
def        lowerCAmelCase       (				snake_case__   :      Optional[int]				,					snake_case__   :      Optional[int] = 1000 )->			str:
    if (not isinstance(snake_case__				,					snake_case__ )) or (digit_position <= 0):
        raise ValueError("Digit position must be a positive integer" )
    elif (not isinstance(snake_case__				,					snake_case__ )) or (precision < 0):
        raise ValueError("Precision must be a nonnegative integer" )

    # compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
    # accurate
    A_								=					(
        4 * _subsum(snake_case__				,					1				,					snake_case__ )
        - 2 * _subsum(snake_case__				,					4				,					snake_case__ )
        - _subsum(snake_case__				,					5				,					snake_case__ )
        - _subsum(snake_case__				,					6				,					snake_case__ )
    )

    # return the first hex digit of the fractional part of the result
    return hex(int((sum_result % 1) * 16 ) )[2:]





def        lowerCAmelCase       (				snake_case__   :      List[str]				,					snake_case__   :      Optional[int]				,					snake_case__   :      Any )->			float:
    A_								=					0.0
    for sum_index in range(digit_pos_to_extract + precision ):
        A_								=					8 * sum_index + denominator_addend
        if sum_index < digit_pos_to_extract:
            # if the exponential term is an integer and we mod it by the denominator
            # before dividing, only the integer part of the sum will change;
            # the fractional part will not
            A_								=					pow(
                16				,					digit_pos_to_extract - 1 - sum_index				,					snake_case__ )
        else:
            A_								=					pow(16				,					digit_pos_to_extract - 1 - sum_index )
        total += exponential_term / denominator
    return total


if __name__ == "__main__":
     import doctest

     doctest.testmod()









'''simple docstring'''


from __future__ import annotations

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

lowerCAmelCase__      				=			TypeVar("T", bound=bool)



class        lowercase    (	Generic[T]			):


							def __init__(      self     ,      _snake_case)				->					None:
								UpperCAmelCase_		:   T													=       value
								UpperCAmelCase_		:   SkewNode[T] | None													=       None
								UpperCAmelCase_		:   SkewNode[T] | None													=       None


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





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

								if not roota:
									return roota

								if roota.value > roota.value:
									UpperCAmelCase_						,     UpperCAmelCase_		:   Union[str, Any]													=       roota, roota

								UpperCAmelCase_		:   Dict													=       roota
								UpperCAmelCase_		:   Dict													=       roota.right
								UpperCAmelCase_		:   Optional[int]													=       roota.left
								UpperCAmelCase_		:   Dict													=       SkewNode.merge(_snake_case     ,      _snake_case)

								return result



class        lowercase    (	Generic[T]			):


							def __init__(      self     ,      _snake_case = ())				->					None:
								UpperCAmelCase_		:   SkewNode[T] | None													=       None
								if data:
									for item in data:
										self.insert(_snake_case)


							def __bool__(      self)				->					bool:
								return self._root is not None


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

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

								return iter(_snake_case)


							def     _snake_case				(      self     ,      _snake_case)				->					None:
								UpperCAmelCase_		:   Any													=       SkewNode.merge(self._root     ,      SkewNode(_snake_case))


							def     _snake_case				(      self)				->					T | None:
								UpperCAmelCase_		:   Union[str, Any]													=       self.top()
								UpperCAmelCase_		:   Tuple													=       (
								    SkewNode.merge(self._root.left     ,      self._root.right) if self._root else None
								)

								return result


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





							def     _snake_case				(      self)				->					None:
								UpperCAmelCase_		:   Union[str, Any]													=       None


if __name__ == "__main__":
						import doctest

						doctest.testmod()






