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>
int a[1000000];
int main() {
  int n, i, j, k, t;
  long long s = 0;
  for (scanf("%d", &n), i = n; i >= 0;) {
    j = i;
    for (t = 0; j; j >>= 1, t++)
      ;
    k = (1 << t) - 1;
    j = k - i;
    while (i >= j) {
      s += k;
      a[i] = k - i;
      i--;
    }
  }
  printf("%I64d\n", s);
  for (i = 0; i <= n; i++) printf("%d ", a[i]);
  puts("");
  return 0;
}
