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;
const int inf = 0x3f3f3f3f;
const long long MOD = 1000000007;
int n, p[1 << 21];
int main() {
  scanf("%d", &n);
  long long s = 0;
  int t = 1;
  while (t <= n) t <<= 1;
  t--;
  memset(p, -1, sizeof(p));
  for (int i = n; i >= 0; --i) {
    if (p[i] != -1) continue;
    while ((t ^ i) > n || p[t ^ i] != -1) t >>= 1;
    s += 2 * t;
    p[i] = t ^ i;
    p[t ^ i] = i;
  }
  cout << s << endl;
  for (int i = 0; i <= n; ++i) printf("%d ", p[i]);
  return 0;
}
