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 = 1000000 + 10;
int vis[N] = {0}, a[N];
int main() {
  int n, len;
  cin >> n;
  for (len = 0; (1 << len) <= n; len++)
    ;
  int all = (1 << len) - 1;
  for (int i = n; i >= 0; i--) {
    int k = i ^ all;
    while ((k > n || vis[k]) && len >= 0) {
      len--;
      all = (1 << len) - 1;
      k = i ^ all;
    }
    vis[k] = 1;
    a[i] = k;
  }
  long long ans = 0;
  for (int i = 0; i <= n; ++i) ans += i ^ a[i];
  cout << ans << endl;
  for (int i = 0; i <= n; ++i) cout << a[i] << " ";
  cout << endl;
  return 0;
}
