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 mas[1000001];
void f(int n) {
  if (n <= 1) return;
  int d = 1;
  while (d * 2 < n) d *= 2;
  int nn = d;
  for (int i = d; i < n; i++) {
    swap(mas[i], mas[d * 2 - i - 1]);
    nn--;
  }
  f(nn);
}
int main() {
  int N;
  scanf("%d", &N);
  for (int i = 0; i < N + 1; i++) mas[i] = i;
  f(N + 1);
  long long m = 0;
  for (int i = 0; i < N + 1; i++) m += mas[i] ^ i;
  cout << m << '\n';
  for (int i = 0; i < N + 1; i++) cout << mas[i] << ' ';
  return 0;
}
