Animal-Alphabetical Sequence The Animal-Alphabetical Sequence is an infinite string of letters built accordingly to the following procedure:

Start with the letter A;

Replace each letter with the name of the animal starting with such letter in the table below;

Go back to step 2.


For instance, the first four steps of the procedure give:

A

ADDAX

ADDAXDINGODINGOADDAXXERUS

ADDAXDINGODINGOADDAXXERUSDINGOINDRINYALAGECKOOTTERDINGOINDRINYALAGECKOOTTERADDAXDINGODINGOADDAXXERUSXERUSEAGLEROBINURIALSQUID


Note that the string obtained at each step is a prefix of the string obtained at the next step. Hence, the procedure does indeed converge to a well-defined infinite string:
ADDAXDINGODINGOADDAXXERUSDINGOIND...
The Challenge
Write a function that takes as input an integer n in the range [0, 2^31 - 1] and returns as output the n-th letter of the Animal-Alphabetical Sequence.
Notes

The first letter is the 0-th.

Letters can be uppercase or lowercase.

It must be possible to run the program in the Try It Online interpreter and get the result in at most 5 minutes.


Test Cases
1511763812 -&gt; M
1603218999 -&gt; I
2049234744 -&gt; X
2060411875 -&gt; K
2147483647 -&gt; D

Table of Animal Names
ADDAX
BISON
CAMEL
DINGO
EAGLE
FOSSA
GECKO
HORSE
INDRI
JAMBU
KOALA
LEMUR
MOUSE
NYALA
OTTER
PRAWN
QUAIL
ROBIN
SQUID
TIGER
URIAL
VIXEN
WHALE
XERUS
YAPOK
ZEBRA
Charcoal, 83 bytes
≔AηＦ↨Ｎ⁵≔§⁺η§⪪”$⌊∧Ｘ;F‖ρ=ＪD θ⊘⊙～'ΣV⦄Ｋ◨｜]≕‖◨⟧TJρ¿¿C´!⁸⁶S/Ｕ¶V×Ｗ⧴a“,=6；‴*Þ↓h!�{≦”⁴⌕αηιηη

Try it online! Link is to verbose version of code. Explanation:
≔Aη

Start with A at the 0th index.
Ｆ↨Ｎ⁵

Input n, convert it to base 5 and loop over the digits.
≔§⁺η§⪪”...”⁴⌕αηιη

Get the current animal from the compressed string of all animal suffixes (excluding EBRA) and lookup the appropriate letter from the current digit.
η

Output the final letter.