How generous is Cornell's aid for international students?

I’m an international student living in the USA (in the process of getting a green card). I’m a strong applicant and believe I have a good chance of getting accepted. However, my family is poor (~$53k). I would need a huge amount of aid in order to attend. On Cornell’s website, aid for international students is mentioned as “limited”, but no details are given. Does anyone have an idea of the chances of getting aid from Cornell as an international student?
Any input is appreciated.