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.