KöMaL 2024 C1793

Function $f$ defined on the real numbers satisfies the following two conditions (for all $x \in \mathbb{R}$): $(1)$ $f(x)=f(147-x),$ $(2)$ $f(x+100)=f(46-x).$ Find the value of $f(200)+f(201)+f(202)$, if we also know that $f(50)+f(51)+f(52)+f(53)=2024$.