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 taken[1000001];
int a[1000001];
int main() {
  int i, n;
  long long msk;
  long long sum = 0;
  scanf("%d", &n);
  for (i = 0; i < n; i++) taken[i] = 0;
  a[0] = 0;
  for (i = n; i > 0; i--) {
    if (!taken[i]) {
      msk = 1;
      while (msk <= i) msk *= 2;
      msk--;
      a[i] = i ^ msk;
      a[i ^ msk] = i;
      taken[i ^ msk] = 1;
      sum += msk * 2;
    }
  }
  printf("%I64d\n", sum);
  for (i = 0; i <= n; i++) printf("%d ", a[i]);
  printf("\n");
  return 0;
}
