



"""simple docstring"""




import math

def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int       ):





     '''simple docstring'''

     if number == 0:
          _UpperCAmelCase    :			Optional[int]              =					"Zero"
          return words
     else:
          _UpperCAmelCase    :			List[str]              =					math.logaa(SCREAMING_SNAKE_CASE__       )
          _UpperCAmelCase    :			Optional[Any]              =					digits + 1
          _UpperCAmelCase    :			Optional[int]              =					{}
          _UpperCAmelCase    :			List[Any]              =					""
          _UpperCAmelCase    :			List[Any]              =					"One"
          _UpperCAmelCase    :			Dict              =					"Two"
          _UpperCAmelCase    :			Dict              =					"Three"
          _UpperCAmelCase    :			List[str]              =					"Four"
          _UpperCAmelCase    :			int              =					"Five"
          _UpperCAmelCase    :			List[Any]              =					"Six"
          _UpperCAmelCase    :			Optional[int]              =					"Seven"
          _UpperCAmelCase    :			Optional[int]              =					"Eight"
          _UpperCAmelCase    :			Dict              =					"Nine"

          _UpperCAmelCase    :			Any              =					{}
          _UpperCAmelCase    :			Optional[int]              =					""
          _UpperCAmelCase    :			int              =					"Twenty"
          _UpperCAmelCase    :			List[Any]              =					"Thirty"
          _UpperCAmelCase    :			Optional[Any]              =					"Forty"
          _UpperCAmelCase    :			int              =					"Fifty"
          _UpperCAmelCase    :			Dict              =					"Sixty"
          _UpperCAmelCase    :			List[str]              =					"Seventy"
          _UpperCAmelCase    :			Optional[int]              =					"Eighty"
          _UpperCAmelCase    :			int              =					"Ninety"

          _UpperCAmelCase    :			int              =					{}
          _UpperCAmelCase    :			Dict              =					"Ten"
          _UpperCAmelCase    :			Optional[Any]              =					"Eleven"
          _UpperCAmelCase    :			Dict              =					"Twelve"
          _UpperCAmelCase    :			str              =					"Thirteen"
          _UpperCAmelCase    :			Tuple              =					"Fourteen"
          _UpperCAmelCase    :			Any              =					"Fifteen"
          _UpperCAmelCase    :			Union[str, Any]              =					"Sixteen"
          _UpperCAmelCase    :			str              =					"Seventeen"
          _UpperCAmelCase    :			int              =					"Eighteen"
          _UpperCAmelCase    :			Optional[Any]              =					"Nineteen"

          _UpperCAmelCase    :			int              =					{}
          _UpperCAmelCase    :			List[str]              =					"Hundred,"
          _UpperCAmelCase    :			Optional[int]              =					"Thousand,"
          _UpperCAmelCase    :			List[str]              =					"Lakh,"
          _UpperCAmelCase    :			List[Any]              =					"Crore,"

          _UpperCAmelCase    :			Any              =					number
          _UpperCAmelCase    :			Any              =					""
          _UpperCAmelCase    :			int              =					0
          _UpperCAmelCase    :			List[str]              =					int(SCREAMING_SNAKE_CASE__       )
          while counter < digits:
               _UpperCAmelCase    :			int              =					temp_num % 10
               if counter % 2 == 0:
                    _UpperCAmelCase    :			Optional[int]              =					""
                    if counter in placevalue and current != 0:
                         _UpperCAmelCase    :			Tuple              =					placevalue[counter]
                    if counter == 2:
                         _UpperCAmelCase    :			Any              =					singles[current] + addition + words
                    elif counter == 0:
                         if ((temp_num % 100) // 10) == 1:
                              _UpperCAmelCase    :			Optional[Any]              =					teens[current] + addition + words
                              _UpperCAmelCase    :			int              =					temp_num // 10
                              counter += 1
                         else:
                              _UpperCAmelCase    :			str              =					singles[current] + addition + words

                    else:
                         _UpperCAmelCase    :			Tuple              =					doubles[current] + addition + words

               else:
                    if counter == 1:
                         if current == 1:
                              _UpperCAmelCase    :			Dict              =					teens[number % 10] + words
                         else:
                              _UpperCAmelCase    :			Dict              =					""
                              if counter in placevalue:
                                   _UpperCAmelCase    :			Tuple              =					placevalue[counter]
                              _UpperCAmelCase    :			Dict              =					doubles[current] + addition + words
                    else:
                         _UpperCAmelCase    :			int              =					""
                         if counter in placevalue:
                              if current == 0 and ((temp_num % 100) // 10) == 0:
                                   _UpperCAmelCase    :			Tuple              =					""
                              else:
                                   _UpperCAmelCase    :			Optional[int]              =					placevalue[counter]
                         if ((temp_num % 100) // 10) == 1:
                              _UpperCAmelCase    :			Dict              =					teens[current] + addition + words
                              _UpperCAmelCase    :			List[str]              =					temp_num // 10
                              counter += 1
                         else:
                              _UpperCAmelCase    :			List[str]              =					singles[current] + addition + words
               counter += 1
               _UpperCAmelCase    :			Union[str, Any]              =					temp_num // 10
     return words


if __name__ == "__main__":
 import doctest

 doctest.testmod()





"""simple docstring"""




_lowerCAmelCase       :      str							=							{
    "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,
}

_lowerCAmelCase       :      Optional[int]							=							{1_45: 1_45}

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

def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int       )						->     int:





     '''simple docstring'''

     if n in CACHE_SUM_DIGIT_FACTORIALS:
          return CACHE_SUM_DIGIT_FACTORIALS[n]
     _UpperCAmelCase    :			Dict              =					sum(DIGIT_FACTORIALS[let] for let in str(SCREAMING_SNAKE_CASE__       )       )
     _UpperCAmelCase    :			Any              =					ret
     return ret

def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		set | None = None       )						->     int:





     '''simple docstring'''

     _UpperCAmelCase    :			Dict              =					previous or set()
     if n in CHAIN_LENGTH_CACHE:
          return CHAIN_LENGTH_CACHE[n]
     _UpperCAmelCase    :			Dict              =					sum_digit_factorials(SCREAMING_SNAKE_CASE__       )
     if next_number in previous:
          _UpperCAmelCase    :			List[str]              =					0
          return 0
     else:
          previous.add(SCREAMING_SNAKE_CASE__       )
          _UpperCAmelCase    :			str              =					1 + chain_length(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
          _UpperCAmelCase    :			str              =					ret
          return ret

def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int = 60		,						SCREAMING_SNAKE_CASE__			:		int = 1_000_000       )						->     int:





     '''simple docstring'''

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


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