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 a[1000001];
char was[1000001];
int main() {
  cin.sync_with_stdio(false);
  int n, msk = 1;
  cin >> n;
  cout << (1LL * n * (n + 1)) << endl;
  for (int i = n; i > 0; i--) {
    if (was[i]) continue;
    for (msk = 1; msk <= i; msk <<= 1)
      ;
    msk--;
    int el = msk ^ i;
    if (!was[el]) {
      a[i] = el;
      a[el] = i;
      was[i] = was[el] = 1;
    }
  }
  if (!was[0]) {
    for (int i = 1; i <= n; i++)
      if (!was[i]) a[0] = i, a[i] = 0;
  }
  for (int i = 0; i <= n; i++) cout << a[i] << " ";
  cout << endl;
  return 0;
}
