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;
int p[1000100];
int main() {
  int i, n, j;
  long long r;
  for (scanf("%d", &n), i = 0; i <= n; p[i] = -1, i++)
    ;
  for (r = 0, i = n; i >= 0; r += i ^ p[i], i--)
    if (p[i] == -1) {
      for (p[i] = 0, j = 0; i >> j; p[i] |= (((i >> j) & 1) ^ 1) << j, j++)
        ;
      p[p[i]] = i;
    }
  printf("%I64d\n", r);
  for (i = 0; i <= n; printf("%d ", p[i]), i++)
    ;
  printf("\n");
  return 0;
}
