def  UpperCAmelCase_  (      _UpperCAmelCase = 1_0_0_0_0_0_0    ):
						lowerCamelCase_:       Optional[Any]					     = [i - 1 for i in range(limit + 1    )]

						for i in range(2			,  limit + 1    ):
												if phi[i] == i - 1:
																		for j in range(2 * i			,  limit + 1			,  _UpperCAmelCase    ):
																								phi[j] -= phi[j] // i

						return sum(phi[2 : limit + 1]    )


if __name__ == "__main__":
			print(solution())






"""simple docstring"""






def      lowerCAmelCase__			(		__magic_name__      )						->int:

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

			__lowercase       =       0
			__lowercase       =       str(__magic_name__      )

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

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

						__lowercase       =       str(__magic_name__      )

						steps += 1
			return steps



def      lowerCAmelCase__			(		__magic_name__      )						->int:

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

			__lowercase       =       0
			__lowercase       =       str(__magic_name__      )

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

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

						__lowercase       =       str(__magic_name__      )

						steps += 1
			return steps


if __name__ == "__main__":
					import doctest

					doctest.testmod()





