The Wizard of Oz witches

I've been wondering about the witches in "The Wizard of Oz" because it seems as if they've left one out. Dorothy's house falls on the Wicked Witch of the East, then Dorothy meets Glinda, the only witch who has a name and also the Good Witch of the North. Soon after, she meets the Wicked Witch of the West, who she eventually melts. The question is: What about the Witch of the South? I wonder if she would have been a good or bad witch and why they left her out.