





from __future__ import annotations

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

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




class 				_a		(   Generic[T]       ):






				def __init__(				self	:					Union[str, Any],				lowerCAmelCase__	:					Optional[Any]							)			->   None:




										'''simple docstring'''



										_UpperCamelCase    :      T						     =					value
										_UpperCamelCase    :      SkewNode[T] | None						     =					None
										_UpperCamelCase    :      SkewNode[T] | None						     =					None






				@property
				def        snake_case			(				self	:					Any							)			->   T:




										'''simple docstring'''



										return self._value






				@staticmethod
				def        snake_case			(				lowerCAmelCase__	:					List[Any],				lowerCAmelCase__	:					Any							)			->   SkewNode[T] | None:




										'''simple docstring'''



										if not roota:
																return roota

										if not roota:
																return roota

										if roota.value > roota.value:
																_UpperCamelCase    :      Optional[int]						     =					roota, roota

										_UpperCamelCase    :      List[str]						     =					roota
										_UpperCamelCase    :      Dict						     =					roota.right
										_UpperCamelCase    :      str						     =					roota.left
										_UpperCamelCase    :      Optional[int]						     =					SkewNode.merge(SCREAMING_SNAKE_CASE_,				SCREAMING_SNAKE_CASE_							)

										return result




class 				_a		(   Generic[T]       ):






				def __init__(				self	:					Optional[Any],				lowerCAmelCase__	:					Union[str, Any] = ()							)			->   None:




										'''simple docstring'''



										_UpperCamelCase    :      SkewNode[T] | None						     =					None
										if data:
																for item in data:
																						self.insert(SCREAMING_SNAKE_CASE_							)






				def __bool__(				self	:					int							)			->   bool:




										'''simple docstring'''



										return self._root is not None






				def __iter__(				self	:					Optional[int]							)			->   Iterator[T]:




										'''simple docstring'''



										_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(SCREAMING_SNAKE_CASE_							)

										return iter(SCREAMING_SNAKE_CASE_							)






				def        snake_case			(				self	:					List[Any],				lowerCAmelCase__	:					Tuple							)			->   None:




										'''simple docstring'''



										_UpperCamelCase    :      Optional[int]						     =					SkewNode.merge(self._root,				SkewNode(SCREAMING_SNAKE_CASE_							)							)






				def        snake_case			(				self	:					Any							)			->   T | None:




										'''simple docstring'''



										_UpperCamelCase    :      Union[str, Any]						     =					self.top()
										_UpperCamelCase    :      Optional[int]						     =					(
										    SkewNode.merge(self._root.left,				self._root.right							) if self._root else None
										)

										return result






				def        snake_case			(				self	:					str							)			->   T:




										'''simple docstring'''



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






				def        snake_case			(				self	:					Tuple							)			->   None:




										'''simple docstring'''



										_UpperCamelCase    :      List[Any]						     =					None


if __name__ == "__main__":
						import doctest

						doctest.testmod()










"""simple docstring"""




UpperCamelCase_     =1_000





def  a_       (							_lowercase     ):
						return x * x





def  a_       (							_lowercase ,		_lowercase ,		_lowercase ,		_lowercase = 4     ):
						assert callable(
						    _lowercase     ), F"""the function(object) passed should be callable your input : {function}"""
						assert isinstance(_lowercase ,		(float, int)     ), F"""a should be float or integer your input : {a}"""
						assert isinstance(function(_lowercase     ) ,		(float, int)     ), (
						    "the function should return integer or float return type of your function, "
						    F"""{type(_lowercase     )}"""
						)
						assert isinstance(_lowercase ,		(float, int)     ), F"""b should be float or integer your input : {b}"""
						assert (
						    isinstance(_lowercase ,		_lowercase     ) and precision > 0
						), F"""precision should be positive integer your input : {precision}"""

						# just applying the formula of simpson for approximate integration written in
						# mentioned article in first comment of this file and above this function

						_UpperCamelCase    :      str						     =					(b - a) / N_STEPS
						_UpperCamelCase    :      Dict						     =					function(_lowercase     ) + function(_lowercase     )

						for i in range(1 ,		_lowercase     ):
												_UpperCamelCase    :      List[Any]						     =					a + h * i
												result += function(_lowercase     ) * (4 if i % 2 else 2)

						result *= h / 3
						return round(_lowercase ,		_lowercase     )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



