



"""simple docstring"""







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

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

# Machine Time
UpperCAmelCase:  Tuple			     =				0


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		global buffer_space, params_space, machine_time, K, m, t

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

				# Control Theory: Orbit Change
				_lowercase				: List[str]     =   (buffer_space[(key + 1) % m] + e) % 1

				# Control Theory: Trajectory Change
				_lowercase				: int     =   (params_space[key] + e) % 1 + 3

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

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

		# Machine Time
		machine_time += 1


def  __SCREAMING_SNAKE_CASE (  ):
		global buffer_space, params_space, machine_time, K, m, t

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

		# Choosing Dynamical Systems (Increment)
		_lowercase				: Optional[Any]     =   machine_time % m

		# Evolution (Time Length)
		for _ in range(0   ,				__UpperCAmelCase      ):
				# Variables (Position + Parameters)
				_lowercase				: str     =   params_space[key]
				_lowercase				: Optional[int]     =   buffer_space[key]

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

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

		# Machine Time
		machine_time += 1

		return xorshift(__UpperCAmelCase   ,				__UpperCAmelCase      ) % 0xff_fff_fff


def  __SCREAMING_SNAKE_CASE (  ):
		global buffer_space, params_space, machine_time, K, m, t

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


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

		# Pushing Data (Input)
		import random

		UpperCAmelCase:  Any			     =				random.sample(range(0xff_ff_ff_ff), 100)
		for chunk in message:
				push(chunk)

		# for controlling
		UpperCAmelCase:  Any			     =				""""""

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








import math







def       lowerCamelCase_  (    _a       :						int    ):



    '''simple docstring'''




    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5   ,		int(math.sqrt(_a    ) + 1    )   ,		6    ):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True







def       lowerCamelCase_  (    _a       :						int = 6008_5147_5143    ):



    '''simple docstring'''




    try:
        UpperCAmelCase_     :       str  		=					int(_a    )
    except (TypeError, ValueError):
        raise TypeError("""Parameter n must be int or castable to int."""    )
    if n <= 0:
        raise ValueError("""Parameter n must be greater than or equal to one."""    )
    UpperCAmelCase_     :       Optional[int]  		=					0
    if is_prime(_a    ):
        return n
    while n % 2 == 0:
        n //= 2
    if is_prime(_a    ):
        return n
    for i in range(3   ,		int(math.sqrt(_a    )    ) + 1   ,		2    ):
        if n % i == 0:
            if is_prime(n // i    ):
                UpperCAmelCase_     :       Optional[int]  		=					n // i
                break
            elif is_prime(_a    ):
                UpperCAmelCase_     :       str  		=					i
    return max_number


if __name__ == "__main__":
      print(F"{solution() = }")
