On the hitting depth in the dynamical system of continued fractions

Let ([0,1),T) be the dynamical system of continued fraction expansions with T the Gauss map. For any irrational point y∈[0,1), let In(y) be the cylinder of order n containing y. For any x∈[0,1), define the maximal hitting depth of x to the irrational point y asRn(x,y)≔max{t∈N0:Ti(x)∈It(y)for some0⩽i