How Far Can You Push the Learning Rate?

A model with a single weight predicts $\hat{y} = wx$, and is trained by gradient descent on the mean squared error over three examples:

$L(w) = \frac{1}{3}\sum_{i=1}^{3}\left(wx_i - y_i\right)^2$

Give the complete set of learning rates $\alpha > 0$ for which the run converges to the minimising weight rather than blowing up.