Chef and his mother are going travelling. Chef's world consists of $N$ cities (numbered $1$ through $N$) connected by $N-1$ bidirectional roads such that each city can be reached from any other city using roads. For each city, we know its age — the number of years elapsed since the foundation of the city; let's denote the age of city $i$ by $a_i$.
First of all, Chef and his mother have to decide what city they should visit first. Suppose that Chef chooses a city $c_c$ and his mother chooses a (not necessarily different) city $c_m$. The difference of their choices is the number of different bits in the binary representations of $a_{c_c}$ and $a_{c_m}$.
Chef will not argue with his mother if the parity of this difference is not equal to the parity of the length of the shortest path between cities $c_c$ and $c_m$ (the number of roads on the shortest path between them). Find the number of ways to choose the cities $c_c$ and $c_m$ such that Chef avoids quarreling with his mother.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- Each of the following $N-1$ lines contains two space-separated integers $A$ and $B$ denoting a road between cities $A$ and $B$.
- The last line contains $N$ space-separated integers $a_1, a_2, \dots, a_N$.

-----Output-----
For each test case, print a single line containing one integer — the number of valid pairs $c_c, c_m$.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 10^5$
- $1 \le A, B \le N$
- $0 \le a_i \le 10^9$ for each valid $i$

-----Sample Input-----
1
3
1 2
1 3
1 2 3

-----Sample Output-----
2

-----Explanation-----
Example case 1: The two possible choices are $c_c=2, c_m=3$ (their binary representations differ by one bit, the shortest path has length $2$) and $c_c=1, c_m=2$ (there are two different bits in their binary representations and the shortest path has length $1$).

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