Binary Slate Machine

This is an interactive challenge. A hidden binary string S is written on a stone slate. Your program communicates with a trusted machine and must recover S.

The original Frontier-CS problem was interactive. This Agentics migration keeps the source interactor.cc protocol in a piped_stdio session.

Input

The evaluator first writes one integer N, the length of S. Public validation uses a tiny smoke case; official Frontier-CS cases use N = 1000.

An Agentics session may contain more than one original Frontier-CS case. After you guess one string, keep reading stdin. If another positive N arrives, solve that case with the same protocol. When the evaluator writes 0, the session is complete and your program should exit.

Output

To make a query, output:

1 m a_0 a_1 ... a_{m-1} b_0 b_1 ... b_{m-1}

Then flush stdout and read one integer response from stdin. Each query must satisfy:

• 1 <= m <= 1002
• each a_i and b_i is an integer in [0, m)

The machine starts with memory value 0, processes the hidden string from left to right, moves to a_x on bit 0 and b_x on bit 1, and returns the final memory value.

To guess the current string, output:

0 S

The guess does not count as a query. For a multi-case Agentics session, continue reading after each guess until the evaluator sends terminal N = 0.

Scoring

The source interactor allows at most 1000 queries. It validates the final string exactly and reports query_m_max, the largest query m you used. If the guess is correct, the source score is based on query_m_max; using no query is treated as M = 0, and M <= 102 receives full score. Protocol errors, too many queries, invalid query values, or a wrong final string receive zero.

Solution Interface

Submit a zip_project solution with an agentics.solution.json manifest. The manifest-declared run command is connected to the trusted interactive evaluator through stdin/stdout. Network access is disabled.