


import math
def 							__lowerCamelCase		(					UpperCAmelCase_		:						int		):




      """simple docstring"""





      a		:str									=			math.loga(math.sqrt(4 * positive_integer + 1		) / 2 + 1 / 2		)

      return exponent == int(UpperCAmelCase_		)
def 							__lowerCamelCase		(					UpperCAmelCase_		:						float = 1 / 1_2345		):




      """simple docstring"""





      a		:Union[str, Any]									=			0
      a		:Tuple									=			0

      a		:Any									=			3
      while True:
            a		:Any									=			(integer**2 - 1) / 4
            # if candidate is an integer, then there is a partition for k
            if partition_candidate == int(UpperCAmelCase_		):
                  a		:str									=			int(UpperCAmelCase_		)
                  total_partitions += 1
                  if check_partition_perfect(UpperCAmelCase_		):
                        perfect_partitions += 1
            if perfect_partitions > 0:
                  if perfect_partitions / total_partitions < max_proportion:
                        return int(UpperCAmelCase_		)
            integer += 1


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









from __future__ import annotations

from typing import Any







class 						_snake_case    ( _snake_case				):
 pass







class 						_snake_case    :




 def __init__(						self   ,    _lowerCamelCase       ):
       a		:Any									=			data
       a		:Node | None									=			None




 def __iter__(						self       ):
       a		:Dict									=			self
       a		:Optional[int]									=			[]
       while node:
             if node in visited:
                   raise ContainsLoopError
             visited.append(_lowerCamelCase       )
             yield node.data
             a		:str									=			node.next_node




 @property
 def 			SCREAMING_SNAKE_CASE__							(						self       ):
       try:
             list(self       )
             return False
       except ContainsLoopError:
             return True


if __name__ == "__main__":
     snake_case							:       int										=	Node(1)
     snake_case							:       int										=	Node(2)
     snake_case							:       Optional[int]										=	Node(3)
     snake_case							:       List[str]										=	Node(4)
     print(root_node.has_loop)  # False
     snake_case							:       Optional[Any]										=	root_node.next_node
     print(root_node.has_loop)  # True

     snake_case							:       Dict										=	Node(5)
     snake_case							:       List[Any]										=	Node(6)
     snake_case							:       Optional[int]										=	Node(5)
     snake_case							:       Union[str, Any]										=	Node(6)
     print(root_node.has_loop)  # False

     snake_case							:       Tuple										=	Node(1)
     print(root_node.has_loop)  # False





