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 an[1000010];
int main() {
  int i, j, k, n;
  cin >> n;
  k = n;
  while (k > 0) {
    for (i = 1; i < k; i = i * 2 + 1)
      ;
    for (j = k; j >= i - k; j--) an[j] = i - j;
    k = i - k - 1;
  }
  cout << (long long)n * (n + 1) << endl;
  for (i = 0; i <= n; i++) {
    if (i) printf(" ");
    printf("%d", an[i]);
  }
  return 0;
}
