Let \( f:\mathbb{R} \to \mathbb{R} \) be a function defined by \( f(x) = \big||x+2| - 2|x|\big| \). 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:
\( 5 \)
\( 4 \)
\( 3 \)
\( 2 \)
