






'''simple docstring'''







from __future__ import annotations

_A	:			Any         ={
    '''A''': ['''B''', '''C''', '''E'''],
    '''B''': ['''A''', '''D''', '''E'''],
    '''C''': ['''A''', '''F''', '''G'''],
    '''D''': ['''B'''],
    '''E''': ['''A''', '''B''', '''D'''],
    '''F''': ['''C'''],
    '''G''': ['''C'''],
}

class _lowercase	:




							def __init__(							self:				Tuple			,							UpperCamelCase__:				dict[str, list[str]]			,							UpperCamelCase__:				str     ):
														lowerCamelCase__					:	str         =       graph
														# mapping node to its parent in resulting breadth first tree
														lowerCamelCase__					:	dict[str, str | None]         =       {}
														lowerCamelCase__					:	Any         =       source_vertex




							def 		lowerCamelCase_				(							self:				List[str]     ):
														lowerCamelCase__					:	List[str]         =       {self.source_vertex}
														lowerCamelCase__					:	List[str]         =       None
														lowerCamelCase__					:	Tuple         =       [self.source_vertex]  # first in first out queue

														while queue:
																					lowerCamelCase__					:	Tuple         =       queue.pop(0     )
																					for adjacent_vertex in self.graph[vertex]:
																												if adjacent_vertex not in visited:
																																			visited.add(UpperCamelCase__     )
																																			lowerCamelCase__					:	List[str]         =       vertex
																																			queue.append(UpperCamelCase__     )




							def 		lowerCamelCase_				(							self:				str			,							UpperCamelCase__:				str     ):
														if target_vertex == self.source_vertex:
																					return self.source_vertex

														lowerCamelCase__					:	Tuple         =       self.parent.get(UpperCamelCase__     )
														if target_vertex_parent is None:
																					lowerCamelCase__					:	int         =       (
																					    F'''No path from vertex: {self.source_vertex} to vertex: {target_vertex}'''
																					)
																					raise ValueError(UpperCamelCase__     )

														return self.shortest_path(UpperCamelCase__     ) + F'''->{target_vertex}'''


if __name__ == "__main__":
			_A	:			int         =Graph(graph, '''G''')
			g.breath_first_search()
			print(g.shortest_path('''D'''))
			print(g.shortest_path('''G'''))
			print(g.shortest_path('''Foo'''))









'''simple docstring'''







def  SCREAMING_SNAKE_CASE_       (UpperCamelCase = 1000      )      ->       int:
							lowerCamelCase__					:	str         =       -1
							lowerCamelCase__					:	Dict         =       0
							for a in range(1				,			n // 3      ):
														# Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
														lowerCamelCase__					:	Dict         =       (n * n - 2 * a * n) // (2 * n - 2 * a)
														lowerCamelCase__					:	Any         =       n - a - b
														if c * c == (a * a + b * b):
																					lowerCamelCase__					:	Dict         =       a * b * c
																					if candidate >= product:
																												lowerCamelCase__					:	Union[str, Any]         =       candidate
							return product


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

