


def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE      )->						int:




      """simple docstring"""

      snake_case_ =   0
      while num > 0:
            digit_sum += num % 10
            num //= 10
      return digit_sum






def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE = 100      )->						int:




      """simple docstring"""

      snake_case_ =   1
      snake_case_ =   2

      for i in range(2      ,      max_n + 1      ):
            snake_case_ =   pre_numerator
            snake_case_ =   2 * i // 3 if i % 3 == 0 else 1
            snake_case_ =   cur_numerator
            snake_case_ =   e_cont * pre_numerator + temp

      return sum_digits(SCREAMING_SNAKE_CASE      )


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



import copy
import re







class lowerCAmelCase_		:

 '''simple docstring'''

 __snake_case				=						"hp"
 __snake_case				=						{}
 __snake_case				=						None



 @classmethod
 def 		UpperCamelCase__  (			cls	,   _UpperCAmelCase	,   _UpperCAmelCase      ):
       snake_case_ =   prefix
       snake_case_ =   defaults
       cls.build_naming_info()



 @staticmethod
 def 		UpperCamelCase__  (			_UpperCAmelCase	,   _UpperCAmelCase      ):
       if len(_UpperCAmelCase      ) == 0:
             return ""
       snake_case_ =   None
       if any(char.isdigit() for char in word      ):
             raise Exception(F'''Parameters should not contain numbers: \'{word}\' contains a number'''      )
       if word in info["short_word"]:
             return info["short_word"][word]
       for prefix_len in range(1	,   len(_UpperCAmelCase      ) + 1      ):
             snake_case_ =   word[:prefix_len]
             if prefix in info["reverse_short_word"]:
                   continue
             else:
                   snake_case_ =   prefix
                   break

       if short_word is None:
             # Paranoid fallback
             def int_to_alphabetic(_UpperCAmelCase      ):
                   snake_case_ =   ''''''
                   while integer != 0:
                         snake_case_ =   chr(ord('''A'''      ) + integer % 10      ) + s
                         integer //= 10
                   return s

             snake_case_ =   0
             while True:
                   snake_case_ =   word + '''#''' + int_to_alphabetic(_UpperCAmelCase      )
                   if sword in info["reverse_short_word"]:
                         continue
                   else:
                         snake_case_ =   sword
                         break

       snake_case_ =   short_word
       snake_case_ =   word
       return short_word



 @staticmethod
 def 		UpperCamelCase__  (			_UpperCAmelCase	,   _UpperCAmelCase      ):
       snake_case_ =   param_name.split('''_'''      )

       snake_case_ =   [TrialShortNamer.shortname_for_word(_UpperCAmelCase	,   _UpperCAmelCase      ) for word in words]

       # We try to create a separatorless short name, but if there is a collision we have to fallback
       # to a separated short name
       snake_case_ =   ['''''', '''_''']

       for separator in separators:
             snake_case_ =   separator.join(_UpperCAmelCase      )
             if shortname not in info["reverse_short_param"]:
                   snake_case_ =   shortname
                   snake_case_ =   param_name
                   return shortname

       return param_name



 @staticmethod
 def 		UpperCamelCase__  (			_UpperCAmelCase	,   _UpperCAmelCase      ):
       snake_case_ =   TrialShortNamer.shortname_for_key(_UpperCAmelCase	,   _UpperCAmelCase      )
       snake_case_ =   short_name
       snake_case_ =   param_name



 @classmethod
 def 		UpperCamelCase__  (			cls      ):
       if cls.NAMING_INFO is not None:
             return

       snake_case_ =   {
           '''short_word''': {},
           '''reverse_short_word''': {},
           '''short_param''': {},
           '''reverse_short_param''': {},
       }

       snake_case_ =   list(cls.DEFAULTS.keys()      )

       for k in field_keys:
             cls.add_new_param_name(_UpperCAmelCase	,   _UpperCAmelCase      )

       snake_case_ =   info



 @classmethod
 def 		UpperCamelCase__  (			cls	,   _UpperCAmelCase      ):
       cls.build_naming_info()
       assert cls.PREFIX is not None
       snake_case_ =   [copy.copy(cls.PREFIX      )]

       for k, v in params.items():
             if k not in cls.DEFAULTS:
                   raise Exception(F'''You should provide a default value for the param name {k} with value {v}'''      )
             if v == cls.DEFAULTS[k]:
                   # The default value is not added to the name
                   continue

             snake_case_ =   cls.NAMING_INFO['''short_param'''][k]

             if isinstance(_UpperCAmelCase	,   _UpperCAmelCase      ):
                   snake_case_ =   1 if v else 0

             snake_case_ =   '''''' if isinstance(_UpperCAmelCase	,   (int, float)      ) else '''-'''
             snake_case_ =   F'''{key}{sep}{v}'''
             name.append(_UpperCAmelCase      )

       return "_".join(_UpperCAmelCase      )





 @classmethod
 def 		UpperCamelCase__  (			cls	,   _UpperCAmelCase      ):
       snake_case_ =   repr[len(cls.PREFIX      ) + 1 :]
       if repr == "":
             snake_case_ =   []
       else:
             snake_case_ =   repr.split('''_'''      )

       snake_case_ =   {}

       for value in values:
             if "-" in value:
                   snake_case_ ,					snake_case_ =   value.split('''-'''      )
             else:
                   snake_case_ =   re.sub('''[0-9.]'''	,   ''''''	,   _UpperCAmelCase      )
                   snake_case_ =   float(re.sub('''[^0-9.]'''	,   ''''''	,   _UpperCAmelCase      )      )

             snake_case_ =   cls.NAMING_INFO['''reverse_short_param'''][p_k]

             snake_case_ =   p_v

       for k in cls.DEFAULTS:
             if k not in parameters:
                   snake_case_ =   cls.DEFAULTS[k]

       return parameters