This is an interactive problem. Seferoglu lives in a small coastal city called Samsun, a city where not many people study competitive programming. Whenever an event takes place, he has to travel to far cities where he can meet his friends. Since he is tired of calculating the length of his journey exactly each time, he is just curious about the maximum distance he will ever have to travel between two cities in the worst case scenario. Your task is to help him find this distance while keeping the amount of web searches he has to make small. There is a hidden tree(^{\text{∗}}) with (n) vertices. You can make queries. In one query, you choose two vertices (1 \le u, v \le n) and an integer (0 \le d \le n); the grader responds with (1) if (\operatorname{dist}(u, v) \ge d) and (0) otherwise. Here, (\operatorname{dist}(u,v)) denotes the distance(^{\text{†}}) between vertices (u) and (v) in the tree. Your task is to determine the diameter's length(^{\text{‡}}) of the tree and any pair of nodes that are this distance apart. You may ask at most (3 \cdot n) queries. (^{\text{∗}})A tree is a connected graph without cycles. (^{\text{†}})The distance between two nodes in a tree is the number of edges in the unique simple path between these nodes. (^{\text{‡}})The diameter's length is the largest distance between two vertices. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 500)). The description of the test cases follows. The first line of each test case contains (n) ((2 \le n \le 1000)), denoting the number of vertices in the tree. It is guaranteed that the sum of (n) over all test cases does not exceed (1000). To make a query, first pick (u), (v) and (d) ((1 \le u, v \le n), (0 \le d \le n)), a pair of nodes and a constant to check the distance between them against, and output the following line (without