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 *solve(int n) {
  int *result = new int[n + 1];
  int R = n;
  while (R >= 2) {
    int pow2 = 1;
    while (pow2 <= R) pow2 *= 2;
    pow2--;
    int L = (~R) & pow2;
    for (int i = L, j = R; i < j; i++, j--) {
      result[i] = j;
      result[j] = i;
    }
    R = L - 1;
  }
  if (R == 0) {
    result[0] = 0;
  } else if (R == 1) {
    result[0] = 1;
    result[1] = 0;
  }
  return result;
}
int main() {
  int n;
  cin >> n;
  int *result = solve(n);
  long long sum = 0;
  for (int i = 0; i <= n; i++) sum += i ^ result[i];
  cout << sum << '\n';
  for (int i = 0; i <= n; i++) cout << result[i] << ' ';
  delete[] result;
  return 0;
}
