Two Paths

给定一个无向图，含有一定的路。从中找出两个最长的路径（每条路径有一些相通路组成）这两个路径不能经过公共的点，求何时二路径的乘积最大。 本题给出的无向图是一棵树，每边权值为 $1$。 原文翻译应为有 $n$ 个点，$n - 1$ 条边，两点之间能够相互到达。 感谢 @Sagittarius 补充翻译

As you know, Bob's brother lives in Flatland. In Flatland there are $ n $ cities, connected by $ n-1 $ two-way roads. The cities are numbered from 1 to $ n $ . You can get from one city to another moving along the roads. The «Two Paths» company, where Bob's brother works, has won a tender to repair two paths in Flatland. A path is a sequence of different cities, connected sequentially by roads. The company is allowed to choose by itself the paths to repair. The only condition they have to meet is that the two paths shouldn't cross (i.e. shouldn't have common cities). It is known that the profit, the «Two Paths» company will get, equals the product of the lengths of the two paths. Let's consider the length of each road equals 1, and the length of a path equals the amount of roads in it. Find the maximum possible profit for the company.

The first line contains an integer $ n $ ( $ 2<=n<=200 $ ), where $ n $ is the amount of cities in the country. The following $ n-1 $ lines contain the information about the roads. Each line contains a pair of numbers of the cities, connected by the road $ a_{i},b_{i} $ ( $ 1<=a_{i},b_{i}<=n $ ).

Output the maximum possible profit.

4
1 2
2 3
3 4

1

7
1 2
1 3
1 4
1 5
1 6
1 7

0

6
1 2
2 3
2 4
5 4
6 4

4