CFG for the language L ={a^n w | w \in {b,c}^*, n= count of b.c in w. } $L =\{a^nw \mid w \in \{b,c\}^*$, $n=$ #$_b$ + #$_c$$\}$

$\bullet $ #$_b$ denotes the number of $b$'s in $w$

$\bullet $ #$_c$ denotes the number of $c$'s in $w$

I have some trouble designing a CFG for the language above. How can I do this?
I believe the following CFG meets the requirements

$$
S \to aSB \mid \varepsilon\\
B \to b \mid c
$$