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() {
  int n;
  cin >> n;
  int tmpn = n;
  vector<int> arr(n + 1);
  long long ans = 0;
  for (int split = 1 << 25; split >= 1; split >>= 1) {
    if (split > n) continue;
    int l = split - 1;
    int r = split;
    while (r <= n) {
      arr[l] = r;
      arr[r] = l;
      ans += (l ^ r) * 2;
      l--;
      r++;
    }
    n = l;
  }
  cout << ans << endl;
  n = tmpn;
  for (int i = 0; i <= n; i++) cout << arr[i] << " ";
  return 0;
}
