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
n = int(input())
p = [i for i in range(n + 1)]

k = 1
while(2 * k <= n):
  k *= 2
m = n + 1
while m > 0:
  while k >= m:
    k //= 2
  for i in range(m - k):
    if k - i - 1 >= 0:
      p[k + i], p[k - i - 1] = p[k - i - 1], p[k + i]
  m = k - i - 1

print(n * (n + 1))
print(' '.join(map(str, p)))