In a country, the relationship between people can be indicated by a tree. If two people are acquainted with each other, there will be an edge between them. If a person can get in touch with another through no more than five people, we should consider these two people can become friends. Now, give you a tree of N people’s relationship. ( 1 <= N <= 1e5), you should compute the number of who can become friends of each people?

In the first line, there is an integer T, indicates the number of the cases.

For each case, there is an integer N indicates the number of people in the first line.

In the next N-1 lines, there are two integers u and v, indicate the people u and the people

v are acquainted with each other directly. People labels from 1.

For each case, the first line is “Case #k :”, k indicates the case number.

In the next N lines, there is an integer in each line, indicates the number of people who can become the ith person’s friends. i is from 1 to n.