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 N = 1000010;
int n, ans[N];
long long sum;
int main() {
  cin >> n;
  memset(ans, -1, sizeof(ans));
  for (int i = n; i >= 0; --i) {
    if (~ans[i]) continue;
    int now = i, tar = 0, cnt = 0;
    while (now) {
      if (~now & 1) tar += (1 << cnt);
      cnt++;
      now >>= 1;
    }
    ans[i] = tar, ans[tar] = i;
  }
  for (int i = 0; i <= n; ++i) sum += i ^ (ans[i]);
  printf("%I64d\n", sum);
  for (int i = 0; i <= n; ++i) printf("%d ", ans[i]);
  return 0;
}
