def 	__A		(      _A       ):



 """simple docstring"""


 if not grid or not grid[0]:
  raise TypeError("The grid does not contain the appropriate information"       )

 for cell_n in range(1				,					len(grid[0]       )       ):
  grid[0][cell_n] += grid[0][cell_n - 1]
 __a							=	grid[0]

 for row_n in range(1				,					len(_A       )       ):
  __a							=	grid[row_n]
  __a							=	fill_row(_A				,					_A       )
  __a							=	grid[row_n]

 return grid[-1][-1]



def 	__A		(      _A				,					_A       ):



 """simple docstring"""


 current_row[0] += row_above[0]
 for cell_n in range(1				,					len(_A       )       ):
  current_row[cell_n] += min(current_row[cell_n - 1]				,					row_above[cell_n]       )

 return current_row


if __name__ == "__main__":
  import doctest

  doctest.testmod()










def   __lowercase       (			snake_case			):







				"""simple docstring"""






				if not isinstance(snake_case,	snake_case			):
								raise ValueError('''multiplicative_persistence() only accepts integral values'''			)
				if num < 0:
								raise ValueError('''multiplicative_persistence() does not accept negative values'''			)

				__magic_name__		:str   =   0
				__magic_name__		:Dict   =   str(snake_case			)

				while len(snake_case			) != 1:
								__magic_name__		:Optional[Any]   =   [int(snake_case			) for i in num_string]

								__magic_name__		:Dict   =   1
								for i in range(0,	len(snake_case			)			):
												total *= numbers[i]

								__magic_name__		:int   =   str(snake_case			)

								steps += 1
				return steps

def   __lowercase       (			snake_case			):







				"""simple docstring"""






				if not isinstance(snake_case,	snake_case			):
								raise ValueError('''additive_persistence() only accepts integral values'''			)
				if num < 0:
								raise ValueError('''additive_persistence() does not accept negative values'''			)

				__magic_name__		:str   =   0
				__magic_name__		:Union[str, Any]   =   str(snake_case			)

				while len(snake_case			) != 1:
								__magic_name__		:str   =   [int(snake_case			) for i in num_string]

								__magic_name__		:Optional[int]   =   0
								for i in range(0,	len(snake_case			)			):
												total += numbers[i]

								__magic_name__		:int   =   str(snake_case			)

								steps += 1
				return steps


if __name__ == "__main__":
					import doctest

					doctest.testmod()






