


_lowerCAmelCase:	str      							=					{
    '0': 1,
    '1': 1,
    '2': 2,
    '3': 6,
    '4': 24,
    '5': 120,
    '6': 720,
    '7': 5_040,
    '8': 40_320,
    '9': 362_880,
}

_lowerCAmelCase:	List[Any]      							=					{145: 145}

_lowerCAmelCase:	List[Any]      							=					{
    145: 0,
    169: 3,
    36_301: 3,
    1_454: 3,
    871: 2,
    45_361: 2,
    872: 2,
}






def      _lowercase(				__a							:	int    ):
							if n in CACHE_SUM_DIGIT_FACTORIALS:
														return CACHE_SUM_DIGIT_FACTORIALS[n]
							a__     						=sum(DIGIT_FACTORIALS[let] for let in str(__a    )    )
							a__     						=ret
							return ret






def      _lowercase(				__a							:	int						,    __a							:	set | None = None    ):
							a__     						=previous or set()
							if n in CHAIN_LENGTH_CACHE:
														return CHAIN_LENGTH_CACHE[n]
							a__     						=sum_digit_factorials(__a    )
							if next_number in previous:
														a__     						=0
														return 0
							else:
														previous.add(__a    )
														a__     						=1 + chain_length(__a						,    __a    )
														a__     						=ret
														return ret






def      _lowercase(				__a							:	int = 60						,    __a							:	int = 100_0000    ):
							return sum(1 for i in range(1						,    __a    ) if chain_length(__a    ) == num_terms    )


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





_lowerCAmelCase:	List[str]      							=					[0.33, 0.44, 0.55, 0.44, 0.33]
_lowerCAmelCase:	Union[str, Any]      							=					3
_lowerCAmelCase:	Dict      							=					5

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

# Machine Time
_lowerCAmelCase:	Optional[Any]      							=					0






def      _lowercase(				__a							:	Optional[Any]    ):
							global buffer_space, params_space, machine_time, K, m, t

							# Choosing Dynamical Systems (All)
							for key, value in enumerate(__a    ):
														# Evolution Parameter
														a__     						=float(seed / value    )

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

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

														# Modification (Transition Function) - Jumps
														a__     						=round(float(r * value * (1 - value)    )						,    10    )
														a__     						=r  # Saving to Parameters Space

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

							# Machine Time
							machine_time += 1






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

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

							# Choosing Dynamical Systems (Increment)
							a__     						=machine_time % m

							# Evolution (Time Length)
							for _ in range(0						,    __a    ):
														# Variables (Position + Parameters)
														a__     						=params_space[key]
														a__     						=buffer_space[key]

														# Modification (Transition Function) - Flow
														a__     						=round(float(r * value * (1 - value)    )						,    10    )
														a__     						=(machine_time * 0.01 + r * 1.01) % 1 + 3

							# Choosing Chaotic Data
							a__     						=int(buffer_space[(key + 2) % m] * (10**10)    )
							a__     						=int(buffer_space[(key - 2) % m] * (10**10)    )

							# Machine Time
							machine_time += 1

							return xorshift(__a						,    __a    ) % 0Xffff_ffff






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

							a__     						=K
							a__     						=[0] * m
							a__     						=0


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

	# Pushing Data (Input)
	import random

	_lowerCAmelCase:	int      							=					random.sample(range(0xff_fff_fff), 100)
	for chunk in message:
		push(chunk)

	# for controlling
	_lowerCAmelCase:	List[Any]      							=					''

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

