# Perl, <s>65</s> 58 bytes

    map{map{$b^=2*y,/\\L,,;$a+=y,/\\V,,||$b}split//}<>;print$a

- Toggle $b between 0 and 2 upon seeing / \ or L.
- Add 1 to $a upon seeing / \ or V.
- Add $b to $a upon seeing anything else.