


from __future__ import annotations

from collections import Counter
def 							UpperCamelCase_  (				__snake_case			:						int     )->      list[int]:




						'''simple docstring'''
						__magic_name__ 		=			[True] * n
						__magic_name__ 		=			False
						__magic_name__ 		=			False
						__magic_name__ 		=			True

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

						__magic_name__ 		=			[2]

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

						return primes
def 							UpperCamelCase_  (				__snake_case			:						int     )->      list[list[int]]:




						'''simple docstring'''
						__magic_name__ 		=			str(__snake_case     )
						__magic_name__ 		=			[]
						__magic_name__ 		=			['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']

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

						return replacements
def 							UpperCamelCase_  (				__snake_case			:						int = 8     )->      int:




						'''simple docstring'''
						__magic_name__ 		=			set()

						# Filter primes with less than 3 replaceable digits
						__magic_name__ 		=			{
						    x for x in set(prime_sieve(1_00_00_00     )     ) if len(str(__snake_case     )     ) - len(set(str(__snake_case     )     )     ) >= 3
						}

						for prime in primes:
												if prime in numbers_checked:
																		continue

												__magic_name__ 		=			digit_replacements(__snake_case     )

												for family in replacements:
																		numbers_checked.update(__snake_case     )
																		__magic_name__ 		=			primes.intersection(__snake_case     )

																		if len(__snake_case     ) != family_length:
																								continue

																		return min(__snake_case     )

						return -1


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





def 							UpperCamelCase_  (				__snake_case			:						int     )->      bool:




						'''simple docstring'''
						if not isinstance(__snake_case	,			__snake_case     ):
												__magic_name__ 		=			F'''Input value of [number={number}] must be an integer'''
												raise TypeError(__snake_case     )
						if number < 0 or number % 2 == 1:
												return False
						__magic_name__ 		=			int(number**0.5     )
						return number == number_sqrt * (number_sqrt + 1)


if __name__ == "__main__":
					import doctest

					doctest.testmod()

