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 n, ans[1111111], cur;
bool w[1111111];
long long res;
int main() {
  scanf("%d", &n), memset(w, 0, sizeof(w)), memset(ans, -1, sizeof(ans));
  for (int i = n; i >= 0; --i)
    if (!w[i]) {
      cur = 1;
      while (cur <= i) cur <<= 1;
      --cur, ans[i] = cur - i, w[ans[i]] = w[ans[ans[i]] = i] = true;
    }
  res = 0;
  for (int i = 0; i <= n; ++i) res += i ^ ans[i];
  printf(
      "%lld"
      "\n",
      res);
  for (int i = 0; i <= n; ++i) printf("%d ", ans[i]);
  return 0;
}
