



from __future__ import annotations

import queue






class 						__a :



	def __init__(						self							:    int				,	snake_case_							:    Optional[int])->							Optional[int]:
						__lowerCAmelCase	   =data
						__lowerCAmelCase	   =None
						__lowerCAmelCase	   =None






def 					__lowerCAmelCase		(  )  ->						TreeNode:
					print("""\n********Press N to stop entering at any point of time********\n"""	)
					__lowerCAmelCase	   =input("""Enter the value of the root node: """	).strip().lower()
					__lowerCAmelCase	   =queue.Queue()
					__lowerCAmelCase	   =TreeNode(int(__lowerCamelCase	)	)
					q.put(__lowerCamelCase	)
					while not q.empty():
										__lowerCAmelCase	   =q.get()
										__lowerCAmelCase	   =f"""Enter the left node of {node_found.data}: """
										__lowerCAmelCase	   =input(__lowerCamelCase	).strip().lower() or """n"""
										if check == "n":
															return tree_node
										__lowerCAmelCase	   =TreeNode(int(__lowerCamelCase	)	)
										__lowerCAmelCase	   =left_node
										q.put(__lowerCamelCase	)
										__lowerCAmelCase	   =f"""Enter the right node of {node_found.data}: """
										__lowerCAmelCase	   =input(__lowerCamelCase	).strip().lower() or """n"""
										if check == "n":
															return tree_node
										__lowerCAmelCase	   =TreeNode(int(__lowerCamelCase	)	)
										__lowerCAmelCase	   =right_node
										q.put(__lowerCamelCase	)
					raise






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






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






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






def 					__lowerCAmelCase		(  __lowerCamelCase	:    TreeNode	)  ->						None:
					if not isinstance(__lowerCamelCase				,   __lowerCamelCase	) or not node:
										return
					__lowerCAmelCase	   =queue.Queue()
					q.put(__lowerCamelCase	)
					while not q.empty():
										__lowerCAmelCase	   =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 					__lowerCAmelCase		(  __lowerCamelCase	:    TreeNode	)  ->						None:
					if not isinstance(__lowerCamelCase				,   __lowerCamelCase	) or not node:
										return
					__lowerCAmelCase	   =queue.Queue()
					q.put(__lowerCamelCase	)
					while not q.empty():
										__lowerCAmelCase	   =[]
										while not q.empty():
															__lowerCAmelCase	   =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(__lowerCamelCase	)






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






def 					__lowerCAmelCase		(  __lowerCamelCase	:    TreeNode	)  ->						None:
					if not isinstance(__lowerCamelCase				,   __lowerCamelCase	) or not node:
										return
					__lowerCAmelCase	   =[]
					__lowerCAmelCase	   =node
					while n or stack:
										while n:
															stack.append(__lowerCamelCase	)
															__lowerCAmelCase	   =n.left
										__lowerCAmelCase	   =stack.pop()
										print(n.data				,   end=""","""	)
										__lowerCAmelCase	   =n.right






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






def 					__lowerCAmelCase		(  __lowerCamelCase	:    str = ""				,   __lowerCamelCase	:    Union[str, Any]=50				,   __lowerCamelCase	:    Union[str, Any]="*"	)  ->						str:
					if not s:
										return "\n" + width * char
					__lowerCAmelCase   ,	__lowerCAmelCase	   =divmod(width - len(__lowerCamelCase	) - 2				,   2	)
					return f"""{left * char} {s} {(left + extra) * char}"""


if __name__ == "__main__":
				import doctest

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

				lowercase_	       =			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())









import math

from numpy import inf
from scipy.integrate import quad






def 					__lowerCAmelCase		(  __lowerCamelCase	:    float	)  ->						float:
					if num <= 0:
										raise ValueError("""math domain error"""	)

					return quad(__lowerCamelCase				,   0				,   __lowerCamelCase				,   args=(__lowerCamelCase)	)[0]






def 					__lowerCAmelCase		(  __lowerCamelCase	:    float				,   __lowerCamelCase	:    float	)  ->						float:
					return math.pow(__lowerCamelCase				,   z - 1	) * math.exp(-x	)


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

				testmod()




