

"""simple docstring"""


def 			_lowercase       (     __lowerCAmelCase				)							->					Any:

      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"""				)

      SCREAMING_SNAKE_CASE__ :   int   		=						0
      SCREAMING_SNAKE_CASE__ :   Optional[int]   		=						str(snake_case__				)

      while len(snake_case__				) != 1:
            SCREAMING_SNAKE_CASE__ :   Dict   		=						[int(snake_case__				) for i in num_string]

            SCREAMING_SNAKE_CASE__ :   Tuple   		=						1
            for i in range(0	,       len(snake_case__				)				):
                  total *= numbers[i]

            SCREAMING_SNAKE_CASE__ :   Dict   		=						str(snake_case__				)

            steps += 1
      return steps




def 			_lowercase       (     __lowerCAmelCase				)							->					Optional[Any]:

      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"""				)

      SCREAMING_SNAKE_CASE__ :   Union[str, Any]   		=						0
      SCREAMING_SNAKE_CASE__ :   Optional[int]   		=						str(snake_case__				)

      while len(snake_case__				) != 1:
            SCREAMING_SNAKE_CASE__ :   Tuple   		=						[int(snake_case__				) for i in num_string]

            SCREAMING_SNAKE_CASE__ :   Optional[Any]   		=						0
            for i in range(0	,       len(snake_case__				)				):
                  total += numbers[i]

            SCREAMING_SNAKE_CASE__ :   List[str]   		=						str(snake_case__				)

            steps += 1
      return steps


if __name__ == "__main__":
  import doctest

  doctest.testmod()






from __future__ import annotations




def 							a		(				snake_case__:   list[list[int]]   ):


				'''simple docstring'''

				# preprocessing the first row
				for i in range(1		,  len(matrix[0]   )   ):
								matrix[0][i] += matrix[0][i - 1]

				# preprocessing the first column
				for i in range(1		,  len(snake_case__   )   ):
								matrix[i][0] += matrix[i - 1][0]

				# updating the path cost for current position
				for i in range(1		,  len(snake_case__   )   ):
								for j in range(1		,  len(matrix[0]   )   ):
												matrix[i][j] += min(matrix[i - 1][j]		,  matrix[i][j - 1]   )

				return matrix[-1][-1]


if __name__ == "__main__":
						import doctest

						doctest.testmod()




