Feynman Diagrams for Interacting Scalar Fields

[MyName]

Homework Statement

Consider four real massive scalar fields, $\phi_1,\phi_2,\phi_3,$ and $\phi_4$, with masses $M_1,M_2,M_3,M_4$.
Let these fields be coupled by the interaction lagrangian $\mathcal{L}_{int}=\frac{-M_3}{2}\phi_1\phi_{3}^{2}-\frac{M_4}{2}\phi_2\phi_{4}^{2}$.
Find the scattering amplitude for $\phi_{3}\phi_{4}\rightarrow\phi_3\phi_4$, to tree level.

Homework Equations

I'm not really sure what to put here.

The Attempt at a Solution

This honestly looks like a trick question to me. The first step is obviously to write down the relevant feynman diagrams and feynman rules to evaluate them, but I can't find a single tree level diagram for this process. A diagram would need an incoming $\phi_3$ and an incoming $\phi_4$, as well as an outgoing $\phi_3$ and an outgoing $\phi_4$.
The interaction lagrangian makes me think that we should have a vertex between a $\phi_1$ and two $\phi_3$'s, as well as a vertex between a $\phi_2$ and two $\phi_4$'s, but this still doesn't allow $\phi_3$ and $\phi_4$ to interact.
Perhaps I am misunderstanding the meaning of tree level (I think it just means one of each type of interaction vertex), or perhaps I am just misunderstanding the interactions.
Could this possibly have to do with interactions via the kinetic terms of the lagrangian? Can a tree level diagram just consist of the $\phi_3$ and the $\phi_4$ propagating along and not interacting (if yes I don't think this would contribute to the scattering), I'm not sure and would appreciate any help. I'm just feeling pretty confused at the moment.
Thanks!

 

[Orodruin]

With that Lagrangian the 13 and 24 sectors do not mix.

 

[MyName]

Thanks, I thought that was the case and really appreciate the confirmation.