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 stmp;
const int MAX = 1000001;
const int INF = 1000000001;
int arr[MAX];
int n;
int main(int argc, char *argv[]) {
  cin >> n;
  int i = n;
  while (i) {
    int k = 1;
    while (k <= i) k *= 2;
    --k;
    for (int t = (k - i); t <= (i); ++t) arr[t] = k ^ t;
    i = k - i - 1;
  }
  long long res = 0;
  for (int t = (0); t <= (n); ++t) res += arr[t] ^ t;
  cout << res << endl;
  for (int t = (0); t <= (n); ++t) cout << arr[t] << ' ';
  cout << endl;
  return 0;
}
