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 equal to :
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