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 kkaass = 1;
int col[1000009 * 2];
int main() {
  int n;
  cin >> n;
  vector<int> vec;
  long long ans = 0;
  for (int i = n; i >= 0; i--) {
    long long l = 1048576;
    while (l - 1 - i > n || col[l - 1 - i] == 1) {
      l /= 2;
    }
    col[l - 1 - i] = 1;
    vec.push_back(l - 1 - i);
    ans += l - 1;
  }
  cout << ans << endl;
  for (int i = (int)vec.size() - 1; i >= 0; i--) cout << vec[i] << " ";
  return 0;
}
