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 ans[1010000], N;
long long ans2 = 0;
int main() {
  scanf("%d", &N);
  int m = 1, n = N;
  while (n >> 1) {
    m = m + m + 1;
    n >>= 1;
  }
  for (int i = 0; i <= N; i++) ans[i] = -1;
  for (int i = N; i >= 0; i--)
    if (ans[i] == -1) {
      int m2 = m;
      while ((m2 ^ i) > N || ans[m2 ^ i] >= 0) m2 >>= 1;
      ans[i] = (m2 ^ i);
      ans[m2 ^ i] = i;
      ans2 += m2 * 2;
    }
  printf("%I64d\n", ans2);
  for (int i = 0; i <= N; i++) printf("%d ", ans[i]);
  return 0;
}
