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 num[1000005];
int f(int x) {
  int tmp = x, i = 0;
  while (tmp) {
    tmp >>= 1;
    i++;
  }
  return i;
}
int main() {
  int n, x, tmp, cnt, s, m;
  long long sum = 0;
  scanf("%d", &n);
  tmp = n;
  while (tmp > 0) {
    x = f(tmp);
    m = (1 << x) - 1;
    s = m - tmp;
    cnt = (tmp - (m >> 1)) * 2;
    while (cnt > 0) {
      num[tmp--] = s++;
      sum += m;
      cnt--;
    }
  }
  cout << sum << endl;
  for (int i = 0; i <= n; i++) {
    cout << num[i];
    if (i != n) cout << " ";
  }
  cout << endl;
}
