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;
stringstream ss;
long long mod = 1000000007LL;
int main() {
  long long n;
  cin >> n;
  cout << n * (n + 1) << endl;
  n++;
  for (int i = 20; i >= 0; i--)
    if ((1LL << i) <= n) {
      n -= (1LL << i);
      for (int j = 0; j < (1LL << i); j++)
        if ((1LL << i) - 1 - j < n)
          cout << ((1LL << i + 1) - 1 - j) << " ";
        else
          cout << ((1LL << i) - 1 - j) << " ";
    }
  cout << endl;
  return 0;
}
