There is a hidden tree with (n) vertices. The (n-1) edges of the tree are numbered from (1) to (n-1). You can ask the following queries of two types: Give the grader an array (a) with (n - 1) positive integers. For each edge from (1) to (n - 1), the weight of edge (i) is set to (a_i). Then, the grader will return the length of the diameter(^\dagger). Give the grader two indices (1 \le a, b \le n - 1). The grader will return the number of edges between edges (a) and (b). In other words, if edge (a) connects (u_a) and (v_a) while edge (b) connects (u_b) and (v_b), the grader will return (\min(\text{dist}(u_a, u_b), \text{dist}(v_a, u_b), \text{dist}(u_a, v_b), \text{dist}(v_a, v_b))), where (\text{dist}(u, v)) represents the number of edges on the path between vertices (u) and (v). Find any tree isomorphic(^\ddagger) to the hidden tree after at most (n) queries of type 1 and (n) queries of type 2 in any order. (^\dagger) The distance between two vertices is the sum of the weights on the unique simple path that connects them. The diameter is the largest of all those distances. (^\ddagger) Two trees, consisting of (n) vertices each, are called isomorphic if there exists a permutation (p) containing integers from (1) to (n) such that edge ((u), (v)) is present in the first tree if and only if the edge ((p_u), (p_v)) is present in the second tree. The first and only line of input contains a single integer (n) ((3 \le n \le 1000)) — the number of vertices in the tree. Begin the interaction by reading (n). You are allowed to make queries in the following way: "(\mathtt{?}\,1\,a_1\,a_2 \ldots a_{n-1})" ((1 \le a_i \le 10^9)). Then, you should read an integer (k) which represents the length of the diameter. You are only allowed to ask this query at most (n) times. "(\mathtt{?}\,2\,a\,b)" (