the solution is:

[mosi-sol]

using the "hilbert curve" on the code, then change the curve to the line, then with "catalan equation" check validation patterns.
this problem fixed years ago with mathematical proof.
cya

for help to understand can to watch this 3 min on youtube: https://www.youtube.com/watch?v=kaInaIUABzY

if after 5 steps can not growth on catalan number, use this idea:
fact check: Levine Sequence "sum of each row show the Catalan number"
Levine Sequence : https://oeis.org/A011784