P1411 Tree

L invented a game related to trees.

He deletes any number (possibly $0$) of edges from the tree and computes the product of the sizes of all connected components after the deletions. L scores that many points. Your task is, for a given tree, to find the maximum score L can obtain.

The first line contains an integer $n$, the number of nodes in the tree. The next $(n-1)$ lines each contain two integers $u, v$, indicating that there is an edge connecting $u$ and $v$.

Output a single integer, the maximum score L can obtain.

#### Constraints - For $10\%$ of the testdata, $n \leq 5$. - For $30\%$ of the testdata, $n \leq 100$. - For another $30\%$ of the testdata, the given tree is a path. - For $100\%$ of the testdata, $1 \leq n \leq 700$, $1 \leq u, v \leq n$. Translated by ChatGPT 5