Numerical Methods: Euler to Runge–Kutta · Challenge problem

Heun's method is applied to $y' = t^2$, $y(0) = 0$ with $n$ equal steps on $[0, 1]$, producing an estimate $Y_n$ of $y(1) = \dfrac{1}{3}$. What is the smallest $n$ for which $\left|Y_n - \dfrac{1}{3}\right| \le \dfrac{1}{1000}$?