Hotels

Byteotia has $n$ towns connected by $n-1$ roads of equal length. The roads form a tree.

The king wants three luxury hotels in three different towns, all at the same pairwise distance. Count how many such triplets exist.

The first line contains $n$ ($1 \le n \le 5000$). Each of the next $n-1$ lines contains two integers $a$ and $b$ ($1 \le a \le b \le n$), the endpoints of a road.

Print the number of valid hotel triplets.