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
once over the entire set of games. For example, she might play "hoof"
for the first \(x\) games, then switch to "paper" for the remaining \(N-x\)
games.

Given the sequence of gestures FJ will be playing, please determine the
maximum number of games that Bessie can win.

Problem credits: Mark Chen and Brian Dean

Problem credits: Mark Chen and Brian Dean

The first line of the input file contains \(N\).

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 once.

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