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 long long maxn = 1e6 + 7;
long long res, n, pw, a[maxn];
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  pw = 1;
  while (pw <= n) pw *= 2;
  for (long long i = n; i >= 0; i--) {
    if (a[i] == 0) {
      while (pw / 2 > i) pw /= 2;
      long long i2 = pw - 1 - i;
      a[i] = i2;
      a[i2] = i;
      res += 2 * (i ^ i2);
    }
  }
  cout << res << endl;
  for (long long i = 0; i <= n; i++) cout << a[i] << " ";
}
