You are given an undirected^{1} tree with each of its nodes assigned a magic .

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 and is .

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 , the number of nodes in the tree.

Each of the following lines contains two integers, and , the labels of nodes connected with an edge.

The of the following lines contains the integer , magic of the node.

#### Output Specification

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

In all test cases, it will hold that the required and are smaller than .

#### Scoring

In test cases worth 3 points total, it will hold .

In test cases worth 4.5 additional points total, there will not be a node that is connected to more than 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 , so the entire path's magic is .

#### 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 and is of magic .

That is also the path with the minimal possible magic.

^{1}An *undirected tree* is a connected graph that consists of nodes and 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.

## Comments

I believe it should be instead of .

Fixed