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>
int n;
long long sum;
int ans[1000050];
int main() {
  scanf("%d", &n);
  int max = n, base = 1;
  while (max > 0) {
    int t_max = max;
    while (t_max >>= 1) base <<= 1;
    for (int i = (base); i <= (max); i++) {
      ans[i] = base * 2 - 1 - i;
      ans[base * 2 - 1 - i] = i;
      sum += 2 * (long long)(i ^ (base * 2 - 1 - i));
    }
    max = 2 * base - 2 - max;
    base = 1;
  }
  printf("%I64d\n", sum);
  for (int i = (0); i <= (n); i++) printf("%d ", ans[i]);
  printf("\n");
}
