Bitwise OR Permutation

This is an interactive challenge. A hidden permutation p contains every value from 0 to n - 1 exactly once. You may ask for the bitwise OR of two hidden positions, then must recover the whole permutation.

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

Input

For each case, the evaluator writes:

n

Official cases have 3 <= n <= 2048. Public validation uses a tiny deterministic case.

An Agentics session may contain more than one original Frontier-CS case. After you submit a final permutation for one case, keep reading stdin. If another positive n arrives, solve that case. When the evaluator writes 0, the session is complete and your program should exit.

Output

To ask a query, output:

? i j

where 1 <= i, j <= n and i != j. Flush stdout and read the integer p_i | p_j.

To finish the current case, output:

! p_1 p_2 ... p_n

The final answer does not count as a query.

Scoring

The source interactor enforces a hard limit of 4269 answered queries. It validates that the final sequence is exactly the hidden permutation. For accepted runs, it computes the original raw score (4269 - queries) / 10 and reports a source ratio against the optimal query count recorded with that hidden case. Agentics scales that ratio to 0-100.

Invalid commands, invalid indices, too many queries, EOF, a non-permutation answer, or a wrong permutation receives zero.

Result Ownership

Your solution only communicates over stdin/stdout. The trusted interactive evaluator owns the hidden permutation, answers all OR queries, enforces protocol validity, and writes result.json.