For all positive integers $n$ less than $2002$, let
\[
a_n = \begin{cases} 
11 & \text{if } n \text{ is divisible by } 13 \text{ and } 14 \\
13 & \text{if } n \text{ is divisible by } 11 \text{ and } 14 \\
14 & \text{if } n \text{ is divisible by } 11 \text{ and } 13 \\
0 & \text{otherwise} \end{cases}
\]
Calculate $\sum_{n = 1}^{2001} a_n$.

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