Tree Reading

A tree with $V$ vertices is given. The vertices are numbered from $1$ to $V$. Vertex $i$ has a digit $S_i$, which is one of the numbers from $1$ to $9$.

For vertices $a$ and $b$ of the tree, let $f(a, b)$ be the decimal integer formed by writing down the digits on the vertices of the shortest path from vertex $a$ to vertex $b$, in path order. For example, if vertices $1$, $2$, and $3$ have the numbers $3$, $4$, and $1$, and the shortest path from vertex $1$ to vertex $2$ is $1 \rightarrow 3 \rightarrow 2$, then $f(1, 2) = 314$.

Find the sum of $f(a, b)$ over all possible integer pairs $(a, b)$ ($1 \le a, b \le V$), modulo $1\,000\,000\,007$.

The first line contains $V$. ($1 \le V \le 200\,000$)

The second line contains $S_1, \cdots, S_V$, separated by spaces. ($1 \le S_i \le 9$)

Each of the next $V-1$ lines contains two vertex numbers $x$ and $y$, separated by a space, meaning that vertices $x$ and $y$ are connected by an edge. ($1 \le x, y \le V$)

All numbers in the input are integers.

Print the answer on the first line.