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 main() {
  ios_base::sync_with_stdio(0);
  int n;
  cin >> n;
  vector<bool> f(n + 1, false);
  vector<int> p(n + 1, -1);
  int mask = n;
  long long ans = 0;
  while ((mask + 1) & mask) mask |= mask >> 1;
  for (int i = n; i >= 0; --i) {
    while (mask - i > n || f[mask - i]) mask >>= 1;
    p[i] = mask - i;
    f[mask - i] = true;
    ans += mask;
  }
  cout << ans << endl;
  for (int i = 0; i < n + 1; ++i) {
    cout << p[i] << " ";
  }
  cout << endl;
  return 0;
}
