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 1\,000~.
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.