


'''simple docstring'''




from itertools import product





def 				a_							(    lowercase = 15     )      ->int:






				'''simple docstring'''

				__lowerCamelCase		:   float           =       0.0
				__lowerCamelCase		:   float
				__lowerCamelCase		:   int
				__lowerCamelCase		:   int
				__lowerCamelCase		:   int
				__lowerCamelCase		:   int
				__lowerCamelCase		:   tuple[int, ...]

				for series in product(range(2     )				,    repeat=lowercase     ):
								__lowerCamelCase		:   str           =       series.count(1     )
								__lowerCamelCase		:   List[str]           =       num_turns - num_blue
								if num_red >= num_blue:
												continue
								__lowerCamelCase		:   Optional[int]           =       1.0
								for ind, col in enumerate(lowercase				,    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 collections import Counter
from functools import total_ordering

from data_structures.heap.heap import Heap





@total_ordering
class _snake_case :
							"""simple docstring"""





							def __init__( self      ,					__A      ,					__A						)  ->None:



											"""simple docstring"""







											__lowerCamelCase		:   List[Any]           =       word
											__lowerCamelCase		:   Optional[Any]           =       count







							def __eq__( self      ,					__A						)  ->bool:



											"""simple docstring"""







											if not isinstance(__A      ,					__A						):
															return NotImplemented
											return self.count == other.count







							def __lt__( self      ,					__A						)  ->bool:



											"""simple docstring"""







											if not isinstance(__A      ,					__A						):
															return NotImplemented
											return self.count < other.count





def 				a_							(    lowercase				,    lowercase     )      ->list[str]:






				'''simple docstring'''

				__lowerCamelCase		:   Heap[WordCount]           =       Heap()
				__lowerCamelCase		:   int           =       Counter(lowercase     )
				heap.build_max_heap(
				    [WordCount(lowercase				,    lowercase     ) for word, count in count_by_word.items()]     )
				return [heap.extract_max().word for _ in range(min(lowercase				,    len(lowercase     )     )     )]


if __name__ == "__main__":
				import doctest

				doctest.testmod()





