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 n, two = 1, vis[1000001];
long long ans = 0;
int main() {
  scanf("%d", &n);
  for (int i = 0; i <= n; i++) vis[i] = -1;
  while (two <= n) two <<= 1;
  for (int i = n - 1; i >= 0; i--) {
    if (vis[i] == -1) {
      while (true) {
        if (two - 1 - i <= n && vis[two - 1 - i] == -1) {
          ans += 2 * two - 2;
          vis[i] = two - 1 - i;
          vis[two - 1 - i] = i;
          break;
        }
        two >>= 1;
      }
    }
  }
  printf("%I64d\n", ans);
  for (int i = 0; i <= n; i++) {
    if (i != 0) printf(" ");
    printf("%d", vis[i]);
  }
  puts("");
}
