Pie plot for 3 layers in R

Question

I woudl like to draw a 3-layers pie plot, here is my example data:

dat = data.frame(Type1=c("A", "A","A","B","B","C","C","D","D"),
                 Type2=c("a","b","c","d","c","a","e","e","a"),
                 Type3=c("I","I","II","II","I","II","I","II","II")
                 )

I was wondering if there is any method or package that I can use for painting in R like the following picture. Many thanks!