You are in a Magic: The Gathering commander game. It is now your first main phase and you control these permanents:
- One Miirym, Sentinel Wyrm: "Whenever another nontoken Dragon enters the battlefield under your control, create a token that’s a copy of it, except the token isn’t legendary if that Dragon is legendary."
- Exactly $n$ instances of the enchantment Parallel Lives*: "If an effect would create one or more tokens under your control, it creates twice that many of those tokens instead". $n$ is positive
You then cast Astral Dragon, which is indeed a Dragon: "When Astral Dragon enters the battlefield, create two tokens that are copies of target noncreature permanent, except they’re 3/3 Dragon creatures in addition to their other types, and they have flying". Assume that
- in the ensuing resolution you only target permanents you control and that have names mentioned in this puzzle (Miirym, Sentinel Wyrm; Parallel Lives; Astral Dragon)
- there is no external interference (instants played by opponents, abilities of other permanents, etc.)
- you cast no other spells before you proceed to combat.
What is the exact maximum number of 3/3 Dragon creature tokens you can create during this first main phase?
The exact answer is a very large number that requires defining auxiliary functions to write down compactly. It is however far less than $2\uparrow\uparrow\uparrow6$.