Why can't $Sigma$ baryons decay strongly?

First of all, I must say this is a homework question. The complete question includes particles like $p$, $e^-$, $Lambda$ and $Omega$.

It’s pretty easy to understand why $Omega$ and $Lambda$ have to decay weakly; $Omega$ has three $s$ quarks so, no other baryon to turn into without changing strangeness. As for $Lambda$, it is the lightest baryon with unit strangeness.

But when it comes to, for example, $Sigma^0$ it can decay to $Lambda + gamma$. And while this particular process doesn’t come from a strong interaction, I can’t think of any reason why a process like $Sigma^0 rightarrow Lambda + A$ where $A$ is a strangeless particle can’t be possible. I’m not sure if the reason should be that there’s simply no particle A that can fit that decay. The mass difference between $Lambda$ and $Sigma^0$ is pretty small, so maybe that is the case, but it sounds a little bit vague. Am I missing something?