HackerLand is a tree consisting of cities connected by undirected roads where each road has length . Ann, Bob, and Clara are whistleblowing citizens living in secret. You want to track them down for an interview using the following pieces of information:

• They live in three different cities expressed as some unordered triplet, , where , , and are the three different cities where Ann, Bob, and Clara live.

  We consider two unordered triplets to be different if one triplet contains an integer not present in the other triplet. For example, and are the same because they both contain the same exact elements, but and are different because both triplets differ by one value.

• The distances between cities , , and form another unordered triplet, , that reduces to , where , , and are given values and is any real number.

For example, suppose , , , and HackerLand looks like this:

In this example, it's possible for Ann, Bob, and Clara to live in cities defined by the unordered triplet , and we express the distances between these cities as . If , then we can rewrite as ; note that because these are unordered triplets, is the same as .

Given , , , and a map of HackerLand, calculate and print the number of different unordered triplets that correspond to the possible locations of Ann, Bob, and Clara.