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 long long l = 1000005;
long long b[20];
long long p[l];
int main() {
  long long n, m, s = 0;
  cin >> n;
  for (int i = 0; i < l; i++) p[i] = -1;
  b[0] = 1;
  for (int i = 0; i < 20; i++) {
    b[i] = 1 << i + 1;
    b[i]--;
  }
  for (int i = n; i >= 0; i--)
    if (p[i] == -1)
      for (int j = 19; j >= 0; j--) {
        m = i ^ b[j];
        if (m <= n && p[m] == -1) {
          p[m] = i;
          p[i] = m;
          break;
        }
      }
  if (p[0] == -1) p[0] = 0;
  for (int i = 0; i <= n; i++) s += i ^ p[i];
  cout << s << endl;
  for (int i = 0; i <= n; i++) {
    if (i) cout << ' ';
    cout << p[i];
  }
  cout << endl;
  return 0;
}
