Path Magic

You are given an undirected tree in which every node has a magic value. Node $i$ has magic $X_i$.

The magic of a path is the product of the magic values of the nodes on that path, divided by the number of nodes on the path. For example, a path made of a node with magic 3 and a node with magic 5 has magic $3 \times 5 / 2 = 7.5$.

Find the path with the smallest magic in the given tree and print the magic of that path.

The first line contains the number of nodes $N$ ($1 \le N \le 10^6$).

Each of the next $N-1$ lines contains the labels $A_i$ and $B_i$ of two nodes joined by an edge ($1 \le A_i, B_i \le N$).

The $i$-th of the next $N$ lines contains the magic $X_i$ of node $i$ ($1 \le X_i \le 10^9$).

The given graph is always a tree.

Print the magic of the path with the smallest magic on one line, as a fully reduced fraction P/Q. $P$ and $Q$ are coprime positive integers, and the denominator is written out even when it is 1. In every test case $P$ and $Q$ are smaller than $10^{18}$.

A path may start and end at the same node, so a path made of a single node is also a candidate.