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 a[1111111];
int main() {
  int n;
  cin >> n;
  int N = n;
  while (N) {
    int b = 1;
    while ((1 << b) <= N) b++;
    int _N = (1 << (b - 1)) - 1;
    for (int i = 1 << (b - 1); i <= N; i++, _N--) {
      a[i] = _N;
      a[_N] = i;
    }
    N = _N;
  }
  long long ans = 0;
  for (int i = 0; i <= n; i++) ans += a[i] ^ i;
  cout << ans << endl;
  for (int i = 0; i <= n; i++) cout << a[i] << endl;
}
