


def 	_lowerCamelCase  (		A_  :	list      )			->			bool:

   '''simple docstring'''






   if not isinstance(A_							,  A_      ):
      raise ValueError("Input series is not valid, valid series - [2, 4, 8]"      )
   if len(A_      ) == 0:
      raise ValueError("Input list must be a non empty list"      )
   if len(A_      ) == 1:
      return True
   try:
      UpperCamelCase__ :			List[Any] 						=series[1] / series[0]
      for index in range(len(A_      ) - 1      ):
         if series[index + 1] / series[index] != common_ratio:
            return False
   except ZeroDivisionError:
      return False
   return True
def 	_lowerCamelCase  (		A_  :	list      )			->			float:

   '''simple docstring'''






   if not isinstance(A_							,  A_      ):
      raise ValueError("Input series is not valid, valid series - [2, 4, 8]"      )
   if len(A_      ) == 0:
      raise ValueError("Input list must be a non empty list"      )
   UpperCamelCase__ :			str 						=1
   for value in series:
      answer *= value
   return pow(A_							,  1 / len(A_      )      )


if __name__ == "__main__":
     import doctest

     doctest.testmod()





from collections import Counter
from functools import total_ordering

from data_structures.heap.heap import Heap



@total_ordering
class 							lowercase__:






      '''simple docstring'''







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







         """simple docstring"""







         UpperCamelCase__ :			Optional[int] 						=word
         UpperCamelCase__ :			Dict 						=count




      def __eq__(		self   ,			__SCREAMING_SNAKE_CASE)					->						bool:







         """simple docstring"""







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




      def __lt__(		self   ,			__SCREAMING_SNAKE_CASE)					->						bool:







         """simple docstring"""







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




def 	_lowerCamelCase  (		A_  :	list[str]							,  A_  :	int      )			->			list[str]:

   '''simple docstring'''






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


if __name__ == "__main__":
     import doctest

     doctest.testmod()

