# Help with context free grammar excercise

So, I have an exercise in which I have to write a context free grammar for this language:

$$L = \{x \in L(a^∗b^∗c^∗) : |x|_a > |x|_c; |x|_b > 0; |x|_c ≥ 0\}$$

meaning every string with any number of $$a$$‘s, $$b$$‘s and $$c$$‘s in that order, with the amount of $$a$$‘s greater than the amount of $$c$$‘s and the amount of $$b$$‘s greater than zero.

I am having trouble figuring out the rule that makes sure there are more $$a$$s than $$c$$s.

I have: \begin{align}S&\to aABC | ab\ A&\to aA | a\ B&\to bB | b\ C&\to cC | c\ \end{align} I know this is wrong because I should be adding an $$a$$ every time I add a $$c$$, but I don’t know how to write that.