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;
  cin >> n;
  int N = n;
  n++;
  vector<int> p(n + 1);
  for (; n > 1;) {
    int b = log2(n - 1);
    int m = (1 << b) - 1;
    for (int i = 1; i < n - m; i++) p[m + i] = m - i + 1, p[m - i + 1] = m + i;
    n = 2 * m + 2 - n;
  }
  cout << ((long long)N) * ((long long)(N) + 1ll) << "\n";
  for (int i = 0; i <= N; i++) cout << p[i] << " ";
}
