F2. Korney Korneevich and XOR (hard version)
time limit per test
1.5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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, so he wished to experiment with it. For this purpose, he decided to find all integers $$$x \ge 0$$$ 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 $$$s_1, s_2, \ldots , s_m$$$ is called increasing if $$$s_1 < s_2 < \ldots < s_m$$$.

Input

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^6$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 5000$$$) — 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 $$$x_1, x_2, \ldots x_k$$$ ($$$0 \le x_1 < \ldots < x_k$$$) — 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 $$$[2, 4]$$$