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;
long long n, a[1000100], s = 0;
long long rev(long long x) {
  int m = 0;
  for (int i = 0; i <= 20; i++)
    if (x & (1 << i)) m = i;
  m++;
  long long g = (1 << m) - 1;
  return g ^ x;
}
int main() {
  cin >> n;
  for (long long i = n; i > 0; i--)
    if (a[i] == 0) {
      long long j = rev(i);
      a[i] = j;
      a[j] = i;
      s += 2 * (i ^ j);
    }
  cout << s << endl;
  for (int i = 0; i <= n; i++) cout << a[i] << " ";
}
