I love the fact that you based this on a question from Answers! I kind of wanted to link back to it, but I can see that you might not want people to see your answer.
This is a short coded solution but it is not efficient. A solution that involves sorting the vector, A, uses less memory and is faster but take a couple more lines of code.
Are you in or are you out?
Permute diagonal and antidiagonal
Generate a vector like 1,2,2,3,3,3,4,4,4,4
multiply by three
Find the distance between runs
Dispatch and collect
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