#include <bits/stdc++.h>
#pragma GCC optimize(2, 3, "Ofast")
namespace MyMinMax {
template <typename T>
inline T mn(const T x, const T y) {
  return x < y ? x : y;
}
template <typename T>
inline T mx(const T x, const T y) {
  return x > y ? x : y;
}
template <typename T>
inline bool chmin(T &x, const T y) {
  return (x > y) && ((x = y), 1);
}
template <typename T>
inline bool chmax(T &x, const T y) {
  return (x < y) && ((x = y), 1);
}
template <typename T, typename... Args>
inline T mx(const T x, const Args... args) {
  return mx(x, mx(args...));
}
template <typename T, typename... Args>
inline T mn(const T x, const Args... args) {
  return mn(x, mn(args...));
}
}  // namespace MyMinMax
using namespace MyMinMax;
namespace IO {
const int DPAIRSIZ = 1 << 18;
char BB[DPAIRSIZ], *SS = BB, *TT = BB;
inline char getcha() {
  return SS == TT && (TT = (SS = BB) + fread(BB, 1, DPAIRSIZ, stdin), SS == TT)
             ? EOF
             : *SS++;
}
template <typename T = int>
inline T read() {
  T x = 0;
  int fu = 1;
  char c = getcha();
  while (c < 48) {
    if (c == 45) {
      fu = -1;
    }
    c = getcha();
  }
  while (c >= 48) {
    x = x * 10 + c - 48;
    c = getcha();
  }
  x *= fu;
  return x;
}
template <typename T>
inline void read(T &x) {
  x = 0;
  int fu = 1;
  char c = getcha();
  while (c < 48) {
    if (c == 45) {
      fu = -1;
    }
    c = getcha();
  }
  while (c >= 48) {
    x = x * 10 + c - 48;
    c = getcha();
  }
  x *= fu;
}
template <typename T>
inline void read(T *bg, T *ed) {
  while (bg != ed) read(*bg++);
}
inline void read(char &ch) {
  ch = getcha();
  while (ch <= 32) ch = getcha();
}
inline void read(char *s) {
  char ch = getcha();
  while (ch <= 32) ch = getcha();
  while (ch > 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void getl(char *s) {
  char ch = getcha();
  while (ch < 32) ch = getcha();
  while (ch >= 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void pread(char *&s) {
  char ch = getcha();
  while (ch <= 32) ch = getcha();
  while (ch > 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void pgetl(char *&s) {
  char ch = getcha();
  while (ch <= 32) ch = getcha();
  while (ch > 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
template <typename T, typename... Args>
inline void read(T &x, Args &...args) {
  read(x);
  read(args...);
}
char out[DPAIRSIZ], *Out = out;
inline void putcha(char x) {
  *Out++ = x;
  if (Out - out >= (DPAIRSIZ)) fwrite(out, 1, Out - out, stdout), Out = out;
}
template <typename T>
inline void fprint(T x) {
  if (x < 0) putcha(45), x = -x;
  if (x > 9) fprint(x / 10);
  putcha(x % 10 + 48);
}
inline void print() { putcha(10); }
template <typename T>
inline void print(T x) {
  fprint(x);
  putcha(10);
}
inline void print(char *ch) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
}
inline void put(char *ch) {
  while (*ch != '\0') putcha(*(ch++));
}
inline void print(const char *ch) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
}
inline void put(const char *ch) {
  while (*ch != '\0') putcha(*(ch++));
}
template <typename T, typename... Args>
inline void print(T x, Args... args) {
  fprint(x);
  putcha(32);
  print(args...);
}
template <typename... Args>
inline void print(const char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(32);
  print(args...);
}
template <typename... Args>
inline void print(char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(32);
  print(args...);
}
template <typename T, typename... Args>
inline void printl(T x, Args... args) {
  fprint(x);
  putcha(10);
  printl(args...);
}
template <typename... Args>
inline void printl(const char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
  printl(args...);
}
template <typename... Args>
inline void printl(char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
  printl(args...);
}
template <typename T>
inline void sprint(T x) {
  fprint(x);
  putcha(32);
}
template <typename T, typename... Args>
inline void sprint(T x, Args... args) {
  fprint(x);
  putcha(32);
  sprint(args...);
}
template <typename T>
inline void sprint(T *bg, T *ed) {
  while (bg != ed) sprint(*bg++);
}
template <typename T>
inline void print(T *bg, T *ed) {
  while (bg != ed) sprint(*bg++);
  putcha(10);
}
template <typename T>
inline void printl(T *bg, T *ed) {
  while (bg != ed) print(*bg++);
}
class AutoFlush {
 public:
  ~AutoFlush() { fwrite(out, 1, Out - out, stdout); }
} __AutoFlush;
}  // namespace IO
using namespace IO;
const int INF = 0x3f3f3f3f;
const long long INFll = 0x3f3f3f3f3f3f3f3fll;
const int MAXN = 1e5 + 5;
int n, a[MAXN];
int f[512], g[512];
std::vector<int> ans;
signed main() {
  read(n);
  read(a + 1, a + n + 1);
  memset(f, 63, sizeof(f));
  f[0] = 0;
  for (int i = (1), iEND = (n); i <= iEND; ++i) {
    memcpy(g, f, sizeof(g));
    for (int j = (0), jEND = (511); j <= jEND; ++j)
      if (a[i] > g[j ^ a[i]]) chmin(f[j], a[i]);
  }
  for (int j = (0), jEND = (511); j <= jEND; ++j)
    if (f[j] < 512) ans.push_back(j);
  print(ans.size());
  for (auto it : ans) sprint(it);
  print();
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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>
#pragma GCC optimize(2, 3, "Ofast")
namespace MyMinMax {
template <typename T>
inline T mn(const T x, const T y) {
  return x < y ? x : y;
}
template <typename T>
inline T mx(const T x, const T y) {
  return x > y ? x : y;
}
template <typename T>
inline bool chmin(T &x, const T y) {
  return (x > y) && ((x = y), 1);
}
template <typename T>
inline bool chmax(T &x, const T y) {
  return (x < y) && ((x = y), 1);
}
template <typename T, typename... Args>
inline T mx(const T x, const Args... args) {
  return mx(x, mx(args...));
}
template <typename T, typename... Args>
inline T mn(const T x, const Args... args) {
  return mn(x, mn(args...));
}
}  // namespace MyMinMax
using namespace MyMinMax;
namespace IO {
const int DPAIRSIZ = 1 << 18;
char BB[DPAIRSIZ], *SS = BB, *TT = BB;
inline char getcha() {
  return SS == TT && (TT = (SS = BB) + fread(BB, 1, DPAIRSIZ, stdin), SS == TT)
             ? EOF
             : *SS++;
}
template <typename T = int>
inline T read() {
  T x = 0;
  int fu = 1;
  char c = getcha();
  while (c < 48) {
    if (c == 45) {
      fu = -1;
    }
    c = getcha();
  }
  while (c >= 48) {
    x = x * 10 + c - 48;
    c = getcha();
  }
  x *= fu;
  return x;
}
template <typename T>
inline void read(T &x) {
  x = 0;
  int fu = 1;
  char c = getcha();
  while (c < 48) {
    if (c == 45) {
      fu = -1;
    }
    c = getcha();
  }
  while (c >= 48) {
    x = x * 10 + c - 48;
    c = getcha();
  }
  x *= fu;
}
template <typename T>
inline void read(T *bg, T *ed) {
  while (bg != ed) read(*bg++);
}
inline void read(char &ch) {
  ch = getcha();
  while (ch <= 32) ch = getcha();
}
inline void read(char *s) {
  char ch = getcha();
  while (ch <= 32) ch = getcha();
  while (ch > 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void getl(char *s) {
  char ch = getcha();
  while (ch < 32) ch = getcha();
  while (ch >= 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void pread(char *&s) {
  char ch = getcha();
  while (ch <= 32) ch = getcha();
  while (ch > 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
inline void pgetl(char *&s) {
  char ch = getcha();
  while (ch <= 32) ch = getcha();
  while (ch > 32) *s++ = ch, ch = getcha();
  *s = '\0';
}
template <typename T, typename... Args>
inline void read(T &x, Args &...args) {
  read(x);
  read(args...);
}
char out[DPAIRSIZ], *Out = out;
inline void putcha(char x) {
  *Out++ = x;
  if (Out - out >= (DPAIRSIZ)) fwrite(out, 1, Out - out, stdout), Out = out;
}
template <typename T>
inline void fprint(T x) {
  if (x < 0) putcha(45), x = -x;
  if (x > 9) fprint(x / 10);
  putcha(x % 10 + 48);
}
inline void print() { putcha(10); }
template <typename T>
inline void print(T x) {
  fprint(x);
  putcha(10);
}
inline void print(char *ch) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
}
inline void put(char *ch) {
  while (*ch != '\0') putcha(*(ch++));
}
inline void print(const char *ch) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
}
inline void put(const char *ch) {
  while (*ch != '\0') putcha(*(ch++));
}
template <typename T, typename... Args>
inline void print(T x, Args... args) {
  fprint(x);
  putcha(32);
  print(args...);
}
template <typename... Args>
inline void print(const char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(32);
  print(args...);
}
template <typename... Args>
inline void print(char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(32);
  print(args...);
}
template <typename T, typename... Args>
inline void printl(T x, Args... args) {
  fprint(x);
  putcha(10);
  printl(args...);
}
template <typename... Args>
inline void printl(const char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
  printl(args...);
}
template <typename... Args>
inline void printl(char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
  printl(args...);
}
template <typename T>
inline void sprint(T x) {
  fprint(x);
  putcha(32);
}
template <typename T, typename... Args>
inline void sprint(T x, Args... args) {
  fprint(x);
  putcha(32);
  sprint(args...);
}
template <typename T>
inline void sprint(T *bg, T *ed) {
  while (bg != ed) sprint(*bg++);
}
template <typename T>
inline void print(T *bg, T *ed) {
  while (bg != ed) sprint(*bg++);
  putcha(10);
}
template <typename T>
inline void printl(T *bg, T *ed) {
  while (bg != ed) print(*bg++);
}
class AutoFlush {
 public:
  ~AutoFlush() { fwrite(out, 1, Out - out, stdout); }
} __AutoFlush;
}  // namespace IO
using namespace IO;
const int INF = 0x3f3f3f3f;
const long long INFll = 0x3f3f3f3f3f3f3f3fll;
const int MAXN = 1e5 + 5;
int n, a[MAXN];
int f[512], g[512];
std::vector<int> ans;
signed main() {
  read(n);
  read(a + 1, a + n + 1);
  memset(f, 63, sizeof(f));
  f[0] = 0;
  for (int i = (1), iEND = (n); i <= iEND; ++i) {
    memcpy(g, f, sizeof(g));
    for (int j = (0), jEND = (511); j <= jEND; ++j)
      if (a[i] > g[j ^ a[i]]) chmin(f[j], a[i]);
  }
  for (int j = (0), jEND = (511); j <= jEND; ++j)
    if (f[j] < 512) ans.push_back(j);
  print(ans.size());
  for (auto it : ans) sprint(it);
  print();
}

```