




import numpy as np







def 		lowercase__ (		__A:						Optional[Any]					):





					'''simple docstring'''






					__magic_name__				:						Union[str, Any]     				=				np.exp(__A					)

					# Add up the all the exponentials
					__magic_name__				:						Optional[int]     				=				np.sum(__A					)

					# Divide every exponent by the sum of all exponents
					__magic_name__				:						str     				=				exponent_vector / sum_of_exponents

					return softmax_vector


if __name__ == "__main__":
	print(softmax((0,)))









import math
from collections.abc import Generator







def 		lowercase__ (		__A:						int					):





					'''simple docstring'''






					__magic_name__				:						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 		lowercase__ (		__A:						int					):





					'''simple docstring'''






					__magic_name__				:						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)
										__magic_name__				:						Tuple     				=				int(math.sqrt(__A					)					) + 1
										for j in range(2				,__A					):
															if (i % j) == 0:
																				break
										else:
															yield i







def 		lowercase__ (		__A:						int					):





					'''simple docstring'''






					__magic_name__				:						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):
										__magic_name__				:						str     				=				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 		lowercase__ (		):





					'''simple docstring'''






					from timeit import timeit

					__magic_name__				:						Dict     				=				'''from __main__ import slow_primes, primes, fast_primes'''
					print(timeit('''slow_primes(1_000_000_000_000)'''				,setup=__A				,number=1_0_0_0_0_0_0					)					)
					print(timeit('''primes(1_000_000_000_000)'''				,setup=__A				,number=1_0_0_0_0_0_0					)					)
					print(timeit('''fast_primes(1_000_000_000_000)'''				,setup=__A				,number=1_0_0_0_0_0_0					)					)


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



