
import math
from collections.abc import Generator





def 							_lowerCamelCase			(					lowerCamelCase_:  int		):



				'''simple docstring'''







				A     :  Generator   =				(i for i in range(1				,	(max_n + 1)		))
				for i in (n for n in numbers if n > 1):
								for j in range(2				,	lowerCamelCase_		):
												if (i % j) == 0:
																break
								else:
												yield i





def 							_lowerCamelCase			(					lowerCamelCase_:  int		):



				'''simple docstring'''







				A     :  Generator   =				(i for i in range(1				,	(max_n + 1)		))
				for i in (n for n in numbers if n > 1):
								# only need to check for factors up to sqrt(i)
								A     :  Optional[int]   =				int(math.sqrt(lowerCamelCase_		)		) + 1
								for j in range(2				,	lowerCamelCase_		):
												if (i % j) == 0:
																break
								else:
												yield i





def 							_lowerCamelCase			(					lowerCamelCase_:  int		):



				'''simple docstring'''







				A     :  Generator   =				(i for i in range(1				,	(max_n + 1)				,	2		))
				# It's useless to test even numbers as they will not be prime
				if max_n > 2:
								yield 2  # Because 2 will not be tested, it's necessary to yield it now
				for i in (n for n in numbers if n > 1):
								A     :  List[str]   =				int(math.sqrt(lowerCamelCase_		)		) + 1
								for j in range(3				,	lowerCamelCase_				,	2		):
												# As we removed the even numbers, we don't need them now
												if (i % j) == 0:
																break
								else:
												yield i





def 							_lowerCamelCase			(					):



				'''simple docstring'''







				from timeit import timeit

				A     :  List[Any]   =				'''from __main__ import slow_primes, primes, fast_primes'''
				print(timeit('''slow_primes(1_000_000_000_000)'''				,	setup=lowerCamelCase_				,	number=100_0000		)		)
				print(timeit('''primes(1_000_000_000_000)'''				,	setup=lowerCamelCase_				,	number=100_0000		)		)
				print(timeit('''fast_primes(1_000_000_000_000)'''				,	setup=lowerCamelCase_				,	number=100_0000		)		)


if __name__ == "__main__":
					UpperCamelCase_  =	int(input("Calculate primes up to:\n>> ").strip())
					for ret in primes(number):
										print(ret)
					benchmark()

from __future__ import annotations





def 							_lowerCamelCase			(					lowerCamelCase_:  str				,	lowerCamelCase_:  dict[str, str]		):



				'''simple docstring'''







				A ,       A ,       A     :  str   =				'''''', '''''', ''''''
				A     :  Union[str, Any]   =				[]

				for character in message_part:
								tmp.append(character_to_number[character]		)

				for each in tmp:
								one += each[0]
								two += each[1]
								three += each[2]

				return one + two + three





def 							_lowerCamelCase			(					lowerCamelCase_:  str				,	lowerCamelCase_:  dict[str, str]		):



				'''simple docstring'''







				A ,       A     :  Tuple   =				'''''', ''''''
				A     :  str   =				[]

				for character in message_part:
								this_part += character_to_number[character]

				for digit in this_part:
								tmp += digit
								if len(lowerCamelCase_		) == len(lowerCamelCase_		):
												result.append(lowerCamelCase_		)
												A     :  Dict   =				''''''

				return result[0], result[1], result[2]





def 							_lowerCamelCase			(					lowerCamelCase_:  str				,	lowerCamelCase_:  str		):



				'''simple docstring'''







				A     :  Dict   =				alphabet.replace(''' '''				,	''''''		).upper()
				A     :  List[str]   =				message.replace(''' '''				,	''''''		).upper()

				# Check length and characters
				if len(lowerCamelCase_		) != 27:
								raise KeyError('''Length of alphabet has to be 27.'''		)
				for each in message:
								if each not in alphabet:
												raise ValueError('''Each message character has to be included in alphabet!'''		)

    # Generate dictionares
				A     :  str   =				(
				    '''111''',
				    '''112''',
				    '''113''',
				    '''121''',
				    '''122''',
				    '''123''',
				    '''131''',
				    '''132''',
				    '''133''',
				    '''211''',
				    '''212''',
				    '''213''',
				    '''221''',
				    '''222''',
				    '''223''',
				    '''231''',
				    '''232''',
				    '''233''',
				    '''311''',
				    '''312''',
				    '''313''',
				    '''321''',
				    '''322''',
				    '''323''',
				    '''331''',
				    '''332''',
				    '''333''',
				)
				A     :  Union[str, Any]   =				{}
				A     :  int   =				{}
				for letter, number in zip(lowerCamelCase_				,	lowerCamelCase_		):
								A     :  Optional[Any]   =				number
								A     :  Union[str, Any]   =				letter

				return message, alphabet, character_to_number, number_to_character





def 							_lowerCamelCase			(					lowerCamelCase_:  str				,	lowerCamelCase_:  str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."				,	lowerCamelCase_:  int = 5		):



				'''simple docstring'''







				A ,       A ,       A ,       A     :  Optional[int]   =				__prepare(
				    lowerCamelCase_				,	lowerCamelCase_		)
				A ,       A     :  int   =				'''''', ''''''

				for i in range(0				,	len(lowerCamelCase_		) + 1				,	lowerCamelCase_		):
								encrypted_numeric += __encrypt_part(
								    message[i : i + period]				,	lowerCamelCase_		)

				for i in range(0				,	len(lowerCamelCase_		)				,	3		):
								encrypted += number_to_character[encrypted_numeric[i : i + 3]]

				return encrypted





def 							_lowerCamelCase			(					lowerCamelCase_:  str				,	lowerCamelCase_:  str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."				,	lowerCamelCase_:  int = 5		):



				'''simple docstring'''







				A ,       A ,       A ,       A     :  Optional[int]   =				__prepare(
				    lowerCamelCase_				,	lowerCamelCase_		)
				A     :  Tuple   =				[]
				A     :  Optional[Any]   =				''''''

				for i in range(0				,	len(lowerCamelCase_		) + 1				,	lowerCamelCase_		):
								A ,       A ,       A     :  List[Any]   =				__decrypt_part(message[i : i + period]				,	lowerCamelCase_		)

								for j in range(0				,	len(lowerCamelCase_		)		):
												decrypted_numeric.append(a[j] + b[j] + c[j]		)

				for each in decrypted_numeric:
								decrypted += number_to_character[each]

				return decrypted


if __name__ == "__main__":
					UpperCamelCase_  =	"DEFEND THE EAST WALL OF THE CASTLE."
					UpperCamelCase_  =	encrypt_message(msg, "EPSDUCVWYM.ZLKXNBTFGORIJHAQ")
					UpperCamelCase_  =	decrypt_message(encrypted, "EPSDUCVWYM.ZLKXNBTFGORIJHAQ")
					print(F'''Encrypted: {encrypted}\nDecrypted: {decrypted}''')