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;
long long ans[2000000], n;
int complement(int n) {
  int ans = 0, p = 1;
  while (n) {
    ans = ans + (1 - n % 2) * p;
    n /= 2;
    p *= 2;
  }
  return ans;
}
int main() {
  ios::sync_with_stdio(0);
  cin >> n;
  for (int i = n; i > -1; i--)
    if (!ans[i]) {
      ans[i] = complement(i);
      ans[complement(i)] = i;
    }
  cout << n * (n + 1) << endl;
  for (int i = 0; i <= n; i++) cout << ans[i] << " ";
  cout << endl;
}
