





_UpperCAmelCase             =							{0: [2, 3], 1: [0], 2: [1], 3: [4], 4: []}

_UpperCAmelCase             =							{0: [1, 2, 3], 1: [2], 2: [0], 3: [4], 4: [5], 5: [3]}






def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:dict[int, list[int]]   ,   SCREAMING_SNAKE_CASE		:int   ,   SCREAMING_SNAKE_CASE		:list[bool]   )      ->   list[int]:
 __lowerCAmelCase					:	str      =       True
 __lowerCAmelCase					:	str      =       []

 for neighbour in graph[vert]:
  if not visited[neighbour]:
   order += topology_sort(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )

 order.append(SCREAMING_SNAKE_CASE   )

 return order






def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:dict[int, list[int]]   ,   SCREAMING_SNAKE_CASE		:int   ,   SCREAMING_SNAKE_CASE		:list[bool]   )      ->   list[int]:
 __lowerCAmelCase					:	Optional[Any]      =       True
 __lowerCAmelCase					:	Union[str, Any]      =       [vert]

 for neighbour in reversed_graph[vert]:
  if not visited[neighbour]:
   component += find_components(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )

 return component







def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:dict[int, list[int]]   )      ->   list[list[int]]:
 __lowerCAmelCase					:	Optional[Any]      =       len(SCREAMING_SNAKE_CASE   ) * [False]
 __lowerCAmelCase					:	dict[int, list[int]]      =       {vert: [] for vert in range(len(SCREAMING_SNAKE_CASE   )   )}

 for vert, neighbours in graph.items():
  for neighbour in neighbours:
   reversed_graph[neighbour].append(SCREAMING_SNAKE_CASE   )

 __lowerCAmelCase					:	Tuple      =       []
 for i, was_visited in enumerate(SCREAMING_SNAKE_CASE   ):
  if not was_visited:
   order += topology_sort(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )

 __lowerCAmelCase					:	Optional[Any]      =       []
 __lowerCAmelCase					:	Any      =       len(SCREAMING_SNAKE_CASE   ) * [False]

 for i in range(len(SCREAMING_SNAKE_CASE   )   ):
  __lowerCAmelCase					:	Optional[int]      =       order[len(SCREAMING_SNAKE_CASE   ) - i - 1]
  if not visited[vert]:
   __lowerCAmelCase					:	Any      =       find_components(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )
   components_list.append(SCREAMING_SNAKE_CASE   )

 return components_list






from __future__ import annotations






def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:list[list[int]]   )      ->   bool:
 __lowerCAmelCase					:	Tuple      =       len(SCREAMING_SNAKE_CASE   )
 # We need to create solution object to save path.
 __lowerCAmelCase					:	str      =       [[0 for _ in range(SCREAMING_SNAKE_CASE   )] for _ in range(SCREAMING_SNAKE_CASE   )]
 __lowerCAmelCase					:	str      =       run_maze(SCREAMING_SNAKE_CASE   ,   0   ,   0   ,   SCREAMING_SNAKE_CASE   )
 if solved:
  print("""\n""".join(str(SCREAMING_SNAKE_CASE   ) for row in solutions   )   )
 else:
  print("""No solution exists!"""   )
 return solved






def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:list[list[int]]   ,   SCREAMING_SNAKE_CASE		:int   ,   SCREAMING_SNAKE_CASE		:int   ,   SCREAMING_SNAKE_CASE		:list[list[int]]   )      ->   bool:
 __lowerCAmelCase					:	List[str]      =       len(SCREAMING_SNAKE_CASE   )
 # Final check point.
 if i == j == (size - 1):
  __lowerCAmelCase					:	str      =       1
  return True

 __lowerCAmelCase					:	Optional[Any]      =       (not i < 0) and (not j < 0)  # Check lower bounds
 __lowerCAmelCase					:	Optional[Any]      =       (i < size) and (j < size)  # Check upper bounds

 if lower_flag and upper_flag:
  # check for already visited and block points.
  __lowerCAmelCase					:	int      =       (not solutions[i][j]) and (not maze[i][j])
  if block_flag:
   # check visited
   __lowerCAmelCase					:	Tuple      =       1

   # check for directions
   if (
       run_maze(SCREAMING_SNAKE_CASE   ,   i + 1   ,   SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )
       or run_maze(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   ,   j + 1   ,   SCREAMING_SNAKE_CASE   )
       or run_maze(SCREAMING_SNAKE_CASE   ,   i - 1   ,   SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )
       or run_maze(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   ,   j - 1   ,   SCREAMING_SNAKE_CASE   )
   ):
    return True

   __lowerCAmelCase					:	Tuple      =       0
   return False
 return False


if __name__ == "__main__":
      import doctest

      doctest.testmod()