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 a[1000005];
int main() {
  int n;
  while (cin >> n) {
    for (int i = n; i >= 0; i--)
      if (!a[i]) {
        int mm = (1 << ((int)(log2(i) + 1))) - 1;
        a[i] = mm ^ i;
        a[mm ^ i] = i;
      }
    long long int ans = 0;
    for (int i = 0; i <= n; i++) {
      ans += a[i] ^ i;
    }
    cout << ans << endl;
    for (int i = 0; i <= n; i++) {
      cout << a[i];
      if (i != n)
        cout << " ";
      else
        cout << "\n";
    }
  }
  return 0;
}
