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;
long long vis[1010000], ans[1010000];
int main() {
  long long n, i, tot = 0, j, x, now = 1;
  scanf("%I64d", &n);
  memset(vis, 0, sizeof(vis));
  for (i = 1;; i++) {
    now = now * 2;
    if ((now - 1) >= n) break;
  }
  now--;
  for (i = n; i >= 0; i--) {
    if (vis[i] == 1) continue;
    x = now - i;
    if (x <= i) {
      for (j = i; j >= x; j--) {
        ans[j] = x + i - j;
        vis[j] = 1;
        tot += now;
      }
      now /= 2;
    } else {
      now /= 2;
      i++;
    }
  }
  printf("%I64d\n", tot);
  for (i = 0; i <= n; i++) printf("%I64d ", ans[i]);
  printf("\n");
  return 0;
}
