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>
void doit(int);
int main() {
  int N;
  scanf("%d", &N);
  printf("%.0lf\n", (double)N * ((double)N + 1));
  doit(N);
  printf("\n");
  return 0;
}
void doit(int n) {
  int i = 0, p = 0;
  while ((1 << (i + 1)) - 1 <= n) i++;
  p = (1 << i) - 1;
  if (p == n)
    for (i = 0; i <= n; i++)
      (i == 0) ? printf("%d", n - i) : printf(" %d", n - i);
  else {
    doit(2 * p - n);
    for (i = 2 * p + 1 - n; i <= n; i++) printf(" %d", 2 * p + 1 - i);
  }
}
