Hide

# Problem EMag

You are given an undirected tree1 with each of its node assigned a magic $X_ i$. The magic of a path2 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

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