human
PYTHON3 solution for "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](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 ≤ 10^5).

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 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, … 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] ":
assistant
#Here is Python code 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.
 def process(A):
    answer = [float('inf') for i in range(512)]
    answer[0] = -1
    my_count = 511
    for x in A:
        for y in range(512):
            if answer[x^y] < x:
                my_count-=1
                answer[y] = min(answer[y], x)
    final_answer = []
    for i in range(512):
        if answer[i] < float('inf'):
            final_answer.append(i)
    return final_answer
            
n = int(input())
A = [int(x) for x in input().split()]
answer = process(A)
print(len(answer))
print(' '.join(map(str,answer)))