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 a[1000005], f[1000005], x, k, i, n;
long long ans = 0;
int main() {
  scanf("%d", &n);
  for (i = n; i; i--)
    if (!f[i]) {
      k = (int)(log2(i)) + 1;
      x = (1 << k) - 1 - i;
      f[x] = 1;
      a[i] = x;
      a[x] = i;
      ans += (long long)((1 << k) - 1) << 1;
    }
  printf("%I64d\n", ans);
  for (i = 0; i <= n; i++) printf("%d ", a[i]);
}
