Three Dimensional Geometry

The distance between two parallel planes $a x+b y+c z+d_1=0, a x+b y+c z+d_2=0$ is given by $\frac{\left|d_1-d_2\right|}{\sqrt{a^2+b^2+c^2}}$. If the plane $2 x-y+2 z+3=0$ has the distances $\frac{1}{3}$ and $\frac{2}{3}$ units from the planes $4 x-2 y+4 z+\lambda=0$ and $2 x-y+2 z+\mu=0$ respectively, then the maximum value of $\lambda+\mu$ is