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[1000010];
int main() {
  double d;
  long long int m, n, i, j, k;
  cin >> n;
  m = (n + 1) * n;
  for (i = 0; i <= n; i++) a[i] = -1;
  for (i = n; i >= 0; i--) {
    if (a[i] != -1)
      continue;
    else {
      j = -1;
      k = i;
      while (k) {
        k = k >> 1;
        j++;
      }
      d = pow(2, j + 1);
      k = d - 1;
      j = k - i;
      if (j > i) continue;
      if (j == i) {
        a[i] = i;
        m = m - 2 * i;
        continue;
      }
      a[j] = i;
      a[i] = j;
    }
  }
  cout << m << "\n";
  for (i = 0; i <= n; i++) {
    cout << a[i] << " ";
  }
  cout << "\n";
  return 0;
}
