Add y-values for density probability in geom_density_ridges

Question

I am working with geom_density_ridges function in ggplot to get different distributions along the y-axis. Below you can find a reproducible example:

datatype = data.frame(x = c(rnorm(40,0,0.5),rnorm(40,0.5,1),rnorm(40,2,1),rnorm(40,1,1)),
                      within = c(rep('TypeA',40),rep('TypeB',40),rep('TypeA',40),rep('TypeB',40)),
                      between = c(rep('BetweenA',80),rep('BetweenB',80)))


p = ggplot(datatype, aes(x = x, y = between)) +
  geom_density_ridges(aes(fill = within),alpha =.7,scale =.9,size=.3,show.legend = F)+
  theme_bw()

The problem is that I cannot find a way to also add the density values on the y-axis, so that I can show in my plot how frequent are the x-values in each distribution.

Any idea on how to solve this? However, I would like to stick with geom_density_ridges, since I have already made several plots with it.