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 = 1000005;
long long n, last, ans[MAXN];
int main() {
  scanf("%I64d", &n);
  for (long long i = n; i >= 0; --i) {
    if (!ans[i]) {
      long long x = i, k = 1;
      while (x) x >>= 1, k <<= 1;
      ans[k - i - 1] = i;
      ans[i] = k - i - 1;
    }
  }
  printf("%I64d\n", n * (n + 1));
  for (int i = 0; i <= n; ++i) printf("%I64d ", ans[i]);
  return 0;
}
