You are given an undirected¹ tree with each of its nodes 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 $7.5$ $(\frac{3\times 5}{2})$.

In the given tree, find the path with the minimal magic and output the magic of that path.

Input Specification

The first line of input contains the integer $N$ $(1\le N\le {10}^6)$, the number of nodes in the tree.
Each of the following $N-1$ lines contains two integers, $A_i$ and $B_i$ $(1\le A_i,B_i\le N)$, the labels of nodes connected with an edge.
The $i^{\text{th}}$ of the following $N$ lines contains the integer $X_i$ $(1\le X_i\le {10}^9)$, magic of the $i^{\text{th}}$ node.

Output Specification

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

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

Scoring

In test cases worth 3 points total, it will hold $N\le 1000$.
In test cases worth 4.5 additional points total, there will not be a node that is connected to more than $2$ other nodes.

Sample Input 1

2
1 2
3
4

Sample Output 1

3/1

Explanation for Sample Output 1

Notice that the path may begin and end in the same node. The path with the minimal magic consists of the node with magic $3$, so the entire path's magic is $\frac{3}{1}$.

Sample Input 2

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

Sample Output 2

1/2

Explanation for Sample Output 2

The path that consists of nodes with labels $2$ and $4$ is of magic $\frac{1\times 1}{2}=\frac{1}{2}$.

That is also the path with the minimal possible magic.

¹An undirected tree is a connected graph that consists of $N$ nodes and $N-1$ undirected edges.

²A path in a graph is a finite sequence of edges which connect a sequence of vertices which are all distinct from one another.