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;
const int MAX = 1000 * 1000 + 10;
int d[MAX], ans[MAX];
int main() {
  ios::sync_with_stdio(false);
  int n, b = 1;
  cin >> n;
  while (b <= n) b *= 2;
  b--;
  fill(ans, ans + n + 1, -1);
  long long javab = 0;
  for (int i = (int)n; i > (int)-1; --i) {
    if (ans[i] == -1) {
      while (b > 0 and ans[b - i] != -1) b /= 2;
      ans[i] = b - i;
      ans[b - i] = i;
      javab += (long long)b * 2;
    }
  }
  cout << javab << endl;
  for (int i = (int)0; i < (int)n + 1; ++i) cout << ans[i] << " ";
  cout << endl;
}
