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;
long long a[1000001];
int main() {
  long long n;
  cin >> n;
  cout << n * (n + 1) << '\n';
  for (int i = n; i >= 0; i--) {
    int x = 0;
    if (a[i]) continue;
    for (int j = 0; j <= 32; j++) {
      if ((1ll << (j)) > i) {
        x = j;
        break;
      }
    }
    int y = i ^ ((1ll << (x)) - 1);
    a[i] = y;
    a[y] = i;
  }
  for (int i = 0; i <= n; i++) printf("%d ", a[i]);
  return 0;
}
