


'''simple docstring'''




# Lint as: python3

import hashlib
from typing import Union

def       __UpperCamelCase     (     _A     :					Union[str, int, bytes]					)     ->   bytes:




	"""simple docstring"""





	if isinstance(_A       , _A					):
		# Data already in bytes, returns as it as
		return hash_data
	elif isinstance(_A       , _A					):
		# We keep the data as it as for it ot be later encoded to UTF-8
		# However replace `\\` with `/` for Windows compatibility
		lowerCAmelCase       :     int   				=			hash_data.replace('\\'       , '/'					)
	elif isinstance(_A       , _A					):
		lowerCAmelCase       :     Any   				=			str(_A					)
	else:
		# If data is not of the required type, raise error
		raise InvalidKeyError(_A					)

	return hash_data.encode('utf-8'					)



class 			lowerCAmelCase					(					a				):



	def __init__(       self			,       snake_case__     ):
		lowerCAmelCase       :     Tuple   				=			'\nFAILURE TO GENERATE DATASET: Invalid key type detected'
		lowerCAmelCase       :     Dict   				=			f"\nFound Key {hash_data} of type {type(snake_case__     )}"
		lowerCAmelCase       :     str   				=			'\nKeys should be either str, int or bytes type'
		super().__init__(f"{self.prefix}{self.err_msg}{self.suffix}"     )



class 			lowerCAmelCase					(					a				):



	def __init__(       self			,       snake_case__			,       snake_case__			,       snake_case__=""     ):
		lowerCAmelCase       :     Any   				=			key
		lowerCAmelCase       :     int   				=			duplicate_key_indices
		lowerCAmelCase       :     Dict   				=			fix_msg
		lowerCAmelCase       :     Union[str, Any]   				=			'Found multiple examples generated with the same key'
		if len(snake_case__     ) <= 20:
			lowerCAmelCase       :     Tuple   				=			f"\nThe examples at index {', '.join(snake_case__     )} have the key {key}"
		else:
			lowerCAmelCase       :     Optional[int]   				=			f"\nThe examples at index {', '.join(duplicate_key_indices[:20]     )}... ({len(snake_case__     ) - 20} more) have the key {key}"
		lowerCAmelCase       :     str   				=			'\n' + fix_msg if fix_msg else ''
		super().__init__(f"{self.prefix}{self.err_msg}{self.suffix}"     )



class 			lowerCAmelCase					:



	def __init__(       self			,       snake_case__     ):
		lowerCAmelCase       :     List[Any]   				=			hashlib.mda(_as_bytes(snake_case__     )     )



	def 					lowercase  (       self			,       snake_case__     ):
		lowerCAmelCase       :     Tuple   				=			self._split_mda.copy()
		lowerCAmelCase       :     Tuple   				=			_as_bytes(snake_case__     )
		mda.update(snake_case__     )
		# Convert to integer with hexadecimal conversion
		return int(mda.hexdigest()			,       16     )




'''simple docstring'''




import math
from collections.abc import Generator

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""simple docstring"""





	lowerCAmelCase       :     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       , _A					):
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""simple docstring"""





	lowerCAmelCase       :     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)
		lowerCAmelCase       :     List[str]   				=			int(math.sqrt(_A					)					) + 1
		for j in range(2       , _A					):
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""simple docstring"""





	lowerCAmelCase       :     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):
		lowerCAmelCase       :     int   				=			int(math.sqrt(_A					)					) + 1
		for j in range(3       , _A       , 2					):
			# As we removed the even numbers, we don't need them now
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     )     ->   Dict:




	"""simple docstring"""





	from timeit import timeit

	lowerCAmelCase       :     Tuple   				=			'from __main__ import slow_primes, primes, fast_primes'
	print(timeit('slow_primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)
	print(timeit('primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)
	print(timeit('fast_primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)


if __name__ == "__main__":
				_lowerCAmelCase	:		Optional[Any]		  =						int(input('Calculate primes up to:\n>> ').strip())
				for ret in primes(number):
								print(ret)
				benchmark()
