Hyrule Warriors thorough optimal refresh paths

After doing all that work on manually brute-forcing fairy paths ( https://imgur.com/a/PH95fq5 ), I still wasn't quite satisfied... so I ended up writing a program to more thoroughly brute-force fairy refresh paths to minimize refreshes.

Basically, using recursion, from a base set of five traits I iterated through every single possible refresh, checking each step if a new skill (out of the ten notable skills determined earlier) was learned, but stopped recursion if the refresh led to a previous set of five traits, or if it went (usually) two total refreshes without learning a new skill, or if it went more refreshes than the current lowest-refresh record; once it learned all ten notable skills, it printed the full refresh path as well as what notable skill is learned at each step. Compared to my manual brute-forcing, it actually improved on my Adventure path, Master Quest path, and Neris path! (I made a typo for Loyla, that second [...] shouldn't be there.)

Note that, as thorough as this is, it doesn't quite list every single path with the fewest refreshes: it only allows for up to two 'refreshes without learning a new skill' despite there being very rare situations where you could learn Glass Cannon + XP Master+ + Total Focus in a single refresh.

I use three-letter shorthands for traits, mainly to save space:
SPK -> Sparkly
RLX -> Relaxed
VAL -> Valiant
DIZ -> Dizzy
FRN -> Friendly
ASP -> Aspiring
RES -> Resolute
SHR -> Shrewd
EAG -> Eager
SMI -> Smiley

Links to other pastebins with all of the brute-forced paths:
(10) Adventure:		https://pastebin.com/yurUHRZQ
(10) Great Sea:		https://pastebin.com/M0hkGTSz
(10) Master Quest:	https://pastebin.com/waYQge70
(11) Termina [1]:	https://pastebin.com/Emh7amfR
			 [2]:	https://pastebin.com/sBcn23Ha
(11) Twilight:		https://pastebin.com/n3au484w
(11) Neris:			https://pastebin.com/2EAUGsH2
(11) Becka:			https://pastebin.com/9FXANqiH
(11) Loyla:			https://pastebin.com/vwm4AbxP

For example, the very first listed path for Loyla:
1   0   SPK,VAL,ASP,RES,SMI,    SPK -> RLX  [Initial] Wall of Water +
1   1   RLX,VAL,ASP,RES,SMI,    RLX -> FRN  Material Master +
1   2   VAL,FRN,ASP,RES,SMI,    ASP -> SPK
1   3   SPK,VAL,FRN,RES,SMI,    SMI -> DIZ  Extreme Crush +
1   4   SPK,VAL,DIZ,FRN,RES,    SPK -> EAG  Glass Cannon
1   5   VAL,DIZ,FRN,RES,EAG,    FRN -> SPK  Total Focus
1   6   SPK,VAL,DIZ,RES,EAG,    DIZ -> ASP  XP Master +
1   7   SPK,VAL,ASP,RES,EAG,    SPK -> RLX  Special Fountain +
1   8   RLX,VAL,ASP,RES,EAG,    RES -> SHR  Food Master +
1   9   RLX,VAL,ASP,SHR,EAG,    VAL -> DIZ  Magic Fountain +
1   10  RLX,DIZ,ASP,SHR,EAG,    ASP -> FRN
1   11  RLX,DIZ,FRN,SHR,EAG,    Done!       Weapon Master +

- the "1" column means that this is path #1, mainly to keep track of total path count while compiling all of these;
- the "0" to "11" mean the number of refreshes to reach that line (so the initial set of traits are from 0 refreshes);
- the set of five traits are the current traits, alongside the trait swap for the following refresh;
- the skill(s) on the right show what notable skill(s) is(/are) learned from the current set of five traits.


Finally, the obligatory disclaimer: I did all of this work because I had a self-imposed challenge to unlock all skills on one fairy in as few refreshes, and using as few Gratitude Crystals, as possible. (With a lightning Termina fairy, I did it in only 11 refreshes and 16 Gratitude Crystals!) Optimally speaking, it's better to take your time and get high refresh counts: refreshing often means the 10% trait bonus to base stats leads to farming for specific perfect food (and Gratitude Crystals!) way less in order to reach trait requirements, and the fairy's magic attack deals 1% more damage with every refresh.