2012 AIME I Problem 10

Let \mathcal{S} be the set of all perfect squares whose rightmost three digits in base 10 are 256. Let \mathcal{T} be the set of all numbers of the form \frac{x-256}{1000}, where x is in \mathcal{S}. In other words, \mathcal{T} is the set of numbers that result when the last three digits of each number in \mathcal{S} are truncated. Find the remainder when the tenth smallest element of \mathcal{T} is divided by 1000 .