Which one of HYPSM/Caltech should I apply early to

hi! i'm a rising senior who wants to apply early to one of HYPSM/Caltech, and was just wondering what other people have to say. i'm a very easygoing person, so feel free to drop any thoughts down below. i'll briefly describe my stats and the gist of my profile. enjoy!

before anything, i'll just say that my profile is pretty boring and unsurprising.

for my background, i'm a bay area asian male from a large public high school with no hooks who intends on majoring in applied math/CS. i have essentially perfect grades/SAT/course rigor and 5s on all APs. my school doesn't rank, but i'm in the top 9%.

for awards, i'm your expected competition grinder. i'm a USAJMO qualifier (no USAMO this year, sadly, but life goes on), USACO Platinum/US Open invitee, and USAPhO medalist. i've done college math contests, being on a team that consistently places t5/t10 at comps, even though i personally have pretty mid individual placements.

for extracurriculars, i've attended 2 top math camps (from Ross/PROMYS/SUMaC/Mathcamp/HCSSiM/MathILy), held high leadership positions at various well-known math/CS nonprofits (w/ very visible impact), done math/CS research at a t10 w/ a publication at a workshop at a top conference (like NeurIPS/ICLR/ICML), been president of my school's math/CS club, been varsity captain of one of my school's sports teams, taught students in math/CS, and volunteered at a humanities nonprofit, yada yada.

as a person, i'm pretty reflective and have many unrelated hobbies/side quests, with (hopefully) fairly strong writing skills. for LORs, i'm likely getting them from my math teacher, english teacher, camp counselor, and school counselor, all of which should be pretty strong.

i'm thinking of applying early to either Yale or Princeton, but i'm open to anything. thanks for reading! :)