
def 							a		(				snake_case__:   int   ):


				'''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'''   )

				lowercase_	    =   0
				lowercase_	    =   str(snake_case__   )

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

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

								lowercase_	    =   str(snake_case__   )

								steps += 1
				return steps




def 							a		(				snake_case__:   int   ):


				'''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'''   )

				lowercase_	    =   0
				lowercase_	    =   str(snake_case__   )

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

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

								lowercase_	    =   str(snake_case__   )

								steps += 1
				return steps


if __name__ == "__main__":
						import doctest

						doctest.testmod()






from __future__ import annotations

from collections.abc import Iterator
from typing import Generic, TypeVar

__magic_name__  							=	TypeVar('''T''')




class        _SCREAMING_SNAKE_CASE	(   Generic[T]			):
      def __init__(      self		,						lowerCamelCase			):
          snake_case__    =					data
          snake_case__    =					None



      def __str__(      self			):
          return F"""{self.data}"""





class        _SCREAMING_SNAKE_CASE	(   Generic[T]			):
      def __init__(      self			):
          snake_case__    =					None
      def __iter__(      self			):
          snake_case__    =					self.top
          while node:
              yield node.data
              snake_case__    =					node.next
      def __str__(      self			):
          return "->".join([str(lowerCamelCase			) for item in self]			)
      def __len__(      self			):
          return len(tuple(iter(self			)			)			)
      def A_      (      self			):
          return self.top is None
      def A_      (      self		,						lowerCamelCase			):
          snake_case__    =					Node(lowerCamelCase			)
          if not self.is_empty():
              snake_case__    =					self.top
          snake_case__    =					node
      def A_      (      self			):
          if self.is_empty():
              raise IndexError("pop from empty stack"			)
          assert isinstance(self.top		,						lowerCamelCase			)
          snake_case__    =					self.top
          snake_case__    =					self.top.next
          return pop_node.data
      def A_      (      self			):
          if self.is_empty():
              raise IndexError("peek from empty stack"			)

          assert self.top is not None
          return self.top.data



      def A_      (      self			):
          snake_case__    =					None


if __name__ == "__main__":
     from doctest import testmod

     testmod()



