



'''simple docstring'''

from __future__ import annotations



def 					__lowerCamelCase					(				lowerCAmelCase_  )      ->				bool:
		_a					:				List[Any]				=							str(lowerCAmelCase_  )
		return len(lowerCAmelCase_  ) == 9 and set(lowerCAmelCase_  ) == set('123456789'  )



def 					__lowerCamelCase					(				)      ->				int | None:
		for base_num in range(9999						,      4999						,      -1  ):
				_a					:				Union[str, Any]				=							100002 * base_num
				if is_9_pandigital(lowerCAmelCase_  ):
						return candidate

		for base_num in range(333						,      99						,      -1  ):
				_a					:				Optional[int]				=							1002003 * base_num
				if is_9_pandigital(lowerCAmelCase_  ):
						return candidate

		return None


if __name__ == "__main__":
							print(f"""{solution() = }""")









'''simple docstring'''

from __future__ import annotations

from collections.abc import Iterator
from typing import Any

class      __magic_name__						:







							def __init__(							self :	Dict     ,_UpperCAmelCase :	Any		):
									_a					:				Any				=							data
									_a					:				Node | None				=							None

class      __magic_name__						:







							def __init__(							self :	Any		):
									_a					:				int				=							None
									_a					:				Optional[int]				=							None







							def __iter__(							self :	Optional[int]		):
									_a					:				List[Any]				=							self.head
									while self.head:
											yield node.data
											_a					:				str				=							node.next
											if node == self.head:
													break







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







							def __repr__(							self :	int		):
									return "->".join(str(_UpperCAmelCase		) for item in iter(self		)		)







							def 							__lowercase      (							self :	Optional[Any]     ,_UpperCAmelCase :	Any		):
									self.insert_nth(len(self		)     ,_UpperCAmelCase		)







							def 							__lowercase      (							self :	str     ,_UpperCAmelCase :	Any		):
									self.insert_nth(0     ,_UpperCAmelCase		)







							def 							__lowercase      (							self :	List[str]     ,_UpperCAmelCase :	int     ,_UpperCAmelCase :	Any		):
									if index < 0 or index > len(self		):
											raise IndexError('list index out of range.'		)
									_a					:				List[str]				=							Node(_UpperCAmelCase		)
									if self.head is None:
											_a					:				Tuple				=							new_node  # first node points itself
											_a					:				int				=							new_node
									elif index == 0:  # insert at head
											_a					:				Any				=							self.head
											_a					:				Tuple				=							new_node
									else:
											_a					:				Any				=							self.head
											for _ in range(index - 1		):
													_a					:				int				=							temp.next
											_a					:				Optional[int]				=							temp.next
											_a					:				int				=							new_node
											if index == len(self		) - 1:  # insert at tail
													_a					:				Optional[int]				=							new_node







							def 							__lowercase      (							self :	List[Any]		):
									return self.delete_nth(0		)







							def 							__lowercase      (							self :	Dict		):
									return self.delete_nth(len(self		) - 1		)







							def 							__lowercase      (							self :	Union[str, Any]     ,_UpperCAmelCase :	int = 0		):
									if not 0 <= index < len(self		):
											raise IndexError('list index out of range.'		)
									_a					:				Optional[int]				=							self.head
									if self.head == self.tail:  # just one node
											_a					:				Optional[int]				=							None
									elif index == 0:  # delete head node
											_a					:				Dict				=							self.tail.next.next
											_a					:				Dict				=							self.head.next
									else:
											_a					:				List[Any]				=							self.head
											for _ in range(index - 1		):
													_a					:				Union[str, Any]				=							temp.next
											_a					:				Optional[int]				=							temp.next
											_a					:				List[str]				=							temp.next.next
											if index == len(self		) - 1:  # delete at tail
													_a					:				int				=							temp
									return delete_node.data







							def 							__lowercase      (							self :	int		):
									return len(self		) == 0



def 					__lowerCamelCase					(				)      ->				None:
		_a					:				int				=							CircularLinkedList()
		assert len(lowerCAmelCase_  ) == 0
		assert circular_linked_list.is_empty() is True
		assert str(lowerCAmelCase_  ) == ""

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

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

		try:
				circular_linked_list.delete_nth(-1  )
				raise AssertionError
		except IndexError:
				assert True

		try:
				circular_linked_list.delete_nth(0  )
				raise AssertionError
		except IndexError:
				assert True

		assert circular_linked_list.is_empty() is True
		for i in range(5  ):
				assert len(lowerCAmelCase_  ) == i
				circular_linked_list.insert_nth(lowerCAmelCase_						,      i + 1  )
		assert str(lowerCAmelCase_  ) == "->".join(str(lowerCAmelCase_  ) for i in range(1						,      6  )  )

		circular_linked_list.insert_tail(6  )
		assert str(lowerCAmelCase_  ) == "->".join(str(lowerCAmelCase_  ) for i in range(1						,      7  )  )
		circular_linked_list.insert_head(0  )
		assert str(lowerCAmelCase_  ) == "->".join(str(lowerCAmelCase_  ) for i in range(0						,      7  )  )

		assert circular_linked_list.delete_front() == 0
		assert circular_linked_list.delete_tail() == 6
		assert str(lowerCAmelCase_  ) == "->".join(str(lowerCAmelCase_  ) for i in range(1						,      6  )  )
		assert circular_linked_list.delete_nth(2  ) == 3

		circular_linked_list.insert_nth(2						,      3  )
		assert str(lowerCAmelCase_  ) == "->".join(str(lowerCAmelCase_  ) for i in range(1						,      6  )  )

		assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
							import doctest

							doctest.testmod()




