Let \(f(x) = \left\lfloor\frac{2 - 3x}{x + 3}\right\rfloor\). Evaluate \(f(1)+f(2) + f(3) + \dots + f(999)+f(1000)\). (This sum has 1000 terms, one for the result when we input each integer from 1 to 1000 into f.)
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