Let f(x) = \left\lfloor\frac{2 - 3x}{3x + 1}\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.)
+862 
