






lowerCamelCase     :							Optional[int]    ={
    '''A''': ['''B''', '''C''', '''E'''],
    '''B''': ['''A''', '''D''', '''E'''],
    '''C''': ['''A''', '''F''', '''G'''],
    '''D''': ['''B'''],
    '''E''': ['''A''', '''B''', '''D'''],
    '''F''': ['''C'''],
    '''G''': ['''C'''],
}







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )			->     list[str]:
     UpperCamelCase__      :       Optional[Any]	    =  set()
     # keep track of all the paths to be checked
     UpperCamelCase__      :       Optional[Any]	    =  [[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__      :       int	    =  queue.pop(0      )
          # get the last node from the path
          UpperCamelCase__      :       Dict	    =  path[-1]
          if node not in explored:
               UpperCamelCase__      :       Tuple	    =  graph[node]
               # go through all neighbour nodes, construct a new path and
               # push it into the queue
               for neighbour in neighbours:
                    UpperCamelCase__      :       List[str]	    =  list(__lowerCAmelCase      )
                    new_path.append(__lowerCAmelCase      )
                    queue.append(__lowerCAmelCase      )
                    # return path if neighbour is goal
                    if neighbour == goal:
                         return new_path

            # mark node as explored
               explored.add(__lowerCAmelCase      )

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







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )			->     int:
     if not graph or start not in graph or target not in graph:
          return -1
     if start == target:
          return 0
     UpperCamelCase__      :       Tuple	    =  [start]
     UpperCamelCase__      :       Optional[int]	    =  set(__lowerCAmelCase      )
     # Keep tab on distances from `start` node.
     UpperCamelCase__      :       str	    =  {start: 0, target: -1}
     while queue:
          UpperCamelCase__      :       Any	    =  queue.pop(0      )
          if node == target:
               UpperCamelCase__      :       Union[str, Any]	    =  (
                   dist[node] if dist[target] == -1 else min(dist[target] ,   dist[node]      )
               )
          for adjacent in graph[node]:
               if adjacent not in visited:
                    visited.add(__lowerCAmelCase      )
                    queue.append(__lowerCAmelCase      )
                    UpperCamelCase__      :       List[Any]	    =  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







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase      )			->     int:
     assert isinstance(__lowerCAmelCase ,   __lowerCAmelCase      ), f'The input value of [n={number}] is not an integer'

     if number == 1:
          return 2
     elif number < 1:
          UpperCamelCase__      :       List[Any]	    =  f'The input value of [n={number}] has to be > 0'
          raise ValueError(__lowerCAmelCase      )
     else:
          UpperCamelCase__      :       Optional[Any]	    =  sylvester(number - 1      )
          UpperCamelCase__      :       str	    =  num - 1
          UpperCamelCase__      :       int	    =  num
          return lower * upper + 1


if __name__ == "__main__":
 print(F"""The 8th number in Sylvester's sequence: {sylvester(8)}""")