





"""simple docstring"""




def 					lowerCamelCase_						(    _UpperCamelCase			)		->						list:






				"""simple docstring"""


				snake_case_						:   List[Any]           =  [0] * len(UpperCAmelCase_			)

				for i in range(1			,    len(UpperCAmelCase_			)			):
								# use last results for better performance - dynamic programming
								snake_case_						:   Optional[int]           =  prefix_result[i - 1]
								while j > 0 and input_string[i] != input_string[j]:
												snake_case_						:   Any           =  prefix_result[j - 1]

								if input_string[i] == input_string[j]:
												j += 1
								snake_case_						:   List[str]           =  j

				return prefix_result






def 					lowerCamelCase_						(    _UpperCamelCase			)		->						int:






				"""simple docstring"""


				return max(prefix_function(UpperCAmelCase_			)			)


if __name__ == "__main__":
	import doctest

	doctest.testmod()







def 					lowerCamelCase_						(    _UpperCamelCase			)		->						int:






				"""simple docstring"""


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

				snake_case_						:   List[Any]           =  0
				snake_case_						:   Tuple           =  str(_UpperCamelCase			)

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

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

								snake_case_						:   str           =  str(_UpperCamelCase			)

								steps += 1
				return steps






def 					lowerCamelCase_						(    _UpperCamelCase			)		->						int:






				"""simple docstring"""


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

				snake_case_						:   Any           =  0
				snake_case_						:   Tuple           =  str(_UpperCamelCase			)

				while len(_UpperCamelCase			) != 1:
								snake_case_						:   List[str]           =  [int(_UpperCamelCase			) for i in num_string]

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

								snake_case_						:   Tuple           =  str(_UpperCamelCase			)

								steps += 1
				return steps


if __name__ == "__main__":
	import doctest

	doctest.testmod()
