A14037. Distinctive Roots in a Tree

You are given a tree with $n$ vertices. Each vertex $i$ has a value $a_i$ associated with it.

Let us root the tree at some vertex $v$ . The vertex $v$ is called a distinctive root if the following holds: in all paths that start at $v$ and end at some other node, all the values encountered are distinct. Two different paths may have values in common but a single path must have all distinct values.

Find the number of distinctive roots in the tree.

The first line of the input contains a single integer $n$ ( $1 \le n \le 2\cdot10^5$ ) — the number of vertices in the tree.

The next line contains $n$ space-separated integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^9$ ).

The following $n-1$ lines each contain two space-separated integers $u$ and $v$ ( $1 \le u$ , $v \le n$ ), denoting an edge from $u$ to $v$ .

It is guaranteed that the edges form a tree.

Print a single integer — the number of distinctive roots in the tree.

In the first example, $1$ , $2$ and $5$ are distinctive roots.