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;
int A[1010101];
long long res;
unsigned int all_bits(unsigned int x) {
  unsigned int res = 0;
  do res = res << 1 | 1, x >>= 1;
  while (x);
  return res;
}
int main() {
  memset(A, -1, sizeof A);
  res = 0;
  scanf("%d", &n);
  for (int i = n; i >= 0; i--) {
    if (A[i] != -1) continue;
    int j = all_bits(i) ^ i;
    if (A[j] == -1)
      A[i] = j, A[j] = i;
    else
      A[i] = i;
  }
  for (int i = 0; i <= n; i++) res += i ^ A[i];
  cout << res << endl;
  for (int i = 0; i <= n; i++) printf("%d ", A[i]);
  return 0;
}
