"""simple docstring"""

def    lowerCAmelCase			(__UpperCamelCase							:    int			):
							"""simple docstring"""


							if not isinstance(__UpperCamelCase							,					__UpperCamelCase			):
														raise TypeError('''recursive_lucas_number accepts only integer arguments.'''			)
							if n_th_number == 0:
														return 2
							if n_th_number == 1:
														return 1

							return recursive_lucas_number(n_th_number - 1			) + recursive_lucas_number(
							    n_th_number - 2			)


def    lowerCAmelCase			(__UpperCamelCase							:    int			):
							"""simple docstring"""


							if not isinstance(__UpperCamelCase							,					__UpperCamelCase			):
														raise TypeError('''dynamic_lucas_number accepts only integer arguments.'''			)
							__UpperCamelCase	,      __UpperCamelCase							=2, 1
							for _ in range(__UpperCamelCase			):
														__UpperCamelCase	,      __UpperCamelCase							=b, a + b
							return a


if __name__ == "__main__":
				from doctest import testmod

				testmod()
				__lowercase    =				int(input('''Enter the number of terms in lucas series:\n''').strip())
				print('''Using recursive function to calculate lucas series:''')
				print(''' '''.join(str(recursive_lucas_number(i)) for i in range(n)))
				print('''\nUsing dynamic function to calculate lucas series:''')
				print(''' '''.join(str(dynamic_lucas_number(i)) for i in range(n)))




"""simple docstring"""

class 		_lowercase :



						"""simple docstring"""




						def __init__(				self							:    List[str]     , UpperCamelCase__							:    int				)				->				None:
													'''simple docstring'''



													__UpperCamelCase							=data
													__UpperCamelCase							=None
													__UpperCamelCase							=None






def    lowerCAmelCase			(__UpperCamelCase							:    BinaryTreeNode | None							,					__UpperCamelCase							:    int			):
							"""simple docstring"""


							if node is None:
														__UpperCamelCase							=BinaryTreeNode(__UpperCamelCase			)
														return node

							# binary search tree is not empty,
							# so we will insert it into the tree
							# if new_value is less than value of data in node,
							#  add it to left subtree and proceed recursively
							if new_value < node.data:
														__UpperCamelCase							=insert(node.left_child							,					__UpperCamelCase			)
							else:
														# if new_value is greater than value of data in node,
														#  add it to right subtree and proceed recursively
														__UpperCamelCase							=insert(node.right_child							,					__UpperCamelCase			)
							return node


def    lowerCAmelCase			(__UpperCamelCase							:    None | BinaryTreeNode			):  # if node is None,return
							"""simple docstring"""


							if node:
														__UpperCamelCase							=inorder(node.left_child			)
														__UpperCamelCase							=[*inorder_array, node.data]
														__UpperCamelCase							=inorder_array + inorder(node.right_child			)
							else:
														__UpperCamelCase							=[]
							return inorder_array


def    lowerCAmelCase			():
							"""simple docstring"""


							__UpperCamelCase							=insert(__UpperCamelCase							,					1_5			)
							insert(__UpperCamelCase							,					1_0			)
							insert(__UpperCamelCase							,					2_5			)
							insert(__UpperCamelCase							,					6			)
							insert(__UpperCamelCase							,					1_4			)
							insert(__UpperCamelCase							,					2_0			)
							insert(__UpperCamelCase							,					6_0			)
							return root


def    lowerCAmelCase			():
							"""simple docstring"""


							__UpperCamelCase							=make_tree()
							print('''Printing values of binary search tree in Inorder Traversal.'''			)
							inorder(__UpperCamelCase			)


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				main()



