
    g[i].push_back(0);
  }
  for (int i = 0; i < 8192; i++) {
    r[i] = 8192;
  }
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    for (const auto& key : g[x]) {
      int to = (key ^ x);
      ans[to] = 1;
      while (r[to] > x) {
        r[to]--;
        if (r[to] != x) g[r[to]].push_back(to);
      }
    }
    g[x].clear();
  }
  int cnt = 0;
  for (int i = 0; i < 8192; i++) {
    cnt += ans[i];
  }
  cout << cnt << "\n";
  for (int i = 0; i < 8192; i++) {
    if (ans[i]) cout << i << " ";
  }
  cout << "\n";
}

```