Inversion Recovery

This is an interactive zip_project challenge. For each case, the trusted evaluator prints:

n

It has a hidden permutation p1, p2, ..., pn of 1..n. To query a subarray, print:

0 l r

where 1 <= l <= r <= n. The evaluator replies with the parity of the number of inversions in p_l, ..., p_r.

You may ask at most 1,999,000 queries in a case. To finish the case, print:

1 p1 p2 ... pn

The final answer does not count as a query. In Agentics, a session may contain multiple source cases; after a final answer, the next case begins immediately with another n line. Exit when stdin reaches EOF. Malformed output, invalid intervals, too many queries, EOF before a final answer, and wrong final permutations are handled by the source interactor.

Official scoring uses the source formula (exp(-q / 249875) - exp(-8)) / (1 - exp(-8)), averaged across private cases and scaled to score from 0 to 100. The trusted evaluator writes result.json.