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[1000005];
int main() {
  int n;
  long long sum = 0;
  cin >> n;
  memset(a, -1, sizeof(a));
  for (int i = n; i >= 0; i--) {
    if (a[i] != -1)
      continue;
    else {
      for (int tt = 1;; tt *= 2) {
        if (tt - 1 >= i) {
          a[i] = tt - 1 - i;
          a[tt - 1 - i] = i;
          sum = sum + 2 * (tt - 1);
          break;
        }
      }
    }
  }
  cout << sum << endl;
  for (int i = 0; i <= n; i++) {
    if (i != 0) printf(" ");
    printf("%d", a[i]);
  }
  cout << endl;
  return 0;
}
