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 main() {
  int n, k;
  cin >> n;
  long long ans = 0;
  int arr[n + 1];
  int count = 0;
  int check[1000202] = {};
  int j1 = n, te = 1, an = 0;
  while (j1) {
    an += te;
    te *= 2;
    j1 >>= 1;
  }
  for (int i = n; i >= 0; i--) {
    if (check[i] == 0) {
      int fuc = 0, j = an;
      while ((j ^ i) > i) {
        j >>= 1;
      }
      check[i] = 1;
      check[i ^ j] = 1;
      arr[i] = i ^ j;
      arr[i ^ j] = i;
      ans = ans + 2 * (j);
    }
  }
  cout << ans << endl;
  for (int i = 0; i <= n; i++) cout << arr[i] << " ";
}
