ggplot letters in x axis replacing a continuos numerical sequence

Question

I would like to replace the numbers on the X-axis with a string.

df <- data.frame(Start = c(1, 3, 8, 10),
                 End = c(5, 10, 12, 15),
                 Height = c(10, 4, 5, 6))

p <- ggplot(df)+
    geom_segment(aes(x = Start,
                     xend = End,
                     y = Height,
                     yend = Height))

This is the string, each letter should go in a distance of 1: The first segment Will have coverage of ADFLK

lettersString <- 'ADFLKENACOINQLWEJI'    

This is what I would like to obtain.

I have tried solving it like this: (It doesn't work)

p + theme(axis.text.x =  strsplit(lettersString, split = "+"))