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 n, a[1000010], i, k, t, j;
long long ans;
int main() {
  scanf("%d", &n);
  t = n;
  k = 1;
  while ((k << 1) <= n) k = k << 1;
  while (t > 0) {
    for (i = k, j = k - 1; i <= t; i++, j--) a[j] = i, a[i] = j;
    t = j;
    while ((t > 0) && (k > t)) k = k >> 1;
  }
  for (i = 0; i <= n; i++) ans += (long long)i ^ (long long)a[i];
  printf("%I64d\n", ans);
  for (i = 0; i <= n; i++) printf("%d ", a[i]);
  return 0;
}
