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 a[1000009];
int main() {
  int i, j, k, n, m;
  scanf("%d", &n);
  for (i = 0; i <= n; i++) a[i] = i;
  for (i = n; i >= 0; i--) {
    if (a[i] != i) continue;
    for (j = 0; (1 << j) <= a[i]; j++)
      ;
    k = (1 << j) - 1 - a[i];
    swap(a[i], a[k]);
  }
  long long s = n;
  cout << s * (s + 1) << endl;
  for (i = 0; i <= n; i++) printf("%d ", a[i]);
  return 0;
}
