A1040 | Hoof Paper Scissors

You have probably heard of the game "Rock, Paper, Scissors". The cows like to
play a similar game they call "Hoof, Paper, Scissors".
The rules of "Hoof, Paper, Scissors" are simple. Two cows play against each-
other. They both count to three and then each simultaneously makes a gesture
that represents either a hoof, a piece of paper, or a pair of scissors. Hoof
beats scissors (since a hoof can smash a pair of scissors), scissors beats
paper (since scissors can cut paper), and paper beats hoof (since the hoof can
get a papercut). For example, if the first cow makes a "hoof" gesture and the
second a "paper" gesture, then the second cow wins. Of course, it is also
possible to tie, if both cows make the same gesture.
Farmer John wants to play against his prize cow, Bessie, at $N$ games of
"Hoof, Paper, Scissors" ($1 \leq N \leq 100,000$). Bessie, being an expert at
the game, can predict each of FJ's gestures before he makes it. Unfortunately,
Bessie, being a cow, is also very lazy. As a result, she tends to play the
same gesture multiple times in a row. In fact, she is only willing to switch
gestures at most $K$ times over the entire set of games ($0 \leq K \leq 20$).
For example, if $K=2$, she might play "hoof" for the first few games, then
switch to "paper" for a while, then finish the remaining games playing "hoof".
Given the sequence of gestures FJ will be playing, please determine the
maximum number of games that Bessie can win.

The first line of the input file contains $N$ and $K$.
The remaining $N$ lines contains FJ's gestures, each either H, P, or S.

Print the maximum number of games Bessie can win, given that she can only
change gestures at most $K$ times.