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 n, t, i, nn, p[2000010], tmp, x;
long long ans;
int main() {
  scanf("%d", &n);
  nn = n;
  while (n >= 0) {
    for (t = 0; n >> t; t++)
      ;
    t--;
    x = (1 << t + 1) - 1;
    for (i = 1 << t; i <= n; i++) p[i] = x - i, p[x - i] = i;
    n = x - n - 1;
  }
  for (i = 0; i <= nn; i++) ans += i ^ p[i];
  printf("%I64d\n", ans);
  for (i = 0; i <= nn; i++) printf("%d ", p[i]);
}
