As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:
Yuta has a non-direct graph with n vertices and n+1 edges. Rikka can choose some of the edges (at least one) and delete them from the graph.
Yuta wants to know the number of the ways to choose the edges in order to make the remaining graph connected.
It is too difficult for Rikka. Can you help her?
Input
The first line contains a number $T(T \leq 30)$¡ª¡ªThe number of the testcases.
For each testcase, the first line contains a number $n(n \leq 100)$.
Then n+1 lines follow. Each line contains two numbers $u,v$ , which means there is an edge between u and v.
