



'''simple docstring'''





from __future__ import annotations

from collections.abc import Iterable, Iterator
from typing import Any, Generic, TypeVar

_UpperCamelCase							    =						TypeVar('T', bound=bool)






class  lowerCamelCase_   (    Generic[T]					):
  """simple docstring"""




  def __init__(			self				:     Optional[int]      ,     _a				:     T       ) -> None:
    __lowerCamelCase	:	T   	=			value
    __lowerCamelCase	:	SkewNode[T] | None   	=			None
    __lowerCamelCase	:	SkewNode[T] | None   	=			None




  @property
  def 						_lowercase					(			self				:     int       ) -> T:
    return self._value




  @staticmethod
  def 						_lowercase					(			_a				:     SkewNode[T] | None      ,     _a				:     SkewNode[T] | None       ) -> SkewNode[T] | None:
    if not roota:
      return roota

    if not roota:
      return roota

    if roota.value > roota.value:
      __lowerCamelCase	,__lowerCamelCase	:	Dict   	=			roota, roota

    __lowerCamelCase	:	int   	=			roota
    __lowerCamelCase	:	Optional[int]   	=			roota.right
    __lowerCamelCase	:	Optional[Any]   	=			roota.left
    __lowerCamelCase	:	Dict   	=			SkewNode.merge(_a      ,     _a       )

    return result






class  lowerCamelCase_   (    Generic[T]					):
  """simple docstring"""




  def __init__(			self				:     int      ,     _a				:     Iterable[T] | None = ()       ) -> None:
    __lowerCamelCase	:	SkewNode[T] | None   	=			None
    if data:
      for item in data:
        self.insert(_a       )




  def __bool__(			self				:     Optional[int]       ) -> bool:
    return self._root is not None




  def __iter__(			self				:     Optional[Any]       ) -> Iterator[T]:
    __lowerCamelCase	:	list[Any]   	=			[]
    while self:
      result.append(self.pop()       )

    # Pushing items back to the heap not to clear it.
    for item in result:
      self.insert(_a       )

    return iter(_a       )




  def 						_lowercase					(			self				:     Optional[Any]      ,     _a				:     T       ) -> None:
    __lowerCamelCase	:	Dict   	=			SkewNode.merge(self._root      ,     SkewNode(_a       )       )




  def 						_lowercase					(			self				:     List[Any]       ) -> T | None:
    __lowerCamelCase	:	Optional[int]   	=			self.top()
    __lowerCamelCase	:	Tuple   	=			(
        SkewNode.merge(self._root.left      ,     self._root.right       ) if self._root else None
    )

    return result




  def 						_lowercase					(			self				:     Optional[int]       ) -> T:
    if not self._root:
      raise IndexError('Can\'t get top element for the empty heap.'       )
    return self._root.value




  def 						_lowercase					(			self				:     Tuple       ) -> None:
    __lowerCamelCase	:	Any   	=			None


if __name__ == "__main__":
   import doctest

   doctest.testmod()











'''simple docstring'''





import random






class  lowerCamelCase_   :
  """simple docstring"""




  def __init__(			self				:     Union[str, Any]      ,     _a				:     float      ,     _a				:     float       ) -> None:
    __lowerCamelCase	:	Optional[int]   	=			x
    __lowerCamelCase	:	Union[str, Any]   	=			y




  def 						_lowercase					(			self				:     Tuple       ) -> bool:
    return (self.x**2 + self.y**2) <= 1




  @classmethod
  def 						_lowercase					(			cls				:     List[Any]       ) -> Optional[int]:
    return cls(x=random.random()      ,     y=random.random()       )




def 	a_					(							_lowerCAmelCase	)				->				float:
  if number_of_simulations < 1:
    raise ValueError('At least one simulation is necessary to estimate PI.'	)

  __lowerCamelCase	:	Optional[int]   	=			0
  for _ in range(_lowerCAmelCase	):
    __lowerCamelCase	:	Dict   	=			Point.random_unit_square()

    if random_point.is_in_unit_circle():
      number_in_unit_circle += 1

  return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
   # import doctest

   # doctest.testmod()
   from math import pi

   _UpperCamelCase							    =						'Please enter the desired number of Monte Carlo simulations: '
   _UpperCamelCase							    =						estimate_pi(int(input(prompt).strip()))
   print(f'''An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}''')






