# Find CSG for $L = \{a^ib^jc^k \mid 0 \leq i \leq j \leq k\}$

I am trying to find a context sensitive grammar for the type-1 language

$$L = \{a^ib^jc^k \mid 0 \leq i \leq j \leq k\}$$

I can construct the first part with

\begin{align*} S &\to aSbB \mid B \mid \epsilon\ B &\to bB \mid \epsilon\ \end{align*}

but how do I continue from there? I tried

\begin{align*} S &\to aSbBcC \mid B \mid \epsilon\ B &\to bBcC \mid \epsilon\ CB &\to BC \ C &\to cC \end{align*} but this does not seem to work e.g. $$S \to aSbBC \to aaSbBCbBC \to aabBCbBC$$