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;
int b;
int res[1000002];
int temp[1000002] = {0};
int main() {
  scanf("%d", &a);
  for (int i = 0; i <= a; i++) {
    int x = i;
    while (x > 0) {
      temp[i]++;
      x /= 2;
    }
  }
  long long total = 0;
  for (int i = a; i >= 0; i--) {
    if (res[i] == 0) {
      res[i] = ((1 << temp[i]) - 1) ^ i;
      res[res[i]] = i;
    }
  }
  for (int i = a; i >= 0; i--) {
    total += (long long)(i ^ res[i]);
  }
  printf("%I64d\n", total);
  for (int i = 0; i <= a; i++) {
    if (i) printf(" ");
    printf("%d", res[i]);
  }
  printf("\n");
  return 0;
}
