Chances for a math-focused junior

Currently a junior. Calculations of GPA etc. are based on what they are tracking to be for this year.

Please chance for:
MIT
UChicago
Harvard
Stanford
Princeton
Columbia
Carnegie Mellon

White Male
Public School

GPA: 3.97 unweighted, 4.88 weighted (weird weighting system)
SAT: 2350 (800 reading, 800 math, 750 writing)
SAT II: 800 Math, 800 Physics, 800 US History
No class rank, but probably ~5th of 800

Significant classes:

Freshman year
AP BC Calculus (A+,5)

Sophomore year
Mutivariable Calculus (A+)
APUSH (A,5)
AP Lang (A,5)

Junior year
AP US Gov (A)
AP Comp Gov (A-)
AP Chem (A+)
Math independent study (topped out of school’s math classes)
Chamber singers (most select school choir)

Senior year
AP Euro
AP Lit
AP Physics C
AP Compsci
Chamber singers
Math independent study

ECs?:
Mostly math (a lot of hours/week), also some algorithmic competitions
Captain of science club state champion math team
Also participated in debate, robotics, programming, history, frisbee clubs, volleyball freshman year.
Have gone to math camps and self studied to some extent linear/abstract algebra, real/complex analysis, combinatorics.
Specifically:
2012: MOP, AMSP
2013: MOP, Canada/USA Mathcamp
2014: MOP, Canada/USA Mathcamp, SPARC (Summer Program in Applied Rationality and Cognition)

Some test scores/awards:
AMC 10: 150
AMC 12: 141
AIME: 13
USAMO: 26
MOP qualifier 2012-2014, 1st place blue MOP 2014
TST group 2014-2015 (top ~20)
Qualified for US international Romanian Master of Mathematics team (6 members), gold medal (top 10)

Don’t know if it’s worth noting but 1st place in middle school state Mathcounts competition in 6th, 7th, 8th grade.

Top 10 Princeton math tournament 2012-2014, top 20 Harvard MIT math tournament 2013, 1st place Columbia math tournament 2014. Went to national Who Wants to Be a Mathematician competitions (top 11), won $1000.

Qualified for Physics semifinals, USACO gold, participated in NACLO.

Co-run an online math competition with ~700 participants

National Merit Scholar, Math honors society, AP History scholar.

These are really tough reach schools for everyone, but you have exceptionally great ECs, test scores and grades with no real weaknesses. Write some good essays, maybe apply ED/EA your top choice and you’ll probably get in at least around 1/2 the schools on your list. I’d be shocked if you didn’t get into at least 1, though as for everyone you should probably apply to a state school or somewhere as a safety just in case (where’d you probably get a free ride or something).