
from math import exp





def 							_lowerCamelCase			(					lowerCamelCase_:  float		):



				'''simple docstring'''







				return 8 * x - 2 * exp(-x		)





def 							_lowerCamelCase			(					lowerCamelCase_:  float				,	lowerCamelCase_:  float				,	lowerCamelCase_:  int		):



				'''simple docstring'''







				A     :  Optional[int]   =				lower_bound
				A     :  Tuple   =				upper_bound
				for _ in range(0				,	lowerCamelCase_		):
								A ,       A     :  Optional[int]   =				xa, xa - (f(lowerCamelCase_		) * (xa - xa)) / (f(lowerCamelCase_		) - f(lowerCamelCase_		))
				return xa


if __name__ == "__main__":
					print(F'''Example: {secant_method(1, 3, 2)}''')

UpperCamelCase_  =	{
    "0": 1,
    "1": 1,
    "2": 2,
    "3": 6,
    "4": 24,
    "5": 1_20,
    "6": 7_20,
    "7": 50_40,
    "8": 4_03_20,
    "9": 36_28_80,
}

UpperCamelCase_  =	{1_45: 1_45}

UpperCamelCase_  =	{
    1_45: 0,
    1_69: 3,
    3_63_01: 3,
    14_54: 3,
    8_71: 2,
    4_53_61: 2,
    8_72: 2,
}





def 							_lowerCamelCase			(					lowerCamelCase_:  int		):



				'''simple docstring'''







				if n in CACHE_SUM_DIGIT_FACTORIALS:
								return CACHE_SUM_DIGIT_FACTORIALS[n]
				A     :  Tuple   =				sum(DIGIT_FACTORIALS[let] for let in str(lowerCamelCase_		)		)
				A     :  Dict   =				ret
				return ret





def 							_lowerCamelCase			(					lowerCamelCase_:  int				,	lowerCamelCase_:  set | None = None		):



				'''simple docstring'''







				A     :  Optional[int]   =				previous or set()
				if n in CHAIN_LENGTH_CACHE:
								return CHAIN_LENGTH_CACHE[n]
				A     :  Dict   =				sum_digit_factorials(lowerCamelCase_		)
				if next_number in previous:
								A     :  Optional[int]   =				0
								return 0
				else:
								previous.add(lowerCamelCase_		)
								A     :  str   =				1 + chain_length(lowerCamelCase_				,	lowerCamelCase_		)
								A     :  Any   =				ret
								return ret





def 							_lowerCamelCase			(					lowerCamelCase_:  int = 60				,	lowerCamelCase_:  int = 100_0000		):



				'''simple docstring'''







				return sum(1 for i in range(1				,	lowerCamelCase_		) if chain_length(lowerCamelCase_		) == num_terms		)


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