






from __future__ import annotations

from collections import defaultdict
from dataclasses import dataclass




@dataclass
class 							__A	:





				"""simple docstring"""







				UpperCamelCase__					: int
				UpperCamelCase__					: TreeNode | None     					=None
				UpperCamelCase__					: TreeNode | None     					=None






def 				A	(			)	->		TreeNode:
					return TreeNode(3				,TreeNode(9   )				,TreeNode(20				,TreeNode(15   )				,TreeNode(7   )   )   )






def 				A	(			a_   )	->		list[int]:

					def depth_first_search(
					    a_				,a_				,a_   ) -> None:
										if not root:
															return

										if depth == len(a_   ):
															right_view.append(root.val   )

										depth_first_search(root.right				,depth + 1				,a_   )
										depth_first_search(root.left				,depth + 1				,a_   )

					__UpperCamelCase :   list									=[]
					if not root:
										return right_view

					depth_first_search(a_				,0				,a_   )
					return right_view






def 				A	(			a_   )	->		list[int]:

					def depth_first_search(
					    a_				,a_				,a_   ) -> None:
										if not root:
															return

										if depth == len(a_   ):
															left_view.append(root.val   )

										depth_first_search(root.left				,depth + 1				,a_   )
										depth_first_search(root.right				,depth + 1				,a_   )

					__UpperCamelCase :   list									=[]
					if not root:
										return left_view

					depth_first_search(a_				,0				,a_   )
					return left_view






def 				A	(			a_   )	->		list[int]:

					def breadth_first_search(a_				,a_   ) -> None:
										__UpperCamelCase :   Dict									=[(root, 0)]
										__UpperCamelCase :   Union[str, Any]									=defaultdict(a_   )

										while queue:
															__UpperCamelCase :   List[str]									=queue.pop(0   )
															__UpperCamelCase						,							__UpperCamelCase :   int									=first

															lookup[hd].append(node.val   )

															if node.left:
																				queue.append((node.left, hd - 1)   )
															if node.right:
																				queue.append((node.right, hd + 1)   )

										for pair in sorted(lookup.items()				,key=lambda a_   : each[0]   ):
															top_view.append(pair[1][0]   )

					__UpperCamelCase :   list									=[]
					if not root:
										return top_view

					breadth_first_search(a_				,a_   )
					return top_view






def 				A	(			a_   )	->		list[int]:
					from collections import defaultdict

					def breadth_first_search(a_				,a_   ) -> None:
										__UpperCamelCase :   Optional[Any]									=[(root, 0)]
										__UpperCamelCase :   List[str]									=defaultdict(a_   )

										while queue:
															__UpperCamelCase :   str									=queue.pop(0   )
															__UpperCamelCase						,							__UpperCamelCase :   Union[str, Any]									=first
															lookup[hd].append(node.val   )

															if node.left:
																				queue.append((node.left, hd - 1)   )
															if node.right:
																				queue.append((node.right, hd + 1)   )

										for pair in sorted(lookup.items()				,key=lambda a_   : each[0]   ):
															bottom_view.append(pair[1][-1]   )

					__UpperCamelCase :   list									=[]
					if not root:
										return bottom_view

					breadth_first_search(a_				,a_   )
					return bottom_view


if __name__ == "__main__":
							import doctest

							doctest.testmod()









import random




class 							__A	:





				"""simple docstring"""







				def __init__(					self				,    lowerCamelCase__				,    lowerCamelCase__       ):




									"""simple docstring"""

									__UpperCamelCase :   Optional[Any]									=x
									__UpperCamelCase :   int									=y


				def  __lowercase				(					self       ):




									"""simple docstring"""

									return (self.x**2 + self.y**2) <= 1







				@classmethod
				def  __lowercase				(					cls       ):




									"""simple docstring"""

									return cls(x=random.random()				,    y=random.random()       )






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

					__UpperCamelCase :   List[str]									=0
					for _ in range(a_   ):
										__UpperCamelCase :   Optional[int]									=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

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

