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 main(void) {
  long long n;
  cin >> n;
  vector<int> V(n + 1, 0);
  cout << n * (n + 1) << endl;
  while (n > 0) {
    int b = 0;
    int tmp = n;
    while (tmp > 1) {
      tmp >>= 1;
      b++;
    }
    tmp = (1 << b);
    V[tmp] = tmp - 1;
    for (int i = 1; (((tmp - i) >= 0) || (tmp + i <= n)); i++) {
      if ((tmp - i >= 0) && (tmp - 1 + i) <= n) V[tmp - i] = (tmp - 1 + i);
      if (tmp + i <= n) V[tmp + i] = (tmp - 1 - i);
    }
    n = tmp - (n - tmp + 1) - 1;
  }
  for (int i = 0; i < V.size(); i++) {
    cout << V[i] << ' ';
  }
  cout << endl;
  return 0;
}
