formal languages – Designing CFG that accepts $a^n b^m c^p$ where $n=m+p+2$

I have generated the CFG of $a^n b^m c^p$ where $m = n+p+2$:

$S rightarrow ASC mid varepsilon$

$A rightarrow aAb mid varepsilon$

$C rightarrow bCc mid varepsilon$

I have been trying $a^n b^m c^p$ where $n=m+p+2$ but cannot figure out how to represent $n=m+p+2$.
Any hint would really be appreciated.