I ended up solving the problem as `c c c c c`, which reminded me of a fun fact I once derived about repeated applications of that composition operator. If we call this sort of expression of `n` chained composition operators `n`-fold composition, then for `n >= 6` (i.e. starting at `c c c c c c`), `n`-fold composition has the same type and semantics as `n+4`-fold composition. Not a particularly deep insight, but neat!