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 n, ans, a[1000005], v[1000005];
long long get(long long x) {
  long long len = (long long)log2(x) + 1;
  long long s = (1 << len) - 1;
  return s - x;
}
int main() {
  scanf("%I64d", &n);
  for (long long i = 1; i <= n; i++) a[i] = i;
  for (long long i = n; i; i--)
    if (!v[i]) {
      long long x = get(i);
      v[x] = 1;
      swap(a[x], a[i]);
      ans += x + i + x + i;
    }
  printf("%I64d\n", ans);
  for (long long i = 0; i <= n; i++) printf("%I64d ", a[i]);
}
