Shuffle Vector in R, But Identical Elements Should Have Minimum Distance

I want to randomize/shuffle a vector. Some of the vector elements are identical. After shuffling, identical elements should have a minimum distance of three (i.e. two other elements should be between identical elements).

Consider the following example vector in R:

x <- rep(LETTERS[1:5], 3)  # Create example vector
x
#  [1] "A" "B" "C" "D" "E" "A" "B" "C" "D" "E" "A" "B" "C" "D" "E"

If I shuffle my vector using the sample function, some of the identical elements may be too close together. For instance, if I use the following R code, the element "C" appears directly after each other at positions 5 and 6:

set.seed(53135)
sample(x)                  # sample() function puts same elements too close
#  [1] "B" "A" "E" "D" "C" "C" "E" "A" "B" "C" "D" "E" "A" "D" "B"

How could I ensure that identical elements have a minimum distance of three?