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 v[1000009] = {0};
int a[1000009];
int inv(int n) {
  int fill = n;
  fill |= (fill >> 1);
  fill |= (fill >> 2);
  fill |= (fill >> 4);
  fill |= (fill >> 8);
  fill |= (fill >> 16);
  n = ~n;
  n &= fill;
  return n;
}
int main() {
  int n, k;
  long long ans = 0;
  scanf("%d", &n);
  for (int i = n; i >= 0; i--)
    if (v[i] == 0) {
      if (i & (i - 1) == 0) {
        a[i] = 0;
        a[0] = i;
        v[0] = 1;
        ans += i;
      } else {
        k = inv(i);
        v[i] = v[k] = 1;
        a[i] = k;
        a[k] = i;
        ans += i ^ k;
      }
    }
  cout << ans * 2 << endl;
  for (int i = 0; i < n + 1; i++) printf("%d ", a[i]);
  return 0;
}
