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 pasang[1050000];
int main() {
  int n;
  cin >> n;
  ++n;
  int orgn = n;
  while (n) {
    if (n == 1) {
      pasang[0] = 0;
      break;
    }
    int bat = 1;
    while (bat < n) bat *= 2;
    int sisa = bat - n;
    for (int i = bat / 2; i < n; ++i) {
      pasang[i] = (bat - 1 - i);
      pasang[(bat - 1 - i)] = i;
    }
    n = sisa;
  }
  long long res = 0LL;
  for (int(i) = 0; (i) < (orgn); ++(i)) {
    res += (long long)(i ^ pasang[i]);
  }
  cout << res << endl;
  for (int(i) = 0; (i) < (orgn); ++(i)) {
    printf("%d ", pasang[i]);
  }
}
