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[1100010];
int main(int argc, char const *argv[]) {
  int n;
  cin >> n;
  int p = 1;
  while (p < 1100010) {
    a[p - 1] = p - 1;
    p *= 2;
  }
  for (int i = 1100010 - 2; i; i--) {
    if (a[i] == 0) a[i] = a[i + 1];
  }
  int ans[n + 1];
  memset(ans, -1, sizeof(ans));
  long long res = 0;
  for (int i = n; i >= 0; i--) {
    if (ans[i] == -1) {
      ans[i] = a[i] - i;
      ans[a[i] - i] = i;
      res += 2 * (long long)(i ^ (a[i] - i));
    }
  }
  cout << res << endl;
  for (int i : ans) cout << i << " ";
  return 0;
}
