Universities offering full need, need-blind financial aid to international students

<p>Hi guys) I have so many questions and other people opinions differ so much that i’ve decided post here as many of you seem to be able to help me.
Now i’m studying in Russia on a math faculty, on the 2nd year out of 4. But the education level seems to be not enough for me and i’m really thinking of chances to find a good university in us.
The problem is i won’t be able to pay more than $2k a year^^ and i’ve seen the cost it’s up to $50-60k… But i’ve read about blind-need system and financial aid and i’m going to ask you smth what you’ve heard hundred times i think)
Is it really possible that, for example, Princeton would take an international student(already with a bachelor degree) and 'd pay up to 100% of the tuition cost, or is it more an exception?
I’ve looked through the Gre in math and it definetely doesn’t seem to be a problem for me, even when i’m 18 and hadn’t listened to the whole course of math disciplines (i’m reading lots of it for myself).
The Toefl is also rather simple though you think it’s not looking at my awful english xD
So, if in 2,5 years, i’d get a degree+successfully pass the exams(gre subj,gre general,toefl,am i right?), is there a chance to be admitted to,e.g.,Princeton?
I know i’ve written too much but you can’t imagine how important it is for me.
Great thx for those who’d read and answer trying to help and enlighten me >.<</p>