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

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