output_description: 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.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
attempt: fact = [1]
  for i in range(1, 101):
      fact.append(fact[-1] * i)
  
  
  def C(a, b):
      return fact[a] // (fact[b] * fact[a - b])
  
  
  def sC(a, b):
      ret = 0
      for i in range(min(b, a - b) + 1):
          ret += C(b, i) * C(a - b, i)
      return ret
  
  
  def calc(n, k):
      if n <= 0:
          return []
      i = 0
      while (1 << (i + 1)) - 1 <= n:
          i += 1
  
      ret = [str(k)] * (i + 1)
      rem = n - ((1 << i) - 1)
      kk = k + 1
      i += 1
      j = i // 2
  
      while j > 0:
          while True:
              tmp = sC(i, j)
              if tmp <= rem:
                  ret.insert(j, str(kk))
                  ret.append(str(kk))
                  kk += 1
                  rem -= tmp
  
              else:
                  break
  
          j -= 1
  
      return ret + calc(rem, kk)
  
  
  N = int(input())
  
  X = calc(N, 1)
  print(len(X))
  print(" ".join(X))
  
problem_description: 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.
samples: [{"input": "7", "output": "4\n    1 1 1 1\n    \n\nThere are two good strings that appear as subsequences of s: (1,1) and\n(1,1,1,1). There are six occurrences of (1,1) and one occurrence of (1,1,1,1),\nfor a total of seven.\n\n* * *"}, {"input": "299", "output": "23\n    32 11 11 73 45 8 11 83 83 8 45 32 32 10 100 73 32 83 45 73 32 11 10"}]