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 arr[1111111];
int main() {
  long long n, m, ans;
  scanf("%lld", &n);
  m = n;
  ans = n * (n + 1);
  for (int i = 0; i <= n; i++) arr[i] = i;
  for (int bit = 29; bit >= 0; bit--) {
    if ((1 << bit) > n) continue;
    for (int i = 1 << bit; i <= n; i++) {
      swap(arr[i], arr[(1 << (bit + 1)) - i - 1]);
    }
    n = (1 << (bit + 1)) - n - 2;
  }
  printf("%lld\n", ans);
  for (int i = 0; i <= m; i++) printf("%d ", arr[i]);
  return 0;
}
