800 Followers problem!

\[ 100^2 + 99^2 - 98^2 - 97^2 + 96^2 + \cdots + 4^2 + 3^2 - 2^2 - 1^2\]

Let \(N\) denote the number above. Find the remainder when \(N\) is divided by \(1000\).

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