What are my chances?

I want to apply at harvard, priceton, dartmouth, amherst (CS course). First of all I want to clarify that I don’t really have a fetish for the ivies but the only reason for me to apply to them only is because of their financial aid programs (my family contribution tops at around 20,000 USD)
percentage in school: 90-95 %
estimated SAT score >2000

Achievements and ECs
member of the organizing committee of my school (head of department of computer services)
international rank 70 in national cyber olympiad organised by www.sofworld.org
3rd rank in district science quiz
4th rank in national aerolympics (related to aviation technology and advancements)
member of NSS (national social service)

I am sure that the teacher’s as well as peer recommendations are going to be excellent. Also I can explain my exceptional intellectual maturity/ability in the essay.

PS. if you have any suggestions for me to apply to any other college with such financial aid for international students i will be grateful to you.