This is an interactive problem. Faker is being naughty again. You asked him to create a nice query problem, but he created an interactive problem where he is answering a query instead! Faker hid a permutation from you, and you have to infer some interesting information by interacting with him. You are given an integer (n). Faker hid a hidden permutation(^{\text{∗}}) (p_1, p_2, \ldots, p_{n^2+1}) of length (n^2+1). Your goal is to find a monotone subsequence (either increasing or decreasing) of the hidden permutation, with length exactly (n+1). It can be proved that every permutation of length (n^2 + 1) contains a monotone subsequence of length (n+1). For more information about the proof, you can check out this Wikipedia page . To find it, you can make at most (n) skyscraper queries to the interactor, which is defined as follows: You provide a set of (k) indices as a strictly increasing sequence: (i_1, i_2, \ldots, i_k). The interactor considers the values of the hidden permutation at these indices: (p_{i_1}, p_{i_2}, \ldots, p_{i_k}). The interactor then returns the indices corresponding to the visible skyscrapers from this set. An index (i_j) is visible if its value (p_{i_j}) is greater than the values of all preceding elements in your query, i.e., (p_{i_j} > p_{i_m}) for all (1 \le m < j). This is equivalent to finding the indices of the left-to-right maxima of the sequence ((p_{i_1}, \ldots, p_{i_k})). After making at most (n) queries, you must report a valid monotone subsequence of length exactly (n+1). Note that the permutation (p) is fixed before any queries are made and does not depend on the queries. (^{\text{∗}})A permutation of length (m) is an array consisting of (m) distinct integers from (1) to (m) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and $$$