



'''simple docstring'''






A_				:					Optional[Any]							=      [0.33, 0.44, 0.55, 0.44, 0.33]
A_				:					str							=      3
A_				:					List[Any]							=      5

# Buffer Space (with Parameters Space)
A_				:					list[float]							=      []
A_				:					list[float]							=      []

# Machine Time
A_				:					str							=      0




def        snake_case_   (	lowerCAmelCase_						)->						List[str]:





       '''simple docstring'''


       global buffer_space, params_space, machine_time, K, m, t

       # Choosing Dynamical Systems (All)
       for key, value in enumerate(lowerCAmelCase_						):
              # Evolution Parameter
              _UpperCAmelCase    :		List[Any]     	=					float(seed / value						)

              # Control Theory: Orbit Change
              _UpperCAmelCase    :		Any     	=					(buffer_space[(key + 1) % m] + e) % 1

              # Control Theory: Trajectory Change
              _UpperCAmelCase    :		List[str]     	=					(params_space[key] + e) % 1 + 3

              # Modification (Transition Function) - Jumps
              _UpperCAmelCase    :		int     	=					round(float(r * value * (1 - value)						)			,  10						)
              _UpperCAmelCase    :		Union[str, Any]     	=					r  # Saving to Parameters Space

       # Logistic Map
       assert max(lowerCAmelCase_						) < 1
       assert max(lowerCAmelCase_						) < 4

       # Machine Time
       machine_time += 1




def        snake_case_   (	)->						str:





       '''simple docstring'''


       global buffer_space, params_space, machine_time, K, m, t

       # PRNG (Xorshift by George Marsaglia)
       def xorshift(lowerCAmelCase_			,  lowerCAmelCase_						):
              x ^= y >> 13
              y ^= x << 17
              x ^= y >> 5
              return x

       # Choosing Dynamical Systems (Increment)
       _UpperCAmelCase    :		int     	=					machine_time % m

       # Evolution (Time Length)
       for _ in range(0			,  lowerCAmelCase_						):
              # Variables (Position + Parameters)
              _UpperCAmelCase    :		Tuple     	=					params_space[key]
              _UpperCAmelCase    :		Optional[Any]     	=					buffer_space[key]

              # Modification (Transition Function) - Flow
              _UpperCAmelCase    :		Any     	=					round(float(r * value * (1 - value)						)			,  10						)
              _UpperCAmelCase    :		str     	=					(machine_time * 0.0_1 + r * 1.0_1) % 1 + 3

       # Choosing Chaotic Data
       _UpperCAmelCase    :		List[Any]     	=					int(buffer_space[(key + 2) % m] * (10**10)						)
       _UpperCAmelCase    :		Union[str, Any]     	=					int(buffer_space[(key - 2) % m] * (10**10)						)

       # Machine Time
       machine_time += 1

       return xorshift(lowerCAmelCase_			,  lowerCAmelCase_						) % 0xFF_FFF_FFF




def        snake_case_   (	)->						Union[str, Any]:





       '''simple docstring'''


       global buffer_space, params_space, machine_time, K, m, t

       _UpperCAmelCase    :		int     	=					K
       _UpperCAmelCase    :		List[Any]     	=					[0] * m
       _UpperCAmelCase    :		Optional[Any]     	=					0


if __name__ == "__main__":
   # Initialization
   reset()

   # Pushing Data (Input)
   import random

   A_				:					Dict							=      random.sample(range(0xffffffff), 1_0_0)
   for chunk in message:
      push(chunk)

   # for controlling
   A_				:					str							=      """"""

   # Pulling Data (Output)
   while inp in ("e", "E"):
      print(f"""{format(pull(), "#04x")}""")
      print(buffer_space)
      print(params_space)
      A_				:					Optional[Any]							=      input("""(e)exit? """).strip()








"""simple docstring"""







import math
from collections.abc import Generator


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_lowercase				: 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   ,				__UpperCAmelCase      ):
						if (i % j) == 0:
								break
				else:
						yield i


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_lowercase				: 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)
				_lowercase				: Union[str, Any]     =   int(math.sqrt(__UpperCAmelCase      )      ) + 1
				for j in range(2   ,				__UpperCAmelCase      ):
						if (i % j) == 0:
								break
				else:
						yield i


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


def  __SCREAMING_SNAKE_CASE (  ):
		from timeit import timeit

		_lowercase				: Tuple     =   """from __main__ import slow_primes, primes, fast_primes"""
		print(timeit("""slow_primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )
		print(timeit("""primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )
		print(timeit("""fast_primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )


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



