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;
const double eps = 1e-8;
int res[1000005], n;
void rec(int k) {
  if (k < 0) return;
  if (k == 0) {
    res[0] = 0;
    return;
  }
  int meja = 1;
  while (meja * 2 <= k) meja *= 2;
  int raz = k - meja;
  for (int i = k; i >= meja - raz - 1; i--) {
    int mim = abs(i - meja);
    if (i >= meja) {
      res[i] = meja - mim - 1;
    } else {
      res[i] = meja + mim - 1;
    }
  }
  rec(meja - raz - 2);
}
int main() {
  scanf("%d", &n);
  long long vsota = (long long)n * (long long)(n + 1);
  cout << vsota << "\n";
  rec(n);
  for (int i = 0; (i) < (n); (i)++) printf("%d ", res[i]);
  printf("%d", res[n]);
  return 0;
}
