VC dimension of finite unions of one-sided intervals What is the VC dimension of $k$ finite unions of one-sided intervals:

If we take 3 one-sided intervals like $(-\infty, a_1] $, $(-\infty, a_2] $ and $(-\infty, a_3] $, I think union of these intervals can shatter $4
$ points as below, assuming that $a_1&gt;a_2&gt;a_3&gt;a_4$:


Point $p_1$ at interval $(-\infty, a_1]$
Point $p_2$ at interval $[a_1, a_2]$
Point $p_3$ at interval $[a_2,a_3]$
Point $p_4$ at interval $(-\infty, a_3]$


For $k$ finite unions I think answer is $k+1$, am I right?
Finite unions of one-sided intervals can shatter only 2 points, because as said by @YuvalFilmus in comments the union of Finite unions is a single one-sided interval, and a single one-sided interval can shatter only 2 points.