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.