Rayleigh scale MLE for dart distances

The distance from the bullseye (in centimeters) where a dart lands is modeled as Rayleigh with unknown scale $\sigma$, density $f(x \mid \sigma) = \dfrac{x}{\sigma^2} e^{-x^2/(2\sigma^2)}$ for $x > 0$. Four throws land at distances 1, 2, 2, 3.

Estimate $\sigma$ by maximum likelihood.