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, ust;
long long int sum, ar[1000005];
int main() {
  scanf("%d", &N);
  int yed = N;
  while (N) {
    ust = 1;
    while (ust <= N) ust *= 2;
    ust--;
    for (int i = N; i >= ust - N; i--) {
      ar[i] = ust - i;
    }
    N = ust - N - 1;
  }
  N = yed;
  for (int i = 0; i <= N; i++) {
    sum = sum + (i ^ ar[i]);
  }
  cout << sum << endl;
  for (int i = 0; i <= N; i++) cout << ar[i] << " ";
}
