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;
const int N = 1e6 + 5;
long long n, ans[N];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  long long bt = log2(n) + 1;
  for (int i = n; i > 0; i--) {
    long long tmp = (1 << bt) - 1, inv = i ^ tmp;
    long long st = inv, en = i;
    while (st < en) {
      ans[st] = en, ans[en] = st, st++, en--;
    }
    i = inv;
    if (i != 0) bt = log2(i - 1) + 1;
  }
  cout << n * (n + 1) << '\n';
  for (int i = 0; i <= n; i++) cout << ans[i] << ' ';
  return 0;
}
