



import itertools
import math






def 					__lowerCAmelCase		(  __lowerCamelCase	:    int	)  ->						bool:

					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(__lowerCamelCase	) + 1	)				,   6	):
										if number % i == 0 or number % (i + 2) == 0:
															return False
					return True






def 					__lowerCAmelCase		(  )  ->						Union[str, Any]:
					__lowerCAmelCase	   =2
					while True:
										if is_prime(__lowerCamelCase	):
															yield num
										num += 1






def 					__lowerCAmelCase		(  __lowerCamelCase	:    int = 10001	)  ->						int:
					return next(itertools.islice(prime_generator()				,   nth - 1				,   __lowerCamelCase	)	)


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









def 					__lowerCAmelCase		(  __lowerCamelCase	:    list[int]	)  ->						int:
					if not numbers:
										return 0

					if not isinstance(__lowerCamelCase				,   (list, tuple)	) or not all(
					    isinstance(__lowerCamelCase				,   __lowerCamelCase	) for number in numbers	):
										raise ValueError("""numbers must be an iterable of integers"""	)

					__lowerCAmelCase	   =__lowerCAmelCase	   =__lowerCAmelCase	   =numbers[0]

					for i in range(1				,   len(__lowerCamelCase	)	):
										# update the maximum and minimum subarray products
										__lowerCAmelCase	   =numbers[i]
										if number < 0:
															__lowerCAmelCase   ,	__lowerCAmelCase	   =min_till_now, max_till_now
										__lowerCAmelCase	   =max(__lowerCamelCase				,   max_till_now * number	)
										__lowerCAmelCase	   =min(__lowerCamelCase				,   min_till_now * number	)

										# update the maximum product found till now
										__lowerCAmelCase	   =max(__lowerCamelCase				,   __lowerCamelCase	)

					return max_prod




