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;
void f(int k) {
  if (k == 0) {
    cout << "0";
    return;
  }
  if (k == 1) {
    cout << "1 0";
    return;
  }
  int p = 1, t = k;
  do {
    t = t / 2;
    p = p * 2;
  } while (t != 0);
  if (p - k - 2 >= 0) {
    f(p - k - 2);
    for (int i = k; i >= p - k - 1; i--) cout << ' ' << i;
  } else {
    for (int i = k; i >= 0; i--) {
      cout << i;
      if (i > 0) cout << ' ';
    }
  }
}
int main() {
  int n;
  cin >> n;
  long long k = (long long)n * (long long)(n + 1);
  cout << k << endl;
  f(n);
  return 0;
}
