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_N = 1000100;
const int INF = 1 << 28;
int n;
int a[MAX_N];
long long rec(int n) {
  if (n == 0) return 0;
  int m = 1;
  while (m <= n) m <<= 1;
  m--;
  int d = m - n;
  long long r = 0;
  for (int i = (d); i <= (n); i++) {
    a[i ^ m] = i;
    r += m;
  }
  r += rec(d - 1);
  return r;
}
long long solve() { return rec(n); }
int main() {
  cin >> n;
  cout << solve() << endl;
  for (int i = (0); i < (n + 1); i++) cout << a[i] << ((i == n) ? '\n' : ' ');
  return 0;
}
