



from math import pow






def     SCREAMING_SNAKE_CASE(      __UpperCamelCase	,				__UpperCamelCase	,				__UpperCamelCase	,				__UpperCamelCase	,				__UpperCamelCase	,				)	->						tuple[int, int]:
				if current_sum == needed_sum:
								# If the sum of the powers is equal to needed_sum, then we have a solution.
								solutions_count += 1
								return current_sum, solutions_count

				a__	:							Optional[int]      						= int(pow(__UpperCamelCase	,				__UpperCamelCase ) )
				if current_sum + i_to_n <= needed_sum:
								# If the sum of the powers is less than needed_sum, then continue adding powers.
								current_sum += i_to_n
								a__						,   a__	:							List[Any]      						= backtrack(
								    __UpperCamelCase	,				__UpperCamelCase	,				current_number + 1	,				__UpperCamelCase	,				__UpperCamelCase )
								current_sum -= i_to_n
				if i_to_n < needed_sum:
								# If the power of i is less than needed_sum, then try with the next power.
								a__						,   a__	:							List[str]      						= backtrack(
								    __UpperCamelCase	,				__UpperCamelCase	,				current_number + 1	,				__UpperCamelCase	,				__UpperCamelCase )
				return current_sum, solutions_count






def     SCREAMING_SNAKE_CASE(      __UpperCamelCase	,				__UpperCamelCase )	->						int:
				if not (1 <= needed_sum <= 10_00 and 2 <= power <= 10):
								raise ValueError(
								    "Invalid input\n"
								    "needed_sum must be between 1 and 1000, power between 2 and 10." )

				return backtrack(__UpperCamelCase	,				__UpperCamelCase	,				1	,				0	,				0 )[1]  # Return the solutions_count


if __name__ == "__main__":
						import doctest

						doctest.testmod()







from __future__ import annotations

import queue


class 				_a						:





							'''simple docstring'''

							def __init__(							self ,					__UpperCAmelCase				):







											"""simple docstring"""



											a__	:							Union[str, Any]      						= data
											a__	:							Tuple      						= None
											a__	:							Optional[Any]      						= None






def     SCREAMING_SNAKE_CASE(      )	->						TreeNode:
				print("\n********Press N to stop entering at any point of time********\n" )
				a__	:							Tuple      						= input("Enter the value of the root node: " ).strip().lower()
				a__	:							queue.Queue      						= queue.Queue()
				a__	:							str      						= TreeNode(int(__UpperCamelCase ) )
				q.put(__UpperCamelCase )
				while not q.empty():
								a__	:							str      						= q.get()
								a__	:							Optional[Any]      						= F'Enter the left node of {node_found.data}: '
								a__	:							List[Any]      						= input(__UpperCamelCase ).strip().lower() or "n"
								if check == "n":
												return tree_node
								a__	:							Optional[int]      						= TreeNode(int(__UpperCamelCase ) )
								a__	:							List[str]      						= left_node
								q.put(__UpperCamelCase )
								a__	:							Dict      						= F'Enter the right node of {node_found.data}: '
								a__	:							List[str]      						= input(__UpperCamelCase ).strip().lower() or "n"
								if check == "n":
												return tree_node
								a__	:							str      						= TreeNode(int(__UpperCamelCase ) )
								a__	:							Any      						= right_node
								q.put(__UpperCamelCase )
				raise






def     SCREAMING_SNAKE_CASE(      __UpperCamelCase )	->						None:
				if not isinstance(__UpperCamelCase	,				__UpperCamelCase ) or not node:
								return
				print(node.data	,				end="," )
				pre_order(node.left )
				pre_order(node.right )






def     SCREAMING_SNAKE_CASE(      __UpperCamelCase )	->						None:
				if not isinstance(__UpperCamelCase	,				__UpperCamelCase ) or not node:
								return
				in_order(node.left )
				print(node.data	,				end="," )
				in_order(node.right )






def     SCREAMING_SNAKE_CASE(      __UpperCamelCase )	->						None:
				if not isinstance(__UpperCamelCase	,				__UpperCamelCase ) or not node:
								return
				post_order(node.left )
				post_order(node.right )
				print(node.data	,				end="," )






def     SCREAMING_SNAKE_CASE(      __UpperCamelCase )	->						None:
				if not isinstance(__UpperCamelCase	,				__UpperCamelCase ) or not node:
								return
				a__	:							queue.Queue      						= queue.Queue()
				q.put(__UpperCamelCase )
				while not q.empty():
								a__	:							Tuple      						= q.get()
								print(node_dequeued.data	,				end="," )
								if node_dequeued.left:
												q.put(node_dequeued.left )
								if node_dequeued.right:
												q.put(node_dequeued.right )






def     SCREAMING_SNAKE_CASE(      __UpperCamelCase )	->						None:
				if not isinstance(__UpperCamelCase	,				__UpperCamelCase ) or not node:
								return
				a__	:							queue.Queue      						= queue.Queue()
				q.put(__UpperCamelCase )
				while not q.empty():
								a__	:							int      						= []
								while not q.empty():
												a__	:							Union[str, Any]      						= q.get()
												print(node_dequeued.data	,				end="," )
												if node_dequeued.left:
																list_.append(node_dequeued.left )
												if node_dequeued.right:
																list_.append(node_dequeued.right )
								print()
								for node in list_:
												q.put(__UpperCamelCase )






def     SCREAMING_SNAKE_CASE(      __UpperCamelCase )	->						None:
				if not isinstance(__UpperCamelCase	,				__UpperCamelCase ) or not node:
								return
				a__	:							list[TreeNode]      						= []
				a__	:							Optional[int]      						= node
				while n or stack:
								while n:  # start from root node, find its left child
												print(n.data	,				end="," )
												stack.append(__UpperCamelCase )
												a__	:							int      						= n.left
								# end of while means current node doesn't have left child
								a__	:							Dict      						= stack.pop()
								# start to traverse its right child
								a__	:							str      						= n.right






def     SCREAMING_SNAKE_CASE(      __UpperCamelCase )	->						None:
				if not isinstance(__UpperCamelCase	,				__UpperCamelCase ) or not node:
								return
				a__	:							list[TreeNode]      						= []
				a__	:							Dict      						= node
				while n or stack:
								while n:
												stack.append(__UpperCamelCase )
												a__	:							List[Any]      						= n.left
								a__	:							str      						= stack.pop()
								print(n.data	,				end="," )
								a__	:							Any      						= n.right






def     SCREAMING_SNAKE_CASE(      __UpperCamelCase )	->						None:
				if not isinstance(__UpperCamelCase	,				__UpperCamelCase ) or not node:
								return
				a__						,   a__	:							List[str]      						= [], []
				a__	:							List[Any]      						= node
				stacka.append(__UpperCamelCase )
				while stacka:  # to find the reversed order of post order, store it in stack2
								a__	:							Optional[Any]      						= stacka.pop()
								if n.left:
												stacka.append(n.left )
								if n.right:
												stacka.append(n.right )
								stacka.append(__UpperCamelCase )
				while stacka:  # pop up from stack2 will be the post order
								print(stacka.pop().data	,				end="," )






def     SCREAMING_SNAKE_CASE(      __UpperCamelCase = ""	,				__UpperCamelCase=50	,				__UpperCamelCase="*" )	->						str:
				if not s:
								return "\n" + width * char
				a__						,   a__	:							int      						= divmod(width - len(__UpperCamelCase ) - 2	,				2 )
				return F'{left * char} {s} {(left + extra) * char}'


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						print(prompt("""Binary Tree Traversals"""))

						lowerCamelCase		       =      build_tree()
						print(prompt("""Pre Order Traversal"""))
						pre_order(node)
						print(prompt() + """\n""")

						print(prompt("""In Order Traversal"""))
						in_order(node)
						print(prompt() + """\n""")

						print(prompt("""Post Order Traversal"""))
						post_order(node)
						print(prompt() + """\n""")

						print(prompt("""Level Order Traversal"""))
						level_order(node)
						print(prompt() + """\n""")

						print(prompt("""Actual Level Order Traversal"""))
						level_order_actual(node)
						print("""*""" * 50 + """\n""")

						print(prompt("""Pre Order Traversal - Iteration Version"""))
						pre_order_iter(node)
						print(prompt() + """\n""")

						print(prompt("""In Order Traversal - Iteration Version"""))
						in_order_iter(node)
						print(prompt() + """\n""")

						print(prompt("""Post Order Traversal - Iteration Version"""))
						post_order_iter(node)
						print(prompt())


