Lamp Ring Permutation

The judge owns a hidden cyclic permutation p_1, ..., p_n of lamp labels. It also owns a hidden set S of currently lit lamp positions, initially empty.

At session start the evaluator writes two integers:

subtask n

To query, write one line with L followed by L labels in [1, n], then flush. The evaluator toggles those labels in order. After each toggle it returns 1 if the current lit set contains an adjacent pair on the hidden cycle, otherwise 0; all L response bits are returned in order on one line. The lit set is not reset between queries.

To answer the current case, write -1 followed by a permutation of all n labels, then flush. Any cyclic shift or reversal of the hidden cycle is accepted. The answer line does not count as a query.

Agentics may chain multiple source test files in one stdin/stdout session. After a correct final answer, keep reading: another positive subtask n starts the next case, while 0 0 means the session is complete and your program should exit. EOF before a final answer, malformed integers, out-of-range labels, excessive query rounds, excessive total operations, or an incorrect final permutation receive zero from the trusted evaluator. The trusted evaluator writes result.json; participant code must only speak the protocol above.

The score is the original Frontier-CS ratio based on query rounds and total toggles, scaled to score from 0 to 100.