# Problem E

Mag

You are given an undirected tree^{1} with
each of its node assigned a magic $X_ i$. The magic of a path^{2} is defined as the product of the
magic of the nodes on that path divided by the number of the
nodes on the path. For example, the magic of a path that
consists of nodes with magic $3$ and $5$ is $7.5$ ($3\cdot 5 / 2$). In the given tree,
find the path with the minimal magic and output the magic of
that path.

## Input

The first line of input contains the integer $N$ ($1 \leq N \leq 10^6$), the number of nodes in the tree. Each of the following $N - 1$ lines contains two integers, $A_ i$ and $B_ i$ ($1 \leq A_ i, B_ i \leq N$), the labels of nodes connected with an edge. The $i$-th of the following $N$ lines contains the integer $X_ i$ ($1 \leq X_ i \leq 10^9$), magic of the $i$-th node.

## Output

Output the magic of the path with minimal magic in the form of a completely reduced fraction $P/Q$ ($P$ and $Q$ are relatively prime integers).

In all test cases, it will hold that the required $P$ and $Q$ are smaller than $10^{18}$.

Sample Input 1 | Sample Output 1 |
---|---|

2 1 2 3 4 |
3/1 |

Sample Input 2 | Sample Output 2 |
---|---|

5 1 2 2 4 1 3 5 2 2 1 1 1 3 |
1/2 |

**Footnotes**

- An undirected tree is a connected graph that consists of $N$ nodes and $N - 1$ undirected edges.
- A path in a graph is a finite sequence of edges which connect a sequence of vertices which are all distinct from one another.