#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 10;
void solve() {
  int n;
  cin >> n;
  vector<int> a(n + 1);
  vector<bool> dp(520, 0);
  vector<int> pos(520, n + 10);
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  dp[0] = 1;
  dp[a[1]] = 1;
  pos[a[1]] = a[1];
  for (int i = 2; i <= n; i++) {
    dp[a[i]] = 1;
    pos[a[i]] = min(pos[a[i]], a[i]);
    for (int k = 0; k < 520; k++) {
      if (dp[k] && pos[k] <= a[i]) {
        dp[k ^ a[i]] = 1;
        pos[k ^ a[i]] = min(pos[k ^ a[i]], a[i]);
      }
    }
  }
  vector<int> ans;
  for (int i = 0; i < 520; i++) {
    if (dp[i]) ans.push_back(i);
  }
  cout << ans.size() << '\n';
  for (auto e : ans) {
    cout << e << ' ';
  }
  cout << '\n';
}
int main() { solve(); }

### Prompt

In Cpp, your task is to solve the following problem:

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] 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 10;
void solve() {
  int n;
  cin >> n;
  vector<int> a(n + 1);
  vector<bool> dp(520, 0);
  vector<int> pos(520, n + 10);
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  dp[0] = 1;
  dp[a[1]] = 1;
  pos[a[1]] = a[1];
  for (int i = 2; i <= n; i++) {
    dp[a[i]] = 1;
    pos[a[i]] = min(pos[a[i]], a[i]);
    for (int k = 0; k < 520; k++) {
      if (dp[k] && pos[k] <= a[i]) {
        dp[k ^ a[i]] = 1;
        pos[k ^ a[i]] = min(pos[k ^ a[i]], a[i]);
      }
    }
  }
  vector<int> ans;
  for (int i = 0; i < 520; i++) {
    if (dp[i]) ans.push_back(i);
  }
  cout << ans.size() << '\n';
  for (auto e : ans) {
    cout << e << ' ';
  }
  cout << '\n';
}
int main() { solve(); }

```