Toy Train Loop Rotation

Ported from Frontier-CS algorithmic/problems/156.

Task

Rotate railway tiles to form two large loop lines.

Each run sends the original problem input to standard input. Your solution must write the original problem output format to standard output.

The expected output format and constraints follow the original Frontier-CS statement for algorithmic/problems/156. The separated evaluator runs the original Frontier-CS checker as trusted evaluator code, validates output shape and task constraints, then computes a normalized score against evaluator-owned reference data.

Scoring

The primary metric is score, an average normalized Frontier-CS checker score on a 0-100 scale. Invalid outputs receive zero for that case. The public validation case is intentionally small and deterministic; official cases and reference answers are private.