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 ans[1000005];
int main() {
  int n;
  scanf("%d", &n);
  memset(ans, -1, sizeof(ans));
  long long sum = 0;
  for (int i = n; i >= 0; --i) {
    if (ans[i] > -1) continue;
    for (int j = 0;; ++j) {
      if ((1 << j) - 1 >= i) {
        int t = (1 << j) - 1;
        ans[i] = t - i;
        ans[t - i] = i;
        sum += ((1 << j) - 1) * 2;
        break;
      }
    }
  }
  cout << sum << endl;
  for (int i = 0; i <= n; ++i) {
    if (!i)
      printf("%d", ans[i]);
    else
      printf(" %d", ans[i]);
  }
  printf("\n");
  return 0;
}
