Confuzzle

You are given an unweighted tree with $N$ vertices. The distance between two vertices in the tree is defined as the number of edges on the path between them.

Each vertex has a number written on it, and at least two vertices are guaranteed to have the same number. Find the smallest possible distance between a pair of vertices that have the same number written on them.

The first line contains the number of vertices in the tree, $N$. ($2 \leq N \leq 100\ 000$)

The second line contains $N$ integers $c_1, c_2, \cdots, c_N$, the distinct values of the vertices. ($1 \leq c_i \leq N$)

The next $N - 1$ lines each contain two integers $u$ and $v$ describing an edge of the tree. This means that an edge connects vertex $u$ and vertex $v$. ($1 \leq u, v \leq N$, $u \neq v$)

Print the smallest distance between a pair of vertices that have the same value.