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 o[1000100];
int main() {
  int n;
  scanf("%d", &n);
  long long ans = 0;
  memset(o, -1, sizeof(o));
  for (int i = n; i >= 0; i--) {
    if (o[i] == -1) {
      int cnt = 0;
      int x = i;
      do {
        cnt++;
        x /= 2;
      } while (x != 0);
      int ret = ((1 << cnt) - 1) ^ i;
      if (o[ret] == -1) {
        o[ret] = i;
        o[i] = ret;
      } else {
        o[i] = i;
      }
    }
    ans += i ^ o[i];
  }
  printf("%I64d\n", ans);
  for (int i = 0; i <= n; i++) {
    printf("%d ", o[i]);
  }
  printf("\n");
  return 0;
}
