Split data into train and test stratified on label

I have a data frame (df) with two columns (Numbers and Letters). See reproducible example:

Numbers<- c(2.370653,3.811336,5.255120, 6.501197,7.848100,9.343938,10.843479,12.164387,13.476807,14.922644,16.419281,17.664224,19.112835,20.660367,21.962732,23.213675)
Letters<-c("a","b","c","c","d","a","b","d","d","a","a","c","b","c","c","c")
df <- as.data.frame(cbind(Numbers,Letters))

I want randomly to split the data frame into two date frames of equal size and with the same number of Letters in each. I have found the stratified() function that takes a sample with 50% of each of the Letters:

test <- stratified(df, "Letters", .5)

But this is not really the same as splitting the data frame into two data frames. I do not want any of the same values from df$Numbers in the two data frames - just the same amount of df$Letters in each. Can you help me?