Time Limit: 20000/10000MS (Java/Others) Memory Limit: 128000/64000KB (Java/Others)

#### Problem Description

Vertex cactus is a connected undirected graph in which every vertex lies on at most one simple cycle. A tree can be converted to a vertex cactus by adding zero or more edges to it. There can be several ways to convert a tree to cactus. The number of ways to do so determines the cactusability of a tree.

For example, the cactusability of the tree on the left picture is 12. The twelve cactuses that it can be converted to are shown on the right.

Given a tree, you have to find its cactusability.

#### Input

The first line of the input file contains one integer number n — the number of vertices in a tree (1 ≤ n ≤ 200). The next n − 1 lines contain edges of a tree.

#### Output

Write to the output file a single integer number — the cactusability of the given tree.

#### Sample Input

#### Sample Output

#### Hint

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#### Source

Andrew Stankevich Contest 16

#### Manager