from itertools import product





def 		__lowerCamelCase							(UpperCAmelCase__   :							int = 1_5     ):
					SCREAMING_SNAKE_CASE				=				0.0
					SCREAMING_SNAKE_CASE				=				42
					SCREAMING_SNAKE_CASE				=				42
					SCREAMING_SNAKE_CASE				=				42
					SCREAMING_SNAKE_CASE				=				42
					SCREAMING_SNAKE_CASE				=				42
					SCREAMING_SNAKE_CASE				=				42

					for series in product(range(2     )					,       repeat=UpperCAmelCase__     ):
										SCREAMING_SNAKE_CASE				=				series.count(1     )
										SCREAMING_SNAKE_CASE				=				num_turns - num_blue
										if num_red >= num_blue:
															continue
										SCREAMING_SNAKE_CASE				=				1.0
										for ind, col in enumerate(UpperCAmelCase__					,       2     ):
															if col == 0:
																				prob *= (ind - 1) / ind
															else:
																				prob *= 1 / ind

										total_prob += prob

					return int(1 / total_prob     )


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





import math





def 		__lowerCamelCase							(UpperCAmelCase__   :							int     ):

					if 1 < number < 4:
										# 2 and 3 are primes
										return True
					elif number < 2 or number % 2 == 0 or number % 3 == 0:
										# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
										return False

					# All primes number are in format of 6k +/- 1
					for i in range(5					,       int(math.sqrt(UpperCAmelCase__     ) + 1     )					,       6     ):
										if number % i == 0 or number % (i + 2) == 0:
															return False
					return True





def 		__lowerCamelCase							(UpperCAmelCase__   :							int = 2_0_0_0_0_0_0     ):
					return sum(num for num in range(3					,       UpperCAmelCase__					,       2     ) if is_prime(UpperCAmelCase__     )     ) + 2 if n > 2 else 0


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




