Second order diagram for the "scalar graviton"

[Hill]

Homework Statement

Write down the next-order diagrams. Check the answer using Green's function method.

Relevant Equations

Equation of motion: $\Box h - \lambda h^2 -J =0$

It has been shown in the text that $h_0 = \frac 1 {\Box} J$ with the diagram

and that $h_1 = \lambda \frac 1 {\Box} (h_0 h_0) = \lambda \frac 1 {\Box} [( \frac 1 {\Box} J)( \frac 1 {\Box}J)]$ with the diagram

I was not sure if the next order diagram is

or rather

Thus, I substitute $h=h_0+h_1+h_2$ in the equation of motion and calculate to the $\mathcal O(\lambda^2)$. I get $\Box h_2 = 2 \lambda h_0 h_1$.
I understand that the factor 2 means that the last diagram above is correct.
Is it so?