





class        snake_case_    :  # Public class to implement a graph






  def __init__(							self			:					int       ,  _snake_case			:					int       ,  _snake_case			:					int       ,  _snake_case			:					list[list[bool]]      )->None:






   '''simple docstring'''

   __lowerCAmelCase					:	Optional[int]      =       row
   __lowerCAmelCase					:	Optional[Any]      =       col
   __lowerCAmelCase					:	Dict      =       graph






  def 				UpperCAmelCase__						(							self			:					int       ,  _snake_case			:					int       ,  _snake_case			:					int       ,  _snake_case			:					list[list[bool]]      )->bool:






   '''simple docstring'''

   return (
       0 <= i < self.ROW
       and 0 <= j < self.COL
       and not visited[i][j]
       and self.graph[i][j]
   )






  def 				UpperCAmelCase__						(							self			:					int       ,  _snake_case			:					int       ,  _snake_case			:					int       ,  _snake_case			:					list[list[bool]]      )->None:






   '''simple docstring'''

   __lowerCAmelCase					:	str      =       [-1, -1, -1, 0, 0, 1, 1, 1]  # Coordinate order
   __lowerCAmelCase					:	List[str]      =       [-1, 0, 1, -1, 1, -1, 0, 1]
   __lowerCAmelCase					:	Union[str, Any]      =       True  # Make those cells visited
   for k in range(8      ):
    if self.is_safe(i + row_nbr[k]       ,  j + col_nbr[k]       ,  _snake_case      ):
     self.diffs(i + row_nbr[k]       ,  j + col_nbr[k]       ,  _snake_case      )






  def 				UpperCAmelCase__						(							self			:					Optional[int]      )->int:  # And finally, count all islands.






   '''simple docstring'''

   __lowerCAmelCase					:	Tuple      =       [[False for j in range(self.COL      )] for i in range(self.ROW      )]
   __lowerCAmelCase					:	Tuple      =       0
   for i in range(self.ROW      ):
    for j in range(self.COL      ):
     if visited[i][j] is False and self.graph[i][j] == 1:
      self.diffs(_snake_case       ,  _snake_case       ,  _snake_case      )
      count += 1
   return count






def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:int   ,   SCREAMING_SNAKE_CASE		:list   )      ->   Dict:
 _enforce_args(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )
 if n == 0:
  return 0
 __lowerCAmelCase					:	Union[str, Any]      =       float("""-inf"""   )
 for i in range(1   ,   n + 1   ):
  __lowerCAmelCase					:	Union[str, Any]      =       max(
      SCREAMING_SNAKE_CASE   ,   prices[i - 1] + naive_cut_rod_recursive(n - i   ,   SCREAMING_SNAKE_CASE   )   )

 return max_revue






def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:int   ,   SCREAMING_SNAKE_CASE		:list   )      ->   List[str]:
 _enforce_args(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )
 __lowerCAmelCase					:	List[str]      =       [float("""-inf"""   ) for _ in range(n + 1   )]
 return _top_down_cut_rod_recursive(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )






def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:int   ,   SCREAMING_SNAKE_CASE		:list   ,   SCREAMING_SNAKE_CASE		:list   )      ->   List[str]:
 if max_rev[n] >= 0:
  return max_rev[n]
 elif n == 0:
  return 0
 else:
  __lowerCAmelCase					:	str      =       float("""-inf"""   )
  for i in range(1   ,   n + 1   ):
   __lowerCAmelCase					:	List[Any]      =       max(
       SCREAMING_SNAKE_CASE   ,   prices[i - 1] + _top_down_cut_rod_recursive(n - i   ,   SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )   ,   )

  __lowerCAmelCase					:	List[str]      =       max_revenue

 return max_rev[n]






def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:int   ,   SCREAMING_SNAKE_CASE		:list   )      ->   Union[str, Any]:
 _enforce_args(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )

 # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
 # length 0.
 __lowerCAmelCase					:	Optional[int]      =       [float("""-inf"""   ) for _ in range(n + 1   )]
 __lowerCAmelCase					:	List[str]      =       0

 for i in range(1   ,   n + 1   ):
  __lowerCAmelCase					:	Optional[Any]      =       max_rev[i]
  for j in range(1   ,   i + 1   ):
   __lowerCAmelCase					:	Optional[int]      =       max(SCREAMING_SNAKE_CASE   ,   prices[j - 1] + max_rev[i - j]   )

  __lowerCAmelCase					:	Optional[int]      =       max_revenue_i

 return max_rev[n]






def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:int   ,   SCREAMING_SNAKE_CASE		:list   )      ->   List[Any]:
 if n < 0:
  __lowerCAmelCase					:	Any      =       F'''n must be greater than or equal to 0. Got n = {n}'''
  raise ValueError(SCREAMING_SNAKE_CASE   )

 if n > len(SCREAMING_SNAKE_CASE   ):
  __lowerCAmelCase					:	Any      =       (
      """Each integral piece of rod must have a corresponding price. """
      F'''Got n = {n} but length of prices = {len(SCREAMING_SNAKE_CASE   )}'''
  )
  raise ValueError(SCREAMING_SNAKE_CASE   )






def 	_SCREAMING_SNAKE_CASE		(      )      ->   Optional[int]:
 __lowerCAmelCase					:	Tuple      =       [6, 10, 12, 15, 20, 23]
 __lowerCAmelCase					:	List[str]      =       len(SCREAMING_SNAKE_CASE   )

 # the best revenue comes from cutting the rod into 6 pieces, each
 # of length 1 resulting in a revenue of 6 * 6 = 36.
 __lowerCAmelCase					:	Union[str, Any]      =       36

 __lowerCAmelCase					:	Optional[int]      =       top_down_cut_rod(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )
 __lowerCAmelCase					:	List[str]      =       bottom_up_cut_rod(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )
 __lowerCAmelCase					:	int      =       naive_cut_rod_recursive(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   )

 assert expected_max_revenue == max_rev_top_down
 assert max_rev_top_down == max_rev_bottom_up
 assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
      main()