Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

Let $f: \mathbb{R}\to\mathbb{R}$ be a function defined by $f(x)=\lvert x+2\rvert - 2\lvert x\rvert.$ If $m$ is the number of points of local minima and $n$ is the number of points of local maxima of $f$, then $m+n$ is: