
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int | float | str				)			->						tuple[int, int]:
       try:
              SCREAMING_SNAKE_CASE_							:				int		=float(UpperCAmelCase_				)
       except ValueError:
              raise ValueError('''Please enter a valid number'''				)
       SCREAMING_SNAKE_CASE_							:				Any		=decimal - int(UpperCAmelCase_				)
       if fractional_part == 0:
              return int(UpperCAmelCase_				), 1
       else:
              SCREAMING_SNAKE_CASE_							:				Any		=len(str(UpperCAmelCase_				).split('''.'''				)[1]				)
              SCREAMING_SNAKE_CASE_							:				str		=int(decimal * (1_0**number_of_frac_digits)				)
              SCREAMING_SNAKE_CASE_							:				Any		=1_0**number_of_frac_digits
              SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_							:				Tuple		=denominator, numerator
              while True:
                     SCREAMING_SNAKE_CASE_							:				Any		=dividend % divisor
                     if remainder == 0:
                            break
                     SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_							:				Optional[int]		=divisor, remainder
              SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_							:				Optional[int]		=numerator / divisor, denominator / divisor
              return int(UpperCAmelCase_				), int(UpperCAmelCase_				)


if __name__ == "__main__":
 print(F"{decimal_to_fraction(2) = }")
 print(F"{decimal_to_fraction(89.0) = }")
 print(F"{decimal_to_fraction('67') = }")
 print(F"{decimal_to_fraction('45.0') = }")
 print(F"{decimal_to_fraction(1.5) = }")
 print(F"{decimal_to_fraction('6.25') = }")
 print(F"{decimal_to_fraction('78td') = }")


from math import ceil, sqrt
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int = 1_0_0_0_0_0_0				)			->						int:
       SCREAMING_SNAKE_CASE_							:				List[Any]		=0

       for outer_width in range(3			,							(limit // 4) + 2				):
              if outer_width**2 > limit:
                     SCREAMING_SNAKE_CASE_							:				List[str]		=max(ceil(sqrt(outer_width**2 - limit				)				)			,							1				)
              else:
                     SCREAMING_SNAKE_CASE_							:				List[str]		=1
              if (outer_width - hole_width_lower_bound) % 2:
                     hole_width_lower_bound += 1

              answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

       return answer


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