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 f[1000005];
int main() {
  long long res = 0;
  int n, i, j, k, l, r;
  cin >> n;
  k = 1;
  while (k < n) k = (k << 1) + 1;
  l = k - n;
  r = n;
  f[0] = 0;
  while (r > 0) {
    for (i = l; i <= r; ++i) {
      f[i] = k - i;
      res += k;
    }
    r = l - 1;
    k = 1;
    while (k < r) k = (k << 1) + 1;
    l = k - r;
  }
  cout << res << endl;
  for (i = 0; i < n; ++i) cout << f[i] << " ";
  cout << f[n] << endl;
  return 0;
}
