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;
const int MAXN = 1000010;
long long a[MAXN];
long long b[32];
int main() {
  int n, temp = 1;
  long long i;
  b[0] = 0;
  for (i = 1; i <= 30; i++) {
    temp = 2 * temp;
    b[i] = temp - 1;
  }
  scanf("%d", &n);
  long long ans = 0;
  int j = 0;
  memset(a, -1, sizeof(a));
  for (j = 0; j <= 30; j++) {
    if (b[j] >= n) break;
  }
  for (i = n; i >= 0; i--) {
    if (j && b[j - 1] >= i) j--;
    if (a[i] != -1) continue;
    a[i] = i ^ b[j];
    a[a[i]] = i;
    ans += 2 * (a[i] ^ i);
  }
  printf("%I64d\n", ans);
  for (i = 0; i <= n; i++) printf("%I64d ", a[i]);
  printf("\n");
  return 0;
}
