Problem:
Score : 1000 points

Problem Statement

We will call a string x good if it satisfies the following condition:

Condition: x can be represented as a concatenation of two copies of another string y of length at least 1.

For example, aa and bubobubo are good; an empty string, a, abcabcabc and abba are not good.

Eagle and Owl created a puzzle on good strings.
Find one string s that satisfies the following conditions. It can be proved that such a string always exists under the constraints in this problem.

1 ≤ |s| ≤ 200

Each character of s is one of the 100 characters represented by the integers 1 through 100.

Among the 2^{|s|} subsequences of s, exactly N are good strings.

Constraints

1 ≤ N ≤ 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

In the first line, print |s|, the length of s.
In the second line, print the elements in s in order, with spaces in between. Any string that satisfies the above conditions will be accepted.

Sample Input 1

7

Sample Output 1

4
1 1 1 1

There are two good strings that appear as subsequences of s: (1,1) and (1,1,1,1). There are six occurrences of (1,1) and one occurrence of (1,1,1,1), for a total of seven.

Sample Input 2

299

Sample Output 2

23
32 11 11 73 45 8 11 83 83 8 45 32 32 10 100 73 32 83 45 73 32 11 10

Solution in Ruby (2.3.3) (judge verdict: Accepted)

def parse i
  ret = []
  while i > 1
    if i % 2 == 1
      i -= 1
      i /= 2
      ret << 1
    else
      i -= 1
      ret << 0
    end
  end
  ret << 0
  return ret.reverse
end
def make arr
  s10 = []
  s11 = []
  s2 = []
  arr.each_with_index do |a, i|
    _i = i + 1
    s2 << _i
    if a == 1
      s11 << _i
    else
      s10 << _i
    end
  end
  _a = s10.reverse + s11 + s2
  puts _a.length
  puts _a*' '
end
make parse gets.to_i