Give a context-free description for the set of words of the form $w_1aw_2aw_3$ such that $w_1,w_2,w_3$ are constructed over the alphabet $\{0,1\}$, the size $w_1$ coincides with the number of $0$’s of $w_2$ plus the number of $1$’s of $w_3$, and $w_1w_2$ has at least one occurrence of $111$.