Little penguin Polo likes permutations. But most of all he likes permutations of integers from 0 to n, inclusive.

For permutation p = p0, p1, ..., pn, Polo has defined its beauty — number <image>.

Expression <image> means applying the operation of bitwise excluding "OR" to numbers x and y. This operation exists in all modern programming languages, for example, in language C++ and Java it is represented as "^" and in Pascal — as "xor".

Help him find among all permutations of integers from 0 to n the permutation with the maximum beauty.

Input

The single line contains a positive integer n (1 ≤ n ≤ 106).

Output

In the first line print integer m the maximum possible beauty. In the second line print any permutation of integers from 0 to n with the beauty equal to m.

If there are several suitable permutations, you are allowed to print any of them.

Examples

Input

4


Output

20
0 2 1 4 3
#include <bits/stdc++.h>
using namespace std;
const int M = 1000000 + 10;
int a[M];
int flag[M];
int main() {
  time_t t_start, t_end;
  t_start = clock();
  int n;
  cin >> n;
  long long int ans = 0;
  for (int i = n; i >= 0; i--) {
    if (flag[i] == 0) {
      int tmp = i;
      int d = 0;
      while (tmp > 0) {
        tmp = tmp >> 1;
        d++;
      }
      int s = (1 << d) - 1;
      int r = s ^ i;
      a[i] = r;
      a[r] = i;
      flag[r] = 1;
      ans = ans + s * 2;
    }
  }
  cout << ans << endl;
  for (int i = 0; i <= n; i++) {
    printf("%d ", a[i]);
  }
  cout << endl;
  t_end = clock();
  return 0;
}
