



UpperCAmelCase__       =	[0, 2, 4, 6, 8]
UpperCAmelCase__       =	[1, 3, 5, 7, 9]





def 							A     (					_UpperCAmelCase    :       int							,       _UpperCAmelCase    :       int							,       _UpperCAmelCase    :       list[int]							,       _UpperCAmelCase    :       int   )    ->			int:







			'''simple docstring'''
			if remaining_length == 0:
						if digits[0] == 0 or digits[-1] == 0:
									return 0

						for i in range(length // 2 - 1							,       -1							,       -1   ):
									remainder += digits[i] + digits[length - i - 1]

									if remainder % 2 == 0:
												return 0

									remainder //= 10

						return 1

			if remaining_length == 1:
						if remainder % 2 == 0:
									return 0

						_UpperCAmelCase			=       0
						for digit in range(10   ):
									_UpperCAmelCase			=       digit
									result += reversible_numbers(
									    0							,       (remainder + 2 * digit) // 10							,       _UpperCAmelCase							,       _UpperCAmelCase   )
						return result

			_UpperCAmelCase			=       0
			for digita in range(10   ):
						_UpperCAmelCase			=       digita

						if (remainder + digita) % 2 == 0:
									_UpperCAmelCase			=       ODD_DIGITS
						else:
									_UpperCAmelCase			=       EVEN_DIGITS

						for digita in other_parity_digits:
									_UpperCAmelCase			=       digita
									result += reversible_numbers(
									    remaining_length - 2							,       (remainder + digita + digita) // 10							,       _UpperCAmelCase							,       _UpperCAmelCase							,       )
			return result





def 							A     (					_UpperCAmelCase    :       int = 9   )    ->			int:







			'''simple docstring'''
			_UpperCAmelCase			=       0
			for length in range(1							,       max_power + 1   ):
						result += reversible_numbers(_UpperCAmelCase							,       0							,       [0] * length							,       _UpperCAmelCase   )
			return result


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





UpperCAmelCase__       =	{
    "A": ["B", "C", "E"],
    "B": ["A", "D", "E"],
    "C": ["A", "F", "G"],
    "D": ["B"],
    "E": ["A", "B", "D"],
    "F": ["C"],
    "G": ["C"],
}





def 							A     (					_UpperCAmelCase    :       dict							,       _UpperCAmelCase    :       Optional[int]							,       _UpperCAmelCase    :       List[Any]   )    ->			list[str]:







			'''simple docstring'''
			_UpperCAmelCase			=       set()
			# keep track of all the paths to be checked
			_UpperCAmelCase			=       [[start]]

			# return path if start is goal
			if start == goal:
						return [start]

			# keeps looping until all possible paths have been checked
			while queue:
						# pop the first path from the queue
						_UpperCAmelCase			=       queue.pop(0   )
						# get the last node from the path
						_UpperCAmelCase			=       path[-1]
						if node not in explored:
									_UpperCAmelCase			=       graph[node]
									# go through all neighbour nodes, construct a new path and
									# push it into the queue
									for neighbour in neighbours:
												_UpperCAmelCase			=       list(_UpperCAmelCase   )
												new_path.append(_UpperCAmelCase   )
												queue.append(_UpperCAmelCase   )
												# return path if neighbour is goal
												if neighbour == goal:
															return new_path

            # mark node as explored
									explored.add(_UpperCAmelCase   )

    # in case there's no path between the 2 nodes
			return []





def 							A     (					_UpperCAmelCase    :       dict							,       _UpperCAmelCase    :       Any							,       _UpperCAmelCase    :       List[str]   )    ->			int:







			'''simple docstring'''
			if not graph or start not in graph or target not in graph:
						return -1
			if start == target:
						return 0
			_UpperCAmelCase			=       [start]
			_UpperCAmelCase			=       set(_UpperCAmelCase   )
			# Keep tab on distances from `start` node.
			_UpperCAmelCase			=       {start: 0, target: -1}
			while queue:
						_UpperCAmelCase			=       queue.pop(0   )
						if node == target:
									_UpperCAmelCase			=       (
									    dist[node] if dist[target] == -1 else min(dist[target]							,       dist[node]   )
									)
						for adjacent in graph[node]:
									if adjacent not in visited:
												visited.add(_UpperCAmelCase   )
												queue.append(_UpperCAmelCase   )
												_UpperCAmelCase			=       dist[node] + 1
			return dist[target]


if __name__ == "__main__":
							print(bfs_shortest_path(demo_graph, "G", "D"))  # returns ['G', 'C', 'A', 'B', 'D']
							print(bfs_shortest_path_distance(demo_graph, "G", "D"))  # returns 4
