How many integer solutions are there to \[\large \lfloor {x + \sin x} \rfloor = \left\lfloor {x^2 + \cos x} \right\rfloor ?\] If you think there are infinitely many solutions, then enter 999.

**Details and Assumptions:**

- \( \lfloor \cdot \rfloor \) denotes the floor function.
- The angles are measured in radians.

Inspired by Hummus A

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