






'''simple docstring'''




from collections import Counter
from functools import total_ordering

from data_structures.heap.heap import Heap

@total_ordering
class      _UpperCAmelCase    :




   """simple docstring"""

   def __init__(	self				:			Dict   ,   __UpperCAmelCase				:			Dict   ,   __UpperCAmelCase				:			Tuple	):





         '''simple docstring'''





         _A      =			word
         _A      =			count

   def __eq__(	self				:			List[str]   ,   __UpperCAmelCase				:			List[Any]	):





         '''simple docstring'''





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

   def __lt__(	self				:			Optional[Any]   ,   __UpperCAmelCase				:			Optional[Any]	):





         '''simple docstring'''





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





def       __lowercase		(    __lowercase     ,						__lowercase ) ->		list[str]:

      '''simple docstring'''


      _A      =			Heap()
      _A      =			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()













'''simple docstring'''




import math

def       __lowercase		(    __lowercase ) ->		bool:

      '''simple docstring'''


      if 1 < number < 4:
            # 2 and 3 are primes
            return True
      elif number < 2 or number % 2 == 0 or number % 3 == 0:
            # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
            return False

      # All primes number are in format of 6k +/- 1
      for i in range(5     ,						int(math.sqrt(__lowercase ) + 1 )     ,						6 ):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True

def       __lowercase		(    __lowercase = 6008_5147_5143 ) ->		int:

      '''simple docstring'''


      try:
            _A      =			int(__lowercase )
      except (TypeError, ValueError):
            raise TypeError("Parameter n must be int or castable to int." )
      if n <= 0:
            raise ValueError("Parameter n must be greater than or equal to one." )
      _A      =			0
      if is_prime(__lowercase ):
            return n
      while n % 2 == 0:
            n //= 2
      if is_prime(__lowercase ):
            return n
      for i in range(3     ,						int(math.sqrt(__lowercase ) ) + 1     ,						2 ):
            if n % i == 0:
                  if is_prime(n // i ):
                        _A      =			n // i
                        break
                  elif is_prime(__lowercase ):
                        _A      =			i
      return max_number


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





