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 num[1000005];
int com(int a) {
  int z = 1;
  while (z <= a) z <<= 1;
  return z - 1;
}
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  memset(num, -1, sizeof(num));
  long long int sum = 0;
  for (int i = n; i >= 0; --i) {
    if (num[i] == -1) {
      num[i] = (com(i) ^ i);
      num[(com(i) ^ i)] = i;
      sum += com(i) * 2;
    }
  }
  cout << sum << endl;
  for (int i = 0; i <= n; ++i) cout << num[i] << ' ';
  cout << endl;
}
