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] 
''' Interesting Pairs
https://codeforces.com/contest/1592/problem/A
'''

import io, os, sys
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline  # decode().strip() if str
output = sys.stdout.write


A = float('inf')
X = 513

def solve(nums, N):
	# dp[xor] = min ending val s.t. running XOR is xor
	dp = [A]*X
	dp[0] = -1

	for num in nums:
		for xor in range(X):
			if dp[xor] >= num: continue
			dp[num^xor] = min(dp[num^xor], num)
	return [xor for xor in range(X) if dp[xor] < A]


def main():
	N = int(input())
	nums = list(map(int, input().split()))
	out = solve(nums, N)
	output(str(len(out)) + '\n')
	output(' '.join(map(str, out)) + '\n')

if __name__ == '__main__':
	main()

