






"""simple docstring"""







import math
from decimal import Decimal, getcontext





def 						lowercase__(A = 4_000_000						)				->int:




						"""simple docstring"""



						try:
												lowercase__				:      int=       int(A						)
						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."						)
						lowercase__				:      Dict=       100
						lowercase__				:      Optional[Any]=       (Decimal(5						) ** Decimal(0.5						) + 1) / Decimal(2						)

						lowercase__				:      str=       (math.floor(math.log(n * (phi + 2)					,		A						) - 1						) // 3) * 3 + 2
						lowercase__				:      Optional[Any]=       Decimal(round(phi ** Decimal(index + 1						)						)						) / (phi + 2)
						lowercase__				:      Tuple=       num // 2
						return int(A						)


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     __UpperCAmelCase:




						"""simple docstring"""




						def __init__(   self       ,  snake_case__       ,  snake_case__			):
												'''simple docstring'''
												lowercase__				:      Optional[Any]=       word
												lowercase__				:      Any=       count




						def __eq__(   self       ,  snake_case__			):
												'''simple docstring'''
												if not isinstance(snake_case__       ,  snake_case__			):
																		return NotImplemented
												return self.count == other.count




						def __lt__(   self       ,  snake_case__			):
												'''simple docstring'''
												if not isinstance(snake_case__       ,  snake_case__			):
																		return NotImplemented
												return self.count < other.count





def 						lowercase__(A					,		A						)				->list[str]:




						"""simple docstring"""



						lowercase__				:      Heap[WordCount]=       Heap()
						lowercase__				:      str=       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()






