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

_A	  =					{145: 145}

_A	  =					{
    145: 0,
    169: 3,
    36_301: 3,
    1_454: 3,
    871: 2,
    45_361: 2,
    872: 2,
}




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




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




def 				lowerCamelCase__				(						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() = }''')





def 				lowerCamelCase__				(						a__  :  float	,      a__  :  float	,      a__  :  float     )		->	float:
       if mass < 0:
              raise ValueError("""The mass of the body cannot be negative"""     )
       if radius <= 0:
              raise ValueError("""The radius is always a positive non zero integer"""     )
       return (mass * (velocity) ** 2) / radius


if __name__ == "__main__":
      import doctest

      doctest.testmod(verbose=True)



