



def 						_UpperCAmelCase							( snake_case     ):





					"""simple docstring"""

					return n * (2 * n - 1)


def 						_UpperCAmelCase							( snake_case     ):





					"""simple docstring"""

					_lowerCAmelCase         =       (1 + 24 * n) ** 0.5
					return ((1 + root) / 6) % 1 == 0


def 						_UpperCAmelCase							( snake_case = 1_44     ):





					"""simple docstring"""

					_lowerCAmelCase         =       start
					_lowerCAmelCase         =       hexagonal_num(snake_case     )
					while not is_pentagonal(snake_case     ):
										n += 1
										_lowerCAmelCase         =       hexagonal_num(snake_case     )
					return num


if __name__ == "__main__":
	print(f"{solution()} = ")








'''simple docstring'''

from __future__ import annotations



class 		lowerCamelCase__   :




					'''simple docstring'''



					def __init__(	self					:						str  ,	UpperCamelCase_					:						int       )	->							None:



						'''simple docstring'''





						_lowercase       :							Any  	=		value
						_lowercase       :							Node | None  	=		None
						_lowercase       :							Node | None  	=		None






class 		lowerCamelCase__   :




					'''simple docstring'''



					A_         =    42




					def __init__(	self					:						List[Any]       )	->							None:



						'''simple docstring'''





						_lowercase       :							Optional[int]  	=		0




					def     __UpperCAmelCase  (	self					:						str  ,	UpperCamelCase_					:						Node | None  ,	UpperCamelCase_					:						int       )	->							None:



						'''simple docstring'''





						if node is None:
							return

						if path_sum == self.target:
							self.paths += 1

						if node.left:
							self.depth_first_search(node.left  ,	path_sum + node.left.value       )
						if node.right:
							self.depth_first_search(node.right  ,	path_sum + node.right.value       )




					def     __UpperCAmelCase  (	self					:						Optional[int]  ,	UpperCamelCase_					:						Node | None  ,	UpperCamelCase_					:						int | None = None       )	->							int:



						'''simple docstring'''





						if node is None:
							return 0
						if target is not None:
							_lowercase       :							Union[str, Any]  	=		target

						self.depth_first_search(UpperCamelCase_  ,	node.value       )
						self.path_sum(node.left       )
						self.path_sum(node.right       )

						return self.paths


if __name__ == "__main__":
		import doctest

		doctest.testmod()
