Permutation Segment Geemu

This is an interactive challenge. The evaluator hides a permutation p of length n. You may query how many value-contiguous segments appear in a current interval and may swap positions in the current hidden state. Your final report must match the current permutation or the source-accepted reverse-value equivalent.

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

Input

For each source case, the evaluator writes:

n l1 l2

where l1 is the maximum number of ask operations and l2 is the maximum number of swap operations. Public validation uses a tiny smoke case; official evaluation uses private Frontier-CS cases.

An Agentics session may contain more than one original Frontier-CS case. After you report one permutation, keep reading stdin. If another positive n l1 l2 arrives, solve that case with the same protocol. When the evaluator writes 0 0 0, the session is complete and your program should exit. EOF before the terminal marker should also be treated as the end of interaction.

Output

To query the number of value-contiguous segments in the current interval [l, r], output:

1 l r

Then flush stdout and read one integer response from stdin.

To swap positions i and j in the current hidden permutation, output:

2 i j

Then flush stdout and read confirmation 1.

To submit the current permutation, output:

3 p_1 p_2 ... p_n

The report must be a valid permutation. The source interactor accepts either the current permutation or the value-reversed permutation n - p_i + 1.

Scoring

Let s1 be the number of ask operations and s2 be the number of swap operations. The source interactor returns zero if s1 > l1, s2 > l2, the command is malformed, or the reported permutation is invalid or wrong. Otherwise the source ratio is min((r1 + r2 + 1) / (s1 + s2 + 1), 1), where r1 and r2 are the private reference costs from the source answer file. Agentics reports the average source ratio as score from 0 to 100.

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.