Mystery Tree

**This is an interactive problem.** You are given a tree with $N$ vertices (numbered $1$ through $N$). Each vertex has a value; let's denote the value of vertex $i$ by $a_i$. Vertex $v$ is a *bad adjacent* of vertex $u$ if there is an edge between vertices $u$ and $v$ and $a_v$ is strictly greater than $a_u$. Your task is to find a vertex without any bad adjacent or determine that there is no su