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;
void solve(int o) {
  if (o < 0) return;
  int tmp = 0;
  int tmp2 = 1;
  int tt = o;
  while (tt != 0) {
    ++tmp;
    tt /= 2;
    tmp2 *= 2;
  }
  int tmp3 = o ^ (tmp2 - 1);
  solve(tmp3 - 1);
  for (int i = o; i >= tmp3; i--) {
    cout << i << " ";
  }
}
int main() {
  long long n;
  cin >> n;
  cout << (n + 1) * n << endl;
  solve(n);
  cout << endl;
  return 0;
}
