





from __future__ import annotations

def     __A      (			a_						:int)		->		Dict:
				__a :						Optional[int]			       =  str(snake_case_)
				return len(snake_case_) == 9 and set(snake_case_) == set('''123456789''')

def     __A      (			)		->		Any:
				for base_num in range(99_99   ,       49_99   ,       -1):
								__a :						str			       =  10_00_02 * base_num
								if is_9_pandigital(snake_case_):
												return candidate

				for base_num in range(3_33   ,       99   ,       -1):
								__a :						int			       =  1_00_20_03 * base_num
								if is_9_pandigital(snake_case_):
												return candidate

				return None


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






"""simple docstring"""






from __future__ import annotations

from collections import deque
from collections.abc import Iterator
from dataclasses import dataclass




@dataclass
class 				__lowercase			:







					'''simple docstring'''




					__lowerCAmelCase  =  42
					__lowerCAmelCase  =  42






class 				__lowercase			:







					'''simple docstring'''




					def __init__(						self	,			_UpperCAmelCase     ):
									__a :						list[list[Edge]]			       =  [[] for _ in range(_UpperCAmelCase     )]
									__a :						Dict			       =  size







					def __getitem__(						self	,			_UpperCAmelCase     ):
									return iter(self._graph[vertex]     )







					@property
					def  _lowerCamelCase		(						self     ):
									return self._size







					def  _lowerCamelCase		(						self	,			_UpperCAmelCase	,			_UpperCAmelCase	,			_UpperCAmelCase     ):
									if weight not in (0, 1):
													raise ValueError('''Edge weight must be either 0 or 1.'''     )

									if to_vertex < 0 or to_vertex >= self.size:
													raise ValueError('''Vertex indexes must be in [0; size).'''     )

									self._graph[from_vertex].append(Edge(_UpperCAmelCase	,			_UpperCAmelCase     )     )







					def  _lowerCamelCase		(						self	,			_UpperCAmelCase	,			_UpperCAmelCase     ):
									__a :						List[str]			       =  deque([start_vertex]     )
									__a :						list[int | None]			       =  [None] * self.size
									__a :						int			       =  0

									while queue:
													__a :						Any			       =  queue.popleft()
													__a :						Tuple			       =  distances[current_vertex]
													if current_distance is None:
																	continue

													for edge in self[current_vertex]:
																	__a :						List[str]			       =  current_distance + edge.weight
																	__a :						str			       =  distances[edge.destination_vertex]
																	if (
																	    isinstance(_UpperCAmelCase	,			_UpperCAmelCase     )
																	    and new_distance >= dest_vertex_distance
																	):
																					continue
																	__a :						str			       =  new_distance
																	if edge.weight == 0:
																					queue.appendleft(edge.destination_vertex     )
																	else:
																					queue.append(edge.destination_vertex     )

									if distances[finish_vertex] is None:
													raise ValueError('''No path from start_vertex to finish_vertex.'''     )

									return distances[finish_vertex]


if __name__ == "__main__":
		import doctest

		doctest.testmod()