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;
const int N = 1e6 + 7;
int a[N];
int main() {
  int n;
  cin >> n;
  for (int i = 0; i <= n; i++) a[i] = i;
  long long ans;
  for (int i = n; i > 0; i--)
    if (a[i] == i) {
      int p = (1 << (32 - __builtin_clz(i))) - 1;
      ans += 2 * p;
      swap(a[i], a[p ^ i]);
    }
  cout << ans << "\n";
  for (int i = 0; i <= n; i++) cout << a[i] << " ";
  cout << "\n";
  return 0;
}
