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[1000010];
int main() {
  long long n, m;
  scanf("%lld", &n);
  m = n;
  printf("%lld\n", n * n + n);
  while (n > 0) {
    int t = log2(n), p = (1 << t);
    for (int i = p; i <= n; ++i) {
      a[i] = p - (i - p + 1);
      a[a[i]] = i;
    }
    n = a[n] - 1;
  }
  if (n == 0) a[0] = 0;
  for (int i = 0; i <= m; ++i) printf("%d ", a[i]);
  printf("\n");
  return 0;
}
