



from __future__ import annotations

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


lowercase_													=      [num for num in range(3, 10_00_01, 2) if not is_prime(num)]






def        __lowerCAmelCase		(	__lowerCamelCase						:     int						)	->    list[int]:
					if not isinstance(lowerCAmelCase__					, lowerCAmelCase__						):
										raise ValueError("""n must be an integer"""						)
					if n <= 0:
										raise ValueError("""n must be >= 0"""						)

					__lowerCAmelCase						 =[]
					for num in range(len(lowerCAmelCase__						)						):
										__lowerCAmelCase						 =0
										while 2 * i * i <= odd_composites[num]:
															__lowerCAmelCase						 =odd_composites[num] - 2 * i * i
															if is_prime(lowerCAmelCase__						):
																				break
															i += 1
										else:
															list_nums.append(odd_composites[num]						)
															if len(lowerCAmelCase__						) == n:
																				return list_nums

					return []






def        __lowerCAmelCase		(	)	->    int:
					return compute_nums(1						)[0]


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











"""simple docstring"""






from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors






def      lowercase__ (					lowerCAmelCase__   :			int			)    ->			int:



			'''simple docstring'''
			a__  :	Tuple		 =			prime_factors(lowerCAmelCase__			)
			if is_square_free(lowerCAmelCase__			):
						return -1 if len(lowerCAmelCase__			) % 2 else 1
			return 0


if __name__ == "__main__":
		import doctest

		doctest.testmod()