import fractions
import typing

MAX_CAPACITY: int = 300


def ratio(
    grade_in: int, grade_out: int, across_categories: bool
) -> typing.Optional[fractions.Fraction]:
    trading_up = grade_out > grade_in
    grade_base = 6 if trading_up else 3
    grade_ratio = fractions.Fraction(grade_base ** grade_out, grade_base ** grade_in)
    category_ratio = (
        fractions.Fraction(6, 1) if across_categories else fractions.Fraction(1, 1)
    )
    result = grade_ratio * category_ratio
    if max(result.numerator, result.denominator) > MAX_CAPACITY:
        return None
    else:
        return result