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;
long long a[1000005];
long long n;
long long step[25];
long long res = 0;
int main() {
  scanf("%I64d", &n);
  long long saveN = n;
  step[0] = 1;
  for (long long i = 1; i < 22; i++) {
    step[i] = step[i - 1] << 1;
  }
  long long cnt = 0;
  while (cnt < saveN) {
    long long br;
    for (long long i = 1; i < 22; i++) {
      if (step[i] > n) {
        br = step[i - 1];
        break;
      }
    }
    long long dec = 1;
    long long up = br;
    long long lo = br - 1;
    while (up <= n) {
      res += up ^ lo;
      a[up] = lo;
      a[lo] = up;
      lo--, up++;
      cnt += 2;
    }
    n = lo;
  }
  printf("%I64d\n", res * 2);
  for (long long i = 0; i <= saveN; i++) printf("%I64d ", a[i]);
  return 0;
}
