You are given the following:

• An integer $N$
• An integer $X$
• An integer $Y$
• An array $A$ of $N$ elements
• An array $B$ of $N$ elements

Find the number of pairs of $(i, j)$ such that:

• $(A[i] \text{^}B[j])\&X = (A[i] \text{^}B[j])\&Y$,  where ^ represents bitwise XOR operator and & represents bitwise AND operator.
• $1 \le i, j \le N$

Note: Assume $1$-based indexing.

Input

• The first line contains a single integer $T$ that denotes the number of test cases. 
• For each test case:
  • The first line contains an integer $N$.
  • The second line contains an integer $X$.
  • The third line contains an integer $Y$.
  • The next line contains $N$ space-separated integers denoting array $A$.
  • The next line contains $N$ space-separated integers denoting array $B$.

Output format

For each test case, print the number of pairs $(i, j)$ that satisfy the conditions in a new line.

Constraints

$1 \le T \le 10 \\ 1 \le N \le 10^5 \\ 1 \le X, Y \le 10^6 \\ 0 \le A[i], B[i] \le 10^6$