


import math
def      _a					( SCREAMING_SNAKE_CASE	):


		"""simple docstring"""




		return math.sqrt(SCREAMING_SNAKE_CASE	) * math.sqrt(SCREAMING_SNAKE_CASE	) == num
def      _a					( SCREAMING_SNAKE_CASE	):


		"""simple docstring"""




		lowercase__				= 0
		lowercase__				= n
		while left <= right:
				lowercase__				= (left + right) // 2
				if mid**2 == n:
						return True
				elif mid**2 > n:
						lowercase__				= mid - 1
				else:
						lowercase__				= mid + 1
		return False


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()






