HMMT 2009 U34

Descartes's Blackjack: How many integer lattice points (points of the form $(m, n)$ for integers $m$ and $n$ ) lie inside or on the boundary of the disk of radius 2009 centered at the origin?

If your answer is higher than the correct answer, you will receive 0 points. If your answer is $d$ less than the correct answer, your score on this problem will be the larger of 0 and $25-\lfloor d / 10\rfloor$.