




def  a_		(							__snake_case					)	->			list:

			'''simple docstring'''


			UpperCamelCase_     				= [True for i in range(n + 1					)]
			UpperCamelCase_     				= [i - 1 for i in range(n + 1					)]
			UpperCamelCase_     				= []
			for i in range(2     ,		n + 1					):
						if is_prime[i]:
									primes.append(__snake_case					)
						for j in range(0     ,		len(__snake_case					)					):
									if i * primes[j] >= n:
												break
									UpperCamelCase_     				= False

									if i % primes[j] == 0:
												UpperCamelCase_     				= totients[i] * primes[j]
												break

									UpperCamelCase_     				= totients[i] * (primes[j] - 1)

			return totients


if __name__ == "__main__":
				import doctest

				doctest.testmod()






import numpy as np




def  a_		(							__snake_case     ,		__snake_case					)	->			List[str]:

			'''simple docstring'''


			UpperCamelCase_     				= np.array(__snake_case					)
			UpperCamelCase_     				= np.array(__snake_case					)

			UpperCamelCase_     				= abs(predict - actual					)
			UpperCamelCase_     				= difference.mean()

			return score




def  a_		(							__snake_case     ,		__snake_case					)	->			Optional[Any]:

			'''simple docstring'''


			UpperCamelCase_     				= np.array(__snake_case					)
			UpperCamelCase_     				= np.array(__snake_case					)

			UpperCamelCase_     				= predict - actual
			UpperCamelCase_     				= np.square(__snake_case					)

			UpperCamelCase_     				= square_diff.mean()
			return score




def  a_		(							__snake_case     ,		__snake_case					)	->			Optional[Any]:

			'''simple docstring'''


			UpperCamelCase_     				= np.array(__snake_case					)
			UpperCamelCase_     				= np.array(__snake_case					)

			UpperCamelCase_     				= predict - actual
			UpperCamelCase_     				= np.square(__snake_case					)
			UpperCamelCase_     				= square_diff.mean()
			UpperCamelCase_     				= np.sqrt(__snake_case					)
			return score




def  a_		(							__snake_case     ,		__snake_case					)	->			Optional[int]:

			'''simple docstring'''


			UpperCamelCase_     				= np.array(__snake_case					)
			UpperCamelCase_     				= np.array(__snake_case					)

			UpperCamelCase_     				= np.log(predict + 1					)
			UpperCamelCase_     				= np.log(actual + 1					)

			UpperCamelCase_     				= log_predict - log_actual
			UpperCamelCase_     				= np.square(__snake_case					)
			UpperCamelCase_     				= square_diff.mean()

			UpperCamelCase_     				= np.sqrt(__snake_case					)

			return score




def  a_		(							__snake_case     ,		__snake_case					)	->			int:

			'''simple docstring'''


			UpperCamelCase_     				= np.array(__snake_case					)
			UpperCamelCase_     				= np.array(__snake_case					)

			UpperCamelCase_     				= predict - actual
			UpperCamelCase_     				= np.sum(__snake_case					) / len(__snake_case					)
			UpperCamelCase_     				= np.sum(__snake_case					) / len(__snake_case					)
			# print(numerator, denumerator)
			UpperCamelCase_     				= float(__snake_case					) / denumerator * 1_0_0

			return score





def  a_		(							__snake_case     ,		__snake_case					)	->			Optional[Any]:

			'''simple docstring'''


			return np.mean(np.array(__snake_case					) == np.array(__snake_case					)					)
