F1. Korney Korneevich and XOR (easy version)
time limit per test
1.5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

This is an easier version of the problem with smaller 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 $$$n$$$ ($$$1 \le n \le 10^5$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 500$$$) — 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 $$$[2, 4]$$$