'''simple docstring'''


def    _lowerCamelCase       ( lowerCamelCase_   :				int      ,	lowerCamelCase_   :				int = 1000  ):



     """simple docstring"""





     if (not isinstance(lowerCamelCase_      ,	lowerCamelCase_  )) or (digit_position <= 0):
          raise ValueError('Digit position must be a positive integer'  )
     elif (not isinstance(lowerCamelCase_      ,	lowerCamelCase_  )) or (precision < 0):
          raise ValueError('Precision must be a nonnegative integer'  )

     # compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
     # accurate
     UpperCAmelCase_				:  Tuple  = (
         4 * _subsum(lowerCamelCase_      ,	1      ,	lowerCamelCase_  )
         - 2 * _subsum(lowerCamelCase_      ,	4      ,	lowerCamelCase_  )
         - _subsum(lowerCamelCase_      ,	5      ,	lowerCamelCase_  )
         - _subsum(lowerCamelCase_      ,	6      ,	lowerCamelCase_  )
     )

     # return the first hex digit of the fractional part of the result
     return hex(int((sum_result % 1) * 16  )  )[2:]


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



     """simple docstring"""





     UpperCAmelCase_				:  Tuple  = 0.0
     for sum_index in range(digit_pos_to_extract + precision  ):
          UpperCAmelCase_				:  List[str]  = 8 * sum_index + denominator_addend
          if sum_index < digit_pos_to_extract:
               # if the exponential term is an integer and we mod it by the denominator
               # before dividing, only the integer part of the sum will change;
               # the fractional part will not
               UpperCAmelCase_				:  Any  = pow(
                   16      ,	digit_pos_to_extract - 1 - sum_index      ,	lowerCamelCase_  )
          else:
               UpperCAmelCase_				:  Optional[int]  = pow(16      ,	digit_pos_to_extract - 1 - sum_index  )
          total += exponential_term / denominator
     return total


if __name__ == "__main__":
 import doctest

 doctest.testmod()












import math

def       lowerCAmelCase_      (	lowerCamelCase:							int    )       ->      str:


      '''simple docstring'''




      if number == 0:
            lowerCamelCase__   	=					'Zero'
            return words
      else:
            lowerCamelCase__   	=					math.logaa(lowerCamelCase    )
            lowerCamelCase__   	=					digits + 1
            lowerCamelCase__   	=					{}
            lowerCamelCase__   	=					''
            lowerCamelCase__   	=					'One'
            lowerCamelCase__   	=					'Two'
            lowerCamelCase__   	=					'Three'
            lowerCamelCase__   	=					'Four'
            lowerCamelCase__   	=					'Five'
            lowerCamelCase__   	=					'Six'
            lowerCamelCase__   	=					'Seven'
            lowerCamelCase__   	=					'Eight'
            lowerCamelCase__   	=					'Nine'

            lowerCamelCase__   	=					{}
            lowerCamelCase__   	=					''
            lowerCamelCase__   	=					'Twenty'
            lowerCamelCase__   	=					'Thirty'
            lowerCamelCase__   	=					'Forty'
            lowerCamelCase__   	=					'Fifty'
            lowerCamelCase__   	=					'Sixty'
            lowerCamelCase__   	=					'Seventy'
            lowerCamelCase__   	=					'Eighty'
            lowerCamelCase__   	=					'Ninety'

            lowerCamelCase__   	=					{}
            lowerCamelCase__   	=					'Ten'
            lowerCamelCase__   	=					'Eleven'
            lowerCamelCase__   	=					'Twelve'
            lowerCamelCase__   	=					'Thirteen'
            lowerCamelCase__   	=					'Fourteen'
            lowerCamelCase__   	=					'Fifteen'
            lowerCamelCase__   	=					'Sixteen'
            lowerCamelCase__   	=					'Seventeen'
            lowerCamelCase__   	=					'Eighteen'
            lowerCamelCase__   	=					'Nineteen'

            lowerCamelCase__   	=					{}
            lowerCamelCase__   	=					'Hundred,'
            lowerCamelCase__   	=					'Thousand,'
            lowerCamelCase__   	=					'Lakh,'
            lowerCamelCase__   	=					'Crore,'

            lowerCamelCase__   	=					number
            lowerCamelCase__   	=					''
            lowerCamelCase__   	=					0
            lowerCamelCase__   	=					int(lowerCamelCase    )
            while counter < digits:
                  lowerCamelCase__   	=					temp_num % 10
                  if counter % 2 == 0:
                        lowerCamelCase__   	=					''
                        if counter in placevalue and current != 0:
                              lowerCamelCase__   	=					placevalue[counter]
                        if counter == 2:
                              lowerCamelCase__   	=					singles[current] + addition + words
                        elif counter == 0:
                              if ((temp_num % 1_00) // 10) == 1:
                                    lowerCamelCase__   	=					teens[current] + addition + words
                                    lowerCamelCase__   	=					temp_num // 10
                                    counter += 1
                              else:
                                    lowerCamelCase__   	=					singles[current] + addition + words

                        else:
                              lowerCamelCase__   	=					doubles[current] + addition + words

                  else:
                        if counter == 1:
                              if current == 1:
                                    lowerCamelCase__   	=					teens[number % 10] + words
                              else:
                                    lowerCamelCase__   	=					''
                                    if counter in placevalue:
                                          lowerCamelCase__   	=					placevalue[counter]
                                    lowerCamelCase__   	=					doubles[current] + addition + words
                        else:
                              lowerCamelCase__   	=					''
                              if counter in placevalue:
                                    if current == 0 and ((temp_num % 1_00) // 10) == 0:
                                          lowerCamelCase__   	=					''
                                    else:
                                          lowerCamelCase__   	=					placevalue[counter]
                              if ((temp_num % 1_00) // 10) == 1:
                                    lowerCamelCase__   	=					teens[current] + addition + words
                                    lowerCamelCase__   	=					temp_num // 10
                                    counter += 1
                              else:
                                    lowerCamelCase__   	=					singles[current] + addition + words
                  counter += 1
                  lowerCamelCase__   	=					temp_num // 10
      return words


if __name__ == "__main__":
      import doctest

      doctest.testmod()