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 = 1000000 + 10;
int num[MAX];
int main() {
  int n, i;
  int x, j;
  int y, t;
  long long sum;
  while (scanf("%d", &n) != EOF) {
    memset(num, -1, sizeof(num));
    for (i = n, sum = 0; i >= 0; i--) {
      if (num[i] != -1) continue;
      x = i;
      y = 0;
      t = 0;
      while (x) {
        j = x % 2;
        x = x >> 1;
        y += (1 ^ j) << t;
        t++;
      }
      num[y] = i;
      num[i] = y;
      sum += 2 * (y ^ i);
    }
    cout << sum << endl;
    for (i = 0; i <= n; i++) printf("%d ", num[i]);
  }
  return 0;
}
