The Rocky Horror Picture Show

0.7 If you’re staying at Dr. Frank N. Furter’s place, you’d better watch
your step! The moment the music kicks in, just look at the squares on
the floor, join the other guests, follow the dance moves, and…let’s do
the Time Warp again!

But hey, there are so many ways you can literally get warped and be sent
back to Transsexual Transylvania:

0.3

[image]

- If you hit any of the room walls (then you get warped!).

- If you bump into another guest mid-air as you try to swap your
  positions (then you both get warped before you can land on your target
  square!).

- If you land your step in the same square as other guests (then you all
  get warped!)

Given how all guests are at the start of the dance, can you tell how
many of you would remain on the dance floor if the music went on
forever?

Input

Input begins with the number of cases n ≥ 0. For every case, we have the
dimensions W and H of the room, followed by the number of people P,
followed by P triplets x_(i), y_(i), b_(i) with the position of the
dancer and the direction he or she is facing. Follow the number of
steps S in the dance, followed by S characters
$s_i \in \{`\texttt{\small F}', `\texttt{\small R}', `\texttt{\small B}', `\texttt{\small L}'\}$
denoting a step forward, right, backward, or left, respectively.

Assume that W and H are between 1 and 10⁶, 1 ≤ P ≤ 10⁴, 1 ≤ x_(i) ≤ W,
1 ≤ y_(i) ≤ H,
$b_i \in \{`\texttt{\small N}', `\texttt{\small E}', `\texttt{\small S}', `\texttt{\small W}'\}$,
1 ≤ S ≤ 10⁴, and that no two dancers will start at the same position.

Output

For each case, print the number of people that will be dancing
indefinitely without ever being warped.

Problem information

Author: Edgar Gonzàlez

Generation: 2026-01-25T10:16:39.523Z

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