Problem D
Mag

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 $10^{18}$.

2
1 2
3
4

3/1

5
1 2
2 4
1 3
5 2
2
1
1
1
3

1/2