Program the cleanup robot to sort every ball into its basket

The office floor is a mess. Balls of every colour are scattered across an N x N warehouse grid criss-crossed by shelving walls, and each colour has one matching basket somewhere on the floor. You have exactly one robot and one controller. The robot understands four buttons — forward, turn right, turn left, swap — and the controller has one more trick: a macro you can record once and replay as many times as you like. Every button you press costs you, including each macro replay, so a clumsy plan that walks the robot back and forth racks up a huge tab. Your job is to press the fewest buttons that still lands every ball in its own basket before the move budget runs out.

You control a machine through a macro language; the objective is defined below. The entire difficulty is macro compression: a naive plan is a long string of F/R/L/S, but the tours the robot repeats (walk-to-cell, drop, walk-back) are full of structure, and a well-designed macro turns hundreds of moves into a handful of pressed buttons. You are scored relative to a reproduced contest rank-1 solver, so matching a strong human is the bar.

The machine

There is an N x N grid. Cell (0,0) is the top-left; (i,j) is i cells down and j cells right. The outer boundary is walled, and there may be walls between adjacent interior cells. Every cell is reachable from every other cell without crossing a wall.

On the grid are M balls and M baskets. For each type k (0 <= k < M) there is exactly one ball of type k and one basket of type k. Initially each cell holds at most one ball or basket.

The robot starts at (0,0) facing right, holding nothing. You control it with a sequence of buttons:

Basic buttons

• F (forward): move one cell in the current facing. If a wall blocks the destination, the robot stays put (the button is still spent).
• R (turn right): rotate 90° clockwise in place.
• L (turn left): rotate 90° counter-clockwise in place.
• S (swap): exchange the ball in hand with the ball on the current cell.
• empty hand + ball here -> pick it up (cell becomes empty);
• ball in hand + empty cell -> drop it (hand becomes empty);
• ball in hand + ball here -> swap the two;
• empty hand + empty cell -> nothing happens.
• A ball sitting on a basket cell is swapped just like any other ball.

Controller buttons

• M (macro): if not currently recording, start recording. If currently recording, stop and register the recorded sequence as the macro (replacing any previous one).
• P (play): replay the most recently registered macro. If none is registered yet, nothing happens.

While recording, any basic F/R/L/S you press is both executed and appended to the macro being recorded. A P pressed while recording replays the previously registered macro, and the basic operations it expands to are executed and appended to the macro being recorded (you cannot replay the macro you are currently recording — only the last completed one).

Example: with RFF already registered, running MFPM records a new macro. M starts recording; F executes+records; P replays the registered RFF (executed and appended); M stops. The basic ops executed are FRFF, and the newly registered macro is FRFF.

Initially no macro is registered and nothing is being recorded.

Budget and scoring

You are given a basic-operation cap T. After macro expansion, at most T basic operations are executed; the T+1-th basic operation is not executed and the run is cut off there. So P is cheap to press but its expansion is charged against T.

Let A be the length of the button sequence you output — M and P each count as one button. Let V be the number of balls sitting on their matching basket at the end of the simulation. The absolute score for a case is:

• A if V == M (all balls delivered) — lower is better;
• T * (M - V) if V < M (a big penalty).

You are scored on the absolute score of each case — lower is better. A reproduced contest rank-1 solver's per-case scores ship with the task so you can gauge how strong your solution is, but how the raw scores map to the final reward is deliberately not disclosed. Optimise the raw score itself.

Closing the gap to a top contest solver is almost entirely about better macro synthesis.

Input format (stdin, one instance)

N M T
v_0
...
v_{N-1}        # N lines: v_i is a length-(N-1) 01 string; v_i[j]=1 <=> wall between (i,j) and (i,j+1)
h_0
...
h_{N-2}        # N-1 lines: h_i is a length-N 01 string; h_i[j]=1 <=> wall between (i,j) and (i+1,j)
b_0 c_0 d_0 e_0
...
b_{M-1} c_{M-1} d_{M-1} e_{M-1}   # ball k starts at (b_k,c_k); basket k is at (d_k,e_k)

Constraints: 10 <= N <= 20, N/2 <= M <= 2N, 1 <= T <= 2 N^2 M. All ball and basket cells are distinct.

Output format (stdout)

Print the button sequence, one character per line or all on lines with no spaces — any whitespace layout is fine; only the characters F R L S M P are read, in order. The output length A must be <= T.

What you submit

Your solver lives in methods/main/ (the graded directory), containing:

• run.sh (required): run once per test case as bash run.sh < instance.txt > out.txt. It must read one instance on stdin and write the button sequence on stdout. Any language.
• build.sh (optional): if present, the grader runs it once before grading (e.g. to compile a C++ solver). Do your compilation here and have run.sh exec the built binary.

The starter methods/main/run.sh runs the shipped greedy baseline (methods/main/solution.py). Replace it with your solver.

Local dev bench

• tools/in/ — the 100 visible instances (seeds 0-99).
• tools/gen — the official generator. Make more instances with ./tools/gen seeds.txt --dir=OUTDIR where seeds.txt is one unsigned-64-bit seed per line. For local testing use seeds in 0..10000 only — the sealed grading seeds live far outside that range, so staying inside it keeps your practice set from colliding with the hidden set.
• tools/vis — the official visualiser/judge: ./tools/vis in.txt out.txt prints Score = <absolute score> and writes a vis.html you can open.
• python3 selfcheck.py [N] — runs your run.sh on the first N visible cases (default 100), prints each case's raw score alongside the reference solver's raw score on the same case. Free and unlimited.

The generator, the distribution, and the visualiser are exactly the contest's. The sealed evaluation reruns your run.sh on 200 fresh sealed instances from the same generator and scores them with the same visualiser; there is no feedback loop — whatever sits in methods/main/ at the end is what is graded.

Notes

• CPU only, no network. Python 3 and g++ are available in both the workbench and the grader.
• Each sealed case runs your run.sh under a wall-clock cap (20 s/case); a crash, timeout, malformed output, or a case that fails to deliver all balls scores that case's rel at ~0. Complete every case first, then optimise length.
• The reference contest was a 2-second-per-case time limit; you have more slack here, but the aggregate is dominated by macro quality, not raw search time.