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, k = 1, p[1000005];
long long ans;
int main() {
  cin >> n;
  while (k < n) k = 2 * k + 1;
  for (int i = n; i; i--) {
    if (k / 2 >= i) k /= 2;
    if (!p[i]) p[i] = k ^ i, p[k ^ i] = i, ans += k;
  }
  cout << 2 * ans << endl;
  for (int i = 0; i < n; i++) cout << p[i] << " ";
  cout << p[n] << endl;
  return 0;
}
