Find the number of real values $x$ that satisfy the equation

$\lfloor x \rfloor + |x| + \lceil x \rceil =1000.$

**Notations**:

- $| \cdot |$ denotes the absolute value function.
- $\lfloor \cdot \rfloor$ denotes the floor function.
- $\lceil \cdot \rceil$ denotes the ceiling function.