Hint 2:

You will need four variables in addition to the start symbol, namely

A runner generator.
An a-runner.
A b-runner.
A runner killer.

The start symbol is replaced by the runner generator and the runner killer.

The runner generator generates an "a" and an a-runner, or a "b" and a
b-runner.

Each of the two kinds of runners can run to the right by exchanging with
either "a" or "b."

The runner killer kills a runner and simultaneously generates either "a"
or "b" as appropriate.

The runner generator and the runner killer can each be replaced by the
empty string.