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 a[1000005];
void work(int x) {
  if (x <= 0) return;
  int t = 1;
  while (t <= x) t *= 2;
  t--;
  int st = t - x;
  for (int i = st; i <= x; i++) a[i] = t - i;
  work(st - 1);
}
int main() {
  int n;
  scanf("%d", &n);
  printf("%I64d\n", (long long)n * (n + 1));
  work(n);
  for (int i = 0; i <= n; i++) printf("%d ", a[i]);
  return 0;
}
