There is a sequence defined by the following conditions:

- $a(2) = 0$
- $a(3) = 1$
- For $n \geq 4$, $a(n) = a\left(\left\lfloor \frac{n}{2} \right\rfloor \right) + a\left(\left\lceil \frac{n}{2} \right\rceil \right)$

Find the value of $a(2014)$.

*Note:*
- $\left\lfloor \frac{n}{2} \right\rfloor$ is the floor function, representing the largest integer less than or equal to $\frac{n}{2}$.
- $\left\lceil \frac{n}{2} \right\rceil$ is the ceiling function, representing the smallest integer greater than or equal to $\frac{n}{2}$.

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