$\large \left \lceil \lfloor \pi \rfloor + \left \lfloor \pi + \dfrac{1}{2016} \right \rfloor + \left \lfloor \pi + \dfrac{2}{2016} \right \rfloor + \cdots + \left \lfloor \pi + \dfrac{2015}{2016} \right \rfloor \right \rceil + 1 =\, ?$

$$ **Notations**: $\lfloor \cdot \rfloor$ denotes the floor function and $\lceil \cdot \rceil$ denotes the ceiling function.