The triple rendezvous time of a synchronizing automaton can be floor(4n/3)

For every $n\ge9$, we construct a strongly connected synchronizing automaton with two input letters and $n$ states whose shortest word merging some three distinct states has length $\lfloor4n/3\rfloor$. One letter is a permutation; the other has an image of size $n-1$. We give complete transition ma