Strange Sequence

From the given number $n$, the following sequence $S$ is obtained:

S_0 = n,

S_i = f(S_{i-1}), where i \geq 1

Here $f(x)$ is equal to the difference between the numbers obtained by rearranging the digits of the number $x$ in descending and ascending order. For example:

f(2214) = 4221 - 1224 = 2997

Note that leading zeros are not counted. Find the value of S_k.