# Sets of Perfect Squares

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 $$\frac{x^2-256}{1000}$$, 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 $$1000$$.

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