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>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
long long kol, n, n1, k, a[1000009];
void w() {
  long long step = 1;
  while (n1 >= 2 * step) {
    step = 2 * step;
  }
  for (int i = step; i < n1 + 1; i++) {
    a[i] = step - (i - step + 1);
    a[step - (i - step + 1)] = i;
  }
  n1 = n1 - 2 * (n1 - step + 1);
  if (n1 > 0) w();
}
int main() {
  long long res = 1;
  cin >> n;
  res = n * (n + 1);
  cout << res << "\n";
  n1 = n;
  w();
  for (int i = 0; i < n + 1; i++) {
    cout << a[i] << " ";
  }
  cin >> kol;
}
