


def 				SCREAMING_SNAKE_CASE (     UpperCAmelCase__							):

				"""simple docstring"""






				if not isinstance(UpperCAmelCase__   ,UpperCAmelCase__							):
								raise ValueError('double_factorial() only accepts integral values'							)
				if n < 0:
								raise ValueError('double_factorial() not defined for negative values'							)
				return 1 if n <= 1 else n * double_factorial(n - 2							)


if __name__ == "__main__":
							import doctest

							doctest.testmod()




from __future__ import annotations

from collections import Counter


def 				SCREAMING_SNAKE_CASE (     UpperCAmelCase__							):

				"""simple docstring"""






				_SCREAMING_SNAKE_CASE      = [True] * n
				_SCREAMING_SNAKE_CASE      = False
				_SCREAMING_SNAKE_CASE      = False
				_SCREAMING_SNAKE_CASE      = True

				for i in range(3   ,int(n**0.5 + 1							)   ,2							):
								_SCREAMING_SNAKE_CASE      = i * 2
								while index < n:
												_SCREAMING_SNAKE_CASE      = False
												_SCREAMING_SNAKE_CASE      = index + i

				_SCREAMING_SNAKE_CASE      = [2]

				for i in range(3   ,UpperCAmelCase__   ,2							):
								if is_prime[i]:
												primes.append(UpperCAmelCase__							)

				return primes


def 				SCREAMING_SNAKE_CASE (     UpperCAmelCase__							):

				"""simple docstring"""






				_SCREAMING_SNAKE_CASE      = str(UpperCAmelCase__							)
				_SCREAMING_SNAKE_CASE      = []
				_SCREAMING_SNAKE_CASE      = ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']

				for duplicate in Counter(UpperCAmelCase__							) - Counter(set(UpperCAmelCase__							)							):
								_SCREAMING_SNAKE_CASE      = [int(number_str.replace(UpperCAmelCase__   ,UpperCAmelCase__							)							) for digit in digits]
								replacements.append(UpperCAmelCase__							)

				return replacements


def 				SCREAMING_SNAKE_CASE (     UpperCAmelCase__ = 8							):

				"""simple docstring"""






				_SCREAMING_SNAKE_CASE      = set()

				# Filter primes with less than 3 replaceable digits
				_SCREAMING_SNAKE_CASE      = {
				    x for x in set(prime_sieve(100_0000							)							) if len(str(UpperCAmelCase__							)							) - len(set(str(UpperCAmelCase__							)							)							) >= 3
				}

				for prime in primes:
								if prime in numbers_checked:
												continue

								_SCREAMING_SNAKE_CASE      = digit_replacements(UpperCAmelCase__							)

								for family in replacements:
												numbers_checked.update(UpperCAmelCase__							)
												_SCREAMING_SNAKE_CASE      = primes.intersection(UpperCAmelCase__							)

												if len(UpperCAmelCase__							) != family_length:
																continue

												return min(UpperCAmelCase__							)

				return -1


if __name__ == "__main__":
							print(solution())
