





from __future__ import annotations

from collections import defaultdict
from dataclasses import dataclass
@dataclass
class SCREAMING_SNAKE_CASE_    :
						__magic_name__:      int
						__magic_name__:      TreeNode | None			   =							None
						__magic_name__:      TreeNode | None			   =							None


def 				SCREAMING_SNAKE_CASE__    (     ):
	return TreeNode(3 ,			TreeNode(9 ) ,			TreeNode(20 ,			TreeNode(15 ) ,			TreeNode(7 ) ) )


def 				SCREAMING_SNAKE_CASE__    (     __a ):

	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 )

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

	depth_first_search(__a ,			0 ,			__a )
	return right_view


def 				SCREAMING_SNAKE_CASE__    (     __a ):

	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 )

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

	depth_first_search(__a ,			0 ,			__a )
	return left_view


def 				SCREAMING_SNAKE_CASE__    (     __a ):

	def breadth_first_search(__a ,			__a ) -> None:
		snake_case_		:      Optional[int]           =						[(root, 0)]
		snake_case_		:      Tuple           =						defaultdict(__a )

		while queue:
			snake_case_		:      Any           =						queue.pop(0 )
			snake_case_    ,snake_case_		:      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] ):
			top_view.append(pair[1][0] )

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

	breadth_first_search(__a ,			__a )
	return top_view


def 				SCREAMING_SNAKE_CASE__    (     __a ):
	from collections import defaultdict

	def breadth_first_search(__a ,			__a ) -> None:
		snake_case_		:      Any           =						[(root, 0)]
		snake_case_		:      int           =						defaultdict(__a )

		while queue:
			snake_case_		:      List[str]           =						queue.pop(0 )
			snake_case_    ,snake_case_		:      Dict           =						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] )

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

	breadth_first_search(__a ,			__a )
	return bottom_view


if __name__ == "__main__":
						import doctest

						doctest.testmod()








def  A					(				UpperCAmelCase	,	UpperCAmelCase					):
					# "Simpson Rule"
					# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)
					_snake_case							:       List[str]												= (boundary[1] - boundary[0]) / steps
					_snake_case							:       List[Any]												= boundary[0]
					_snake_case							:       Tuple												= boundary[1]
					_snake_case							:       str												= make_points(UpperCAmelCase	,	UpperCAmelCase	,	UpperCAmelCase					)
					_snake_case							:       str												= 0.0
					y += (h / 3.0) * f(UpperCAmelCase					)
					_snake_case							:       Tuple												= 2
					for i in x_i:
										y += (h / 3) * (4 - 2 * (cnt % 2)) * f(UpperCAmelCase					)
										cnt += 1
					y += (h / 3.0) * f(UpperCAmelCase					)
					return y







def  A					(				UpperCAmelCase	,	UpperCAmelCase	,	UpperCAmelCase					):
					_snake_case							:       Union[str, Any]												= a + h
					while x < (b - h):
										yield x
										_snake_case							:       Optional[Any]												= x + h







def  A					(				UpperCAmelCase					):  # enter your function here
					_snake_case							:       Dict												= (x - 0) * (x - 0)
					return y







def  A					(				):
					_snake_case							:       int												= 0.0  # Lower bound of integration
					_snake_case							:       Union[str, Any]												= 1.0  # Upper bound of integration
					_snake_case							:       List[str]												= 1_0.0  # define number of steps or resolution
					_snake_case							:       Optional[int]												= [a, b]  # define boundary of integration
					_snake_case							:       List[str]												= method_a(UpperCAmelCase	,	UpperCAmelCase					)
					print(F"""y = {y}"""					)


if __name__ == "__main__":
							main()