CF23E.Tree

Recently Bob invented a new game with a tree (we should remind you, that a tree is a connected graph without cycles): he deletes any (possibly, zero) amount of edges of the tree, and counts the product of sizes of the connected components left after the deletion. Your task is to find out the maximum number that Bob can get in his new game for a given tree.

最近，鲍勃发明了一种基于树的新游戏（需要提醒您：树是一种无环的连通图）：他删除树中的任意数量（可能为零）的边，并计算删除后剩余各连通分量大小的乘积。您的任务是：对于给定的树，求出鲍勃在该新游戏中所能得到的最大数值。

The first input line contains integer number n (1 ≤ n ≤ 700) — amount of vertices in the tree. The following n - 1 lines contain the description of the edges. Each line contains the pair of vertices' indexes, joined by an edge, a__i, b__i (1 ≤ a__i, b__i ≤ n). It's guaranteed that the graph described in the input is a tree.

第一行输入包含一个整数 $ n $（$ 1 \leq n \leq 700 $）——树中顶点的数量。接下来的 $ n-1 $ 行描述了树的边。每行包含由一条边连接的两个顶点的下标 $ a_i $、$ b_i $（$ 1 \leq a_i, b_i \leq n $）。保证输入所描述的图是一棵树。

Output the only number — the maximum product of sizes of the connected components, that Bob can get after deleting some of the tree's edges.

输出唯一的一个数字——鲍勃在删除树中的若干条边后，所能得到的连通块大小乘积的最大值。