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] 
import java.util.*;
import java.io.*;

public class _751 {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = 1;
        int MAX = 8194;
        int poss = 8192;
        while (t-- > 0) {
            int n = sc.nextInt();
            int [] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = sc.nextInt();
            int [] min = new int[MAX];
            Arrays.fill(min, n + 1);
            ArrayList<Pair> b = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                b.add(new Pair(i, a[i]));
            }
            Collections.sort(b);
            int cur = 0;
            min[0] = -1;
            int count = 1;
            for (int i = 0; i < MAX; i++) {
                TreeSet<Integer> set = new TreeSet<>();
                while (cur < b.size() && b.get(cur).x == i) {
                    set.add(b.get(cur).i);
                    ++cur;
                }
                if (set.size() == 0) continue;
                for (int j = 0; j < MAX; j++) {
                    if (min[j] != n + 1) {
                        Integer high = set.higher(min[j]);
                        if (high != null) {
                            int v = i ^ j;
                            if (min[v] == n + 1) ++count;
                            min[v] = Math.min(min[v], high);
                        }
                    }
                }
                if (count == poss) break;
            }
            ArrayList<Integer> res = new ArrayList<>();
            for (int i = 0; i < MAX; i++) {
                if (min[i] != n + 1) {
                    res.add(i);
                }
            }
            out.println(res.size());
            for (Integer x: res) out.print(x + " ");
        }
        out.close();
    }

    static class Pair implements Comparable<Pair> {
        int i; int x;
        Pair(int i, int x) {
            this.i = i; this.x = x;
        }

        @Override
        public int compareTo(Pair o) {
            if (x == o.x) return Integer.compare(i, o.i);
            return Integer.compare(x, o.x);
        }
    }




    static void sort(int[] a) {
        ArrayList<Integer> q = new ArrayList<>();
        for (int i : a) q.add(i);
        Collections.sort(q);
        for (int i = 0; i < a.length; i++) a[i] = q.get(i);
    }

    static void sort(long[] a) {
        ArrayList<Long> q = new ArrayList<>();
        for (long i : a) q.add(i);
        Collections.sort(q);
        for (int i = 0; i < a.length; i++) a[i] = q.get(i);
    }


    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }


    }

}