18498번 - Interactive Algorithm 다국어인터랙티브

This is an interactive problem.

I have a hidden permutation p₁, p₂, . . . , p_n. You are to guess it.

You can make some queries. In one query you tell me a permutation q₁, q₂, . . . , q_n of length n, and I reply you with similarity of permutations p and q.

The similarity of two permutations is defined as follows. Let w₁, w₂, . . . , w_n be a permutation, then define N(w) as the set of unordered pairs of adjacent elements in w. For example, N([4, 1, 3, 2]) = {{1, 4}, {1, 3}, {2, 3}}. This way, the similarity of p and q is the size of N(p) ∩ N(q).

You can make at most 25 000 queries. Note that no algorithm in the world can distinguish between p and reversed p, so both of these permutations will be accepted as correct answer.

This time I will not mess with you and will not change the hidden permutation. Though I could. You should be thankful, really.

Initially you get a single line with a single integer n (2 ≤ n ≤ 400) — the size of the hidden permutation.

When you know the hidden permutation, print an exclamation mark “!” and then n integers p₁, p₂, . . . , p_n, or p_n, p_n−1, . . . , p₁.

This does not count towards query limit.