




'''simple docstring'''
from __future__ import annotations





def  lowerCamelCase(       SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )		->		list:
			A_       		=   [None] * (len(SCREAMING_SNAKE_CASE_    ) + len(SCREAMING_SNAKE_CASE_    ))

			A_       		=   0  # pointer to current index for left Half
			A_       		=   0  # pointer to current index for the right Half
			A_       		=   0  # pointer to current index for the sorted array Half

			while pointera < len(SCREAMING_SNAKE_CASE_    ) and pointera < len(SCREAMING_SNAKE_CASE_    ):
						if left_half[pointera] < right_half[pointera]:
									A_       		=   left_half[pointera]
									pointera += 1
									index += 1
						else:
									A_       		=   right_half[pointera]
									pointera += 1
									index += 1
			while pointera < len(SCREAMING_SNAKE_CASE_    ):
						A_       		=   left_half[pointera]
						pointera += 1
						index += 1

			while pointera < len(SCREAMING_SNAKE_CASE_    ):
						A_       		=   right_half[pointera]
						pointera += 1
						index += 1

			return sorted_array





def  lowerCamelCase(       SCREAMING_SNAKE_CASE_    )		->		list:
			if len(SCREAMING_SNAKE_CASE_    ) <= 1:
						return array
			# the actual formula to calculate the middle element = left + (right - left) // 2
			# this avoids integer overflow in case of large N
			A_       		=   0 + (len(SCREAMING_SNAKE_CASE_    ) - 0) // 2

			# Split the array into halves till the array length becomes equal to One
			# merge the arrays of single length returned by mergeSort function and
			# pass them into the merge arrays function which merges the array
			A_       		=   array[:middle]
			A_       		=   array[middle:]

			return merge(merge_sort(SCREAMING_SNAKE_CASE_    )					,merge_sort(SCREAMING_SNAKE_CASE_    )    )


if __name__ == "__main__":
							import doctest

							doctest.testmod()










'''simple docstring'''
def  lowerCamelCase(       SCREAMING_SNAKE_CASE_    )		->		list:
			A_       		=   [True for i in range(n + 1    )]
			A_       		=   [i - 1 for i in range(n + 1    )]
			A_       		=   []
			for i in range(2					,n + 1    ):
						if is_prime[i]:
									primes.append(SCREAMING_SNAKE_CASE_    )
						for j in range(0					,len(SCREAMING_SNAKE_CASE_    )    ):
									if i * primes[j] >= n:
												break
									A_       		=   False

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

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

			return totients


if __name__ == "__main__":
							import doctest

							doctest.testmod()




