






"""simple docstring"""






from math import sqrt






def   snake_case__     (	__lowerCamelCase       :					int			):
			"""simple docstring"""

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






def   snake_case__     (	__lowerCamelCase       :					int = 10001			):
			"""simple docstring"""
			lowerCamelCase__	:	Optional[Any]				=0
			lowerCamelCase__	:	Any				=1
			while count != nth and number < 3:
						number += 1
						if is_prime(__lowerCamelCase			):
									count += 1
			while count != nth:
						number += 2
						if is_prime(__lowerCamelCase			):
									count += 1
			return number


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









"""simple docstring"""






def   snake_case__     (	__lowerCamelCase       :					list[int]			):
			"""simple docstring"""
			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__	:	Any				=numbers[0]

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

						# update the maximum product found till now
						lowerCamelCase__	:	Tuple				=max(__lowerCamelCase							,	__lowerCamelCase			)

			return max_prod




