Find the number of fractions in the following list that are in their lowest terms (i.e., for $\frac{p}{q}$, $\gcd(p,q) = 1$):

$$\frac{1}{2014}, \frac{2}{2013}, \dots, \frac{1007}{1008}$$

Let's think step by step and output the final answer within \boxed{}.
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