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If you want to make an array problem harder — solve it on a tree. If you want to make a tree problem harder — solve it on a cactus
NEERC featured a number of problems in previous years about cactuses — connected undirected graphs in which every edge belongs to at most one simple cycle. Intuitively, a cactus is a generalization of a tree where some cycles are allowed. An example of a cactus from NEERC 2007 problem is given on the picture below.
You are playing a game on a cactus with Chloe. You are given a cactus. Chloe had secretly picked one vertex v from the cactus and your goal is to find it. You can make at most 10 guesses. If your guess is vertex v — you win. Otherwise, if your guess is another vertex u — Chloe helps you and tells you some vertex w which is adjacent to u and such that the distance from w to v is strictly less than the distance from u to v (here the distance is the number of edges in the shortest path between vertices).
First, the testing system writes a line with two integers n and m (1 ≤ n ≤ 500; 0 ≤ m ≤ 500). Here n is the number of vertices in the graph. Vertices are numbered from 1 to n. Edges of the graph are represented by a set of edge-distinct paths, where m is the number of such paths. Each of the following m lines contains a path in the graph. A path starts with an integer ki (2 ≤ ki ≤ 500) followed by ki integers from 1 to n. These ki integers represent vertices of a path. Adjacent vertices in a path are distinct. The path can go to the same vertex multiple times, but every edge is traversed exactly once in the whole input. The graph in the input is a cactus.
To prove that your program can find a secret vertex in at most 10 queries, you need to do that n times. Each time testing system picks some vertex before interacting with your program. Your program makes guesses by writing lines with a single number u (1 ≤ u ≤ n).
Testing system responds by writing lines with one of the two responses:
Do not forget to flush the output after each guess!
5 2 5 1 2 3 4 5 2 1 3 FOUND GO 4 FOUND GO 2 FOUND GO 1 FOUND GO 4 GO 5 FOUND
3 3 4 3 2 3 1 3 4 5
Empty lines are added to the standard input and the standard output examples for clarity only. They are not present during the actual interaction.