

def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__	, lowerCamelCase__			)  ->     int:
	while b:
		__lowerCamelCase       , __lowerCamelCase				:				Any					       = b, a % b
	return a






def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__	, lowerCamelCase__			)  ->     int:
	return a if b == 0 else euclidean_gcd_recursive(lowerCamelCase__	, a % b			)






def    SCREAMING_SNAKE_CASE__       (  )  ->     str:
	print(F"euclidean_gcd(3, 5) = {euclidean_gcd(3	, 5			)}"			)
	print(F"euclidean_gcd(5, 3) = {euclidean_gcd(5	, 3			)}"			)
	print(F"euclidean_gcd(1, 3) = {euclidean_gcd(1	, 3			)}"			)
	print(F"euclidean_gcd(3, 6) = {euclidean_gcd(3	, 6			)}"			)
	print(F"euclidean_gcd(6, 3) = {euclidean_gcd(6	, 3			)}"			)

	print(F"euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3	, 5			)}"			)
	print(F"euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5	, 3			)}"			)
	print(F"euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1	, 3			)}"			)
	print(F"euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3	, 6			)}"			)
	print(F"euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6	, 3			)}"			)


if __name__ == "__main__":
					main()






"""simple docstring"""





from math import isqrt, loga



def 						_lowerCAmelCase				(				UpperCamelCase_				):
		__SCREAMING_SNAKE_CASE            = [True] * max_number
		for i in range(2  ,				isqrt(max_number - 1				) + 1				):
				if is_prime[i]:
						for j in range(i**2  ,				UpperCamelCase_  ,				UpperCamelCase_				):
								__SCREAMING_SNAKE_CASE            = False

		return [i for i in range(2  ,				UpperCamelCase_				) if is_prime[i]]



def 						_lowerCAmelCase				(				UpperCamelCase_ = 80_0800  ,				UpperCamelCase_ = 80_0800				):
		__SCREAMING_SNAKE_CASE            = degree * loga(UpperCamelCase_				)
		__SCREAMING_SNAKE_CASE            = int(UpperCamelCase_				)
		__SCREAMING_SNAKE_CASE            = calculate_prime_numbers(UpperCamelCase_				)

		__SCREAMING_SNAKE_CASE            = 0
		__SCREAMING_SNAKE_CASE            = 0
		__SCREAMING_SNAKE_CASE            = len(UpperCamelCase_				) - 1
		while left < right:
				while (
				    prime_numbers[right] * loga(prime_numbers[left]				)
				    + prime_numbers[left] * loga(prime_numbers[right]				)
				    > upper_bound
				):
						right -= 1
				hybrid_integers_count += right - left
				left += 1

		return hybrid_integers_count


if __name__ == "__main__":
							print(F"""{solution() = }""")




