




'''simple docstring'''



from itertools import product







def      _UpperCamelCase	(_lowerCamelCase							:       Union[str, Any] = 15		)->				List[Any]:




     '''simple docstring'''





     __snake_case         =					0.0
     __snake_case         =					42
     __snake_case         =					42
     __snake_case         =					42
     __snake_case         =					42
     __snake_case         =					42
     __snake_case         =					42

     for series in product(range(2		)				,		repeat=_lowerCamelCase		):
          __snake_case         =					series.count(1		)
          __snake_case         =					num_turns - num_blue
          if num_red >= num_blue:
               continue
          __snake_case         =					1.0
          for ind, col in enumerate(_lowerCamelCase				,		2		):
               if col == 0:
                    prob *= (ind - 1) / ind
               else:
                    prob *= 1 / ind

          total_prob += prob

     return int(1 / total_prob		)


if __name__ == "__main__":
     print(F"""{solution() = }""")









'''simple docstring'''



from __future__ import annotations

from collections.abc import Iterator
from typing import Any





class       lowerCAmelCase				:


       def __init__(				self      ,					__SCREAMING_SNAKE_CASE					) ->					None:



            '''simple docstring'''




            __snake_case         =					data
            __snake_case         =					None




       def __str__(				self					) ->					str:



            '''simple docstring'''




            return F'''{self.data}'''





class       lowerCAmelCase				:


       def __init__(				self					) ->					None:



            '''simple docstring'''




            __snake_case         =					None
            __snake_case         =					None


       def __iter__(				self					) ->					Iterator[Any]:



            '''simple docstring'''




            __snake_case         =					self.front
            while node:
                 yield node.data
                 __snake_case         =					node.next


       def __len__(				self					) ->					int:



            '''simple docstring'''




            return len(tuple(iter(self					)					)					)


       def __str__(				self					) ->					str:



            '''simple docstring'''




            return " <- ".join(str(__SCREAMING_SNAKE_CASE					) for item in self					)


       def  lowerCAmelCase (				self					) ->					bool:



            '''simple docstring'''




            return len(self					) == 0


       def  lowerCAmelCase (				self      ,					__SCREAMING_SNAKE_CASE					) ->					None:



            '''simple docstring'''




            __snake_case         =					Node(__SCREAMING_SNAKE_CASE					)
            if self.is_empty():
                 __snake_case         =					__snake_case         =					node
            else:
                 assert isinstance(self.rear      ,					__SCREAMING_SNAKE_CASE					)
                 __snake_case         =					node
                 __snake_case         =					node


       def  lowerCAmelCase (				self					) ->					Any:



            '''simple docstring'''




            if self.is_empty():
                 raise IndexError('''dequeue from empty queue'''					)
            assert isinstance(self.front      ,					__SCREAMING_SNAKE_CASE					)
            __snake_case         =					self.front
            __snake_case         =					self.front.next
            if self.front is None:
                 __snake_case         =					None
            return node.data




       def  lowerCAmelCase (				self					) ->					None:



            '''simple docstring'''




            __snake_case         =					__snake_case         =					None


if __name__ == "__main__":
     from doctest import testmod

     testmod()






