





"""simple docstring"""




class  _a						:






				def __init__( self		:    int, lowerCAmelCase__		:    int							)	->      None:




										'''simple docstring'''



										_UpperCamelCase			:					List[Any]     =    data
										_UpperCamelCase			:					BinaryTreeNode | None     =    None
										_UpperCamelCase			:					BinaryTreeNode | None     =    None





def        a_				(							_lowercase       ,						_lowercase   ):
						if node is None:
												_UpperCamelCase			:					str     =    BinaryTreeNode(_lowercase   )
												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			:					int     =    insert(node.left_child       ,						_lowercase   )
						else:
												# if new_value is greater than value of data in node,
												#  add it to right subtree and proceed recursively
												_UpperCamelCase			:					Tuple     =    insert(node.right_child       ,						_lowercase   )
						return node





def        a_				(							_lowercase   ):  # if node is None,return
						if node:
												_UpperCamelCase			:					Union[str, Any]     =    inorder(node.left_child   )
												_UpperCamelCase			:					Dict     =    [*inorder_array, node.data]
												_UpperCamelCase			:					Optional[int]     =    inorder_array + inorder(node.right_child   )
						else:
												_UpperCamelCase			:					Optional[int]     =    []
						return inorder_array





def        a_				(							):
						_UpperCamelCase			:					Union[str, Any]     =    insert(_lowercase       ,						15   )
						insert(_lowercase       ,						10   )
						insert(_lowercase       ,						25   )
						insert(_lowercase       ,						6   )
						insert(_lowercase       ,						14   )
						insert(_lowercase       ,						20   )
						insert(_lowercase       ,						60   )
						return root





def        a_				(							):
						# main function
						_UpperCamelCase			:					Tuple     =    make_tree()
						print('''Printing values of binary search tree in Inorder Traversal.'''   )
						inorder(_lowercase   )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()










"""simple docstring"""




from functools import lru_cache





@lru_cache
def        a_				(							_lowercase   ):
						if not isinstance(_lowercase       ,						_lowercase   ):
												raise TypeError('''k must be an integer.'''   )
						if k < 0:
												raise ValueError('''k integer must be greater or equal to zero.'''   )
						if k == 0:
												return 0
						elif k == 1:
												return 1
						else:
												return fibonacci(k - 1   ) + fibonacci(k - 2   )





def        a_				(							_lowercase       ,						_lowercase   ):
						_UpperCamelCase			:					Any     =    len(_lowercase   )
						# Find m such that F_m >= n where F_i is the i_th fibonacci number.
						_UpperCamelCase			:					Optional[int]     =    0
						while True:
												if fibonacci(_lowercase   ) >= len_list:
																		_UpperCamelCase			:					List[Any]     =    i
																		break
												i += 1
						_UpperCamelCase			:					Tuple     =    0
						while fibb_k > 0:
												_UpperCamelCase			:					Union[str, Any]     =    min(
												    offset + fibonacci(fibb_k - 1   )       ,						len_list - 1   )  # Prevent out of range
												_UpperCamelCase			:					Any     =    arr[index_k]
												if item_k_1 == val:
																		return index_k
												elif val < item_k_1:
																		fibb_k -= 1
												elif val > item_k_1:
																		offset += fibonacci(fibb_k - 1   )
																		fibb_k -= 2
						else:
												return -1


if __name__ == "__main__":
						import doctest

						doctest.testmod()



