



from typing import Any






class      UpperCamelCase    :



	def __init__(       self			,	UpperCAmelCase__		):
							A__							=       data
							A__							=       None



	def __repr__(       self		):
							return F"""Node({self.data})"""






class      UpperCamelCase    :



	def __init__(       self		):
							A__							=       None



	def __iter__(       self		):
							A__							=       self.head
							while node:
													yield node.data
													A__							=       node.next



	def __len__(       self		):
							return sum(1 for _ in self		)



	def __repr__(       self		):
							return "->".join([str(UpperCAmelCase__		) for item in self]		)



	def __getitem__(       self			,	UpperCAmelCase__		):
							if not 0 <= index < len(self		):
													raise ValueError("list index out of range."		)
							for i, node in enumerate(self		):
													if i == index:
																			return node
							return None



	def __setitem__(       self			,	UpperCAmelCase__			,	UpperCAmelCase__		):
							if not 0 <= index < len(self		):
													raise ValueError("list index out of range."		)
							A__							=       self.head
							for _ in range(UpperCAmelCase__		):
													A__							=       current.next
							A__							=       data



	def 			__A							(       self			,	UpperCAmelCase__		):
							self.insert_nth(len(self		)			,	UpperCAmelCase__		)



	def 			__A							(       self			,	UpperCAmelCase__		):
							self.insert_nth(0			,	UpperCAmelCase__		)



	def 			__A							(       self			,	UpperCAmelCase__			,	UpperCAmelCase__		):
							if not 0 <= index <= len(self		):
													raise IndexError("list index out of range"		)
							A__							=       Node(UpperCAmelCase__		)
							if self.head is None:
													A__							=       new_node
							elif index == 0:
													A__							=       self.head  # link new_node to head
													A__							=       new_node
							else:
													A__							=       self.head
													for _ in range(index - 1		):
																			A__							=       temp.next
													A__							=       temp.next
													A__							=       new_node



	def 			__A							(       self		):  # print every node data
							print(self		)



	def 			__A							(       self		):
							return self.delete_nth(0		)



	def 			__A							(       self		):  # delete from tail
							return self.delete_nth(len(self		) - 1		)



	def 			__A							(       self			,	UpperCAmelCase__ = 0		):
							if not 0 <= index <= len(self		) - 1:  # test if index is valid
													raise IndexError("List index out of range."		)
							A__							=       self.head  # default first node
							if index == 0:
													A__							=       self.head.next
							else:
													A__							=       self.head
													for _ in range(index - 1		):
																			A__							=       temp.next
													A__							=       temp.next
													A__							=       temp.next.next
							return delete_node.data



	def 			__A							(       self		):
							return self.head is None



	def 			__A							(       self		):
							A__							=       None
							A__							=       self.head

							while current:
													# Store the current node's next node.
													A__							=       current.next
													# Make the current node's next point backwards
													A__							=       prev
													# Make the previous node be the current node
													A__							=       current
													# Make the current node the next node (to progress iteration)
													A__							=       next_node
							# Return prev in order to put the head at the end
							A__							=       prev





def  UpperCamelCase						(       )->       None:





						"""simple docstring"""





						A__							=       LinkedList()
						assert linked_list.is_empty() is True
						assert str(_A    ) == ""

						try:
												linked_list.delete_head()
												raise AssertionError  # This should not happen.
						except IndexError:
												assert True  # This should happen.

						try:
												linked_list.delete_tail()
												raise AssertionError  # This should not happen.
						except IndexError:
												assert True  # This should happen.

						for i in range(10    ):
												assert len(_A    ) == i
												linked_list.insert_nth(_A			,							i + 1    )
						assert str(_A    ) == "->".join(str(_A    ) for i in range(1			,							11    )    )

						linked_list.insert_head(0    )
						linked_list.insert_tail(11    )
						assert str(_A    ) == "->".join(str(_A    ) for i in range(0			,							12    )    )

						assert linked_list.delete_head() == 0
						assert linked_list.delete_nth(9    ) == 10
						assert linked_list.delete_tail() == 11
						assert len(_A    ) == 9
						assert str(_A    ) == "->".join(str(_A    ) for i in range(1			,							10    )    )

						assert all(linked_list[i] == i + 1 for i in range(0			,							9    )    ) is True

						for i in range(0			,							9    ):
												A__							=       -i
						assert all(linked_list[i] == -i for i in range(0			,							9    )    ) is True

						linked_list.reverse()
						assert str(_A    ) == "->".join(str(_A    ) for i in range(-8			,							1    )    )
def  UpperCamelCase						(       )->       None:





						"""simple docstring"""





						A__							=       [
						    -9,
						    100,
						    Node(77345112    ),
						    "dlrow olleH",
						    7,
						    5555,
						    0,
						    -192.5_5555,
						    "Hello, world!",
						    77.9,
						    Node(10    ),
						    None,
						    None,
						    12.20,
						]
						A__							=       LinkedList()

						for i in test_input:
												linked_list.insert_tail(_A    )

						# Check if it's empty or not
						assert linked_list.is_empty() is False
						assert (
						    str(_A    ) == "-9->100->Node(77345112)->dlrow olleH->7->5555->0->"
						    "-192.55555->Hello, world!->77.9->Node(10)->None->None->12.2"
						)

						# Delete the head
						A__							=       linked_list.delete_head()
						assert result == -9
						assert (
						    str(_A    ) == "100->Node(77345112)->dlrow olleH->7->5555->0->-192.55555->"
						    "Hello, world!->77.9->Node(10)->None->None->12.2"
						)

						# Delete the tail
						A__							=       linked_list.delete_tail()
						assert result == 12.2
						assert (
						    str(_A    ) == "100->Node(77345112)->dlrow olleH->7->5555->0->-192.55555->"
						    "Hello, world!->77.9->Node(10)->None->None"
						)

						# Delete a node in specific location in linked list
						A__							=       linked_list.delete_nth(10    )
						assert result is None
						assert (
						    str(_A    ) == "100->Node(77345112)->dlrow olleH->7->5555->0->-192.55555->"
						    "Hello, world!->77.9->Node(10)->None"
						)

						# Add a Node instance to its head
						linked_list.insert_head(Node("Hello again, world!"    )    )
						assert (
						    str(_A    )
						    == "Node(Hello again, world!)->100->Node(77345112)->dlrow olleH->"
						    "7->5555->0->-192.55555->Hello, world!->77.9->Node(10)->None"
						)

						# Add None to its tail
						linked_list.insert_tail(_A    )
						assert (
						    str(_A    )
						    == "Node(Hello again, world!)->100->Node(77345112)->dlrow olleH->"
						    "7->5555->0->-192.55555->Hello, world!->77.9->Node(10)->None->None"
						)

						# Reverse the linked list
						linked_list.reverse()
						assert (
						    str(_A    )
						    == "None->None->Node(10)->77.9->Hello, world!->-192.55555->0->5555->"
						    "7->dlrow olleH->Node(77345112)->100->Node(Hello again, world!)"
						)
def  UpperCamelCase						(       )->       int:





						"""simple docstring"""





						from doctest import testmod

						testmod()

						A__							=       LinkedList()
						linked_list.insert_head(input("Inserting 1st at head "    ).strip()    )
						linked_list.insert_head(input("Inserting 2nd at head "    ).strip()    )
						print("\nPrint list:"    )
						linked_list.print_list()
						linked_list.insert_tail(input("\nInserting 1st at tail "    ).strip()    )
						linked_list.insert_tail(input("Inserting 2nd at tail "    ).strip()    )
						print("\nPrint list:"    )
						linked_list.print_list()
						print("\nDelete head"    )
						linked_list.delete_head()
						print("Delete tail"    )
						linked_list.delete_tail()
						print("\nPrint list:"    )
						linked_list.print_list()
						print("\nReverse linked list"    )
						linked_list.reverse()
						print("\nPrint list:"    )
						linked_list.print_list()
						print("\nString representation of linked list:"    )
						print(_A    )
						print("\nReading/changing Node data using indexing:"    )
						print(f"""Element at Position 1: {linked_list[1]}"""    )
						A__							=       input("Enter New Value: "    ).strip()
						print("New list:"    )
						print(_A    )
						print(f"""length of linked_list is : {len(_A    )}"""    )


if __name__ == "__main__":
						main()










from __future__ import annotations

from random import random






class      UpperCamelCase    :



	def __init__(       self			,	UpperCAmelCase__ = None		):
							A__							=       value
							A__							=       random()
							A__							=       None
							A__							=       None



	def __repr__(       self		):
							from pprint import pformat

							if self.left is None and self.right is None:
													return F"""'{self.value}: {self.prior:.5}'"""
							else:
													return pformat(
													    {F"""{self.value}: {self.prior:.5}""": (self.left, self.right)}			,	indent=1		)



	def __str__(       self		):
							A__							=       str(self.value		) + " "
							A__							=       str(self.left or ""		)
							A__							=       str(self.right or ""		)
							return value + left + right





def  UpperCamelCase						(       _A			:				Node | None			,							_A			:				int    )->       tuple[Node | None, Node | None]:





						"""simple docstring"""





						if root is None:  # None tree is split into 2 Nones
												return None, None
						elif root.value is None:
												return None, None
						else:
												if value < root.value:
																		A__						,       A__							=       split(root.left			,							_A    )
																		return left, root
												else:
																		A__						,       A__							=       split(root.right			,							_A    )
																		return root, right
def  UpperCamelCase						(       _A			:				Node | None			,							_A			:				Node | None    )->       Node | None:





						"""simple docstring"""





						if (not left) or (not right):  # If one node is None, return the other
												return left or right
						elif left.prior < right.prior:
												A__							=       merge(left.right			,							_A    )
												return left
						else:
												A__							=       merge(_A			,							right.left    )
												return right
def  UpperCamelCase						(       _A			:				Node | None			,							_A			:				int    )->       Node | None:





						"""simple docstring"""





						A__							=       Node(_A    )
						A__						,       A__							=       split(_A			,							_A    )
						return merge(merge(_A			,							_A    )			,							_A    )
def  UpperCamelCase						(       _A			:				Node | None			,							_A			:				int    )->       Node | None:





						"""simple docstring"""





						A__						,       A__							=       split(_A			,							value - 1    )
						A__						,       A__							=       split(_A			,							_A    )
						return merge(_A			,							_A    )
def  UpperCamelCase						(       _A			:				Node | None    )->       None:





						"""simple docstring"""





						if not root:  # None
												return
						else:
												inorder(root.left    )
												print(root.value			,							end=","    )
												inorder(root.right    )
def  UpperCamelCase						(       _A			:				Node | None			,							_A			:				str    )->       Node | None:





						"""simple docstring"""





						for arg in args.split():
												if arg[0] == "+":
																		A__							=       insert(_A			,							int(arg[1:]    )    )

												elif arg[0] == "-":
																		A__							=       erase(_A			,							int(arg[1:]    )    )

												else:
																		print("Unknown command"    )

						return root
def  UpperCamelCase						(       )->       None:





						"""simple docstring"""





						A__							=       None
						print(
						    "enter numbers to create a tree, + value to add value into treap, "
						    "- value to erase all nodes with value. 'q' to quit. "    )

						A__							=       input()
						while args != "q":
												A__							=       interact_treap(_A			,							_A    )
												print(_A    )
												A__							=       input()

						print("good by!"    )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()





