
"""simple docstring"""






import math



def     lowerCAmelCase__ (		__magic_name__			)	->list:
			if n <= 0:
						raise ValueError("Only positive integers have prime factors"			)
			__lowercase						      =					[]
			while n % 2 == 0:
						pf.append(2			)
						__lowercase						      =					int(n / 2			)
			for i in range(3 ,      int(math.sqrt(__magic_name__			)			) + 1 ,      2			):
						while n % i == 0:
									pf.append(__magic_name__			)
									__lowercase						      =					int(n / i			)
			if n > 2:
						pf.append(__magic_name__			)
			return pf



def     lowerCAmelCase__ (		__magic_name__			)	->int:
			if n <= 0:
						raise ValueError("Only positive numbers are accepted"			)
			__lowercase						      =					1
			__lowercase						      =					1
			while n % 2 == 0:
						temp += 1
						__lowercase						      =					int(n / 2			)
			div *= temp
			for i in range(3 ,      int(math.sqrt(__magic_name__			)			) + 1 ,      2			):
						__lowercase						      =					1
						while n % i == 0:
									temp += 1
									__lowercase						      =					int(n / i			)
						div *= temp
			if n > 1:
						div *= 2
			return div



def     lowerCAmelCase__ (		__magic_name__			)	->int:
			if n <= 0:
						raise ValueError("Only positive numbers are accepted"			)
			__lowercase						      =					1
			__lowercase						      =					1
			while n % 2 == 0:
						temp += 1
						__lowercase						      =					int(n / 2			)
			if temp > 1:
						s *= (2**temp - 1) / (2 - 1)
			for i in range(3 ,      int(math.sqrt(__magic_name__			)			) + 1 ,      2			):
						__lowercase						      =					1
						while n % i == 0:
									temp += 1
									__lowercase						      =					int(n / i			)
						if temp > 1:
									s *= (i**temp - 1) / (i - 1)
			return int(__magic_name__			)



def     lowerCAmelCase__ (		__magic_name__			)	->int:
			__lowercase						      =					n
			for x in set(prime_factors(__magic_name__			)			):
						s *= (x - 1) / x
			return int(__magic_name__			)


if __name__ == "__main__":
					import doctest

					doctest.testmod()







"""simple docstring"""






def     lowerCAmelCase__ (		__magic_name__ ,      __magic_name__			)	->list:
			__lowercase						      =					len(__magic_name__			)
			__lowercase						      =					len(__magic_name__			)
			__lowercase						      =					(
			    first_input_list_length
			    if first_input_list_length > second_input_list_length
			    else second_input_list_length
			)
			__lowercase						      =					[]
			for char_count in range(__magic_name__			):
						if char_count < first_input_list_length:
									output_result_list.append(first_input_list[char_count]			)
						if char_count < second_input_list_length:
									output_result_list.append(second_input_list[char_count]			)

			return output_result_list


if __name__ == "__main__":
					print(alternative_list_arrange(['''A''', '''B''', '''C'''], [1, 2, 3, 4, 5]), end=''' ''')





