It freaks me out!

Number Theory Level pending

If \(S\) is the sum of all positive integers satisfying \(x\) in the equation below:

\[x^{2} + (x+1)^{2} + (x+2)^{2}+ \cdots +(x+500)^{2} = (x+501)^{2} + (x+502)^{2} +\cdots + (x+1000)^{2}\]

Find \(S \bmod 9\).

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