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, M;
int p[1000005];
bool f[1000005];
int cal(int m) {
  int n = 1;
  while (m) {
    n <<= 1;
    m >>= 1;
  }
  return n - 1;
}
int main() {
  int i, j;
  cin >> N;
  M = (1 + N) * N;
  cout << M << endl;
  (memset(p, 0, sizeof(p)));
  (memset(f, 0, sizeof(f)));
  for (i = N; i >= 0; --i) {
    if (f[i]) continue;
    j = cal(i) - i;
    ;
    p[i] = j;
    p[j] = i;
    f[i] = f[j] = 1;
  }
  for (i = 0; i <= N; ++i) printf("%d ", p[i]);
  return 0;
}
