Bob is a brilliant student in the class, so his teacher assigned him a problem. He has been given an array \(A\) containing \(N\) positive integers and two integers \(U\) and \(V\). He has been asked to find the number of magic pairs of array indices.

A pair of integers \((i, j)\) is called a magic pair if \(i < j\) and \(U ≤ A[i] \text{^} A[j] ≤ V\) where \(\text{^}\) denotes the bitwise XOR operation.

Help Bob to find the number of magic pairs in the given array.

Input Format:

The first line contains a single integer \(T\) denoting the number of test cases.
The first line of each test case contains the integers \(N\), \(U\), and \(V\) separated by spaces.
The second line of each test case contains \(N\) spaced integers, the elements of the array \(A\).

Output Format:

For each test case, print the number of magic pairs in the given array.

Constraints:

\(1 \leq T \leq 10 \\ 1 \leq N \leq 10^4 \\ 0 \leq A[i] \leq 10^9 \\ 0 \leq U \leq V \leq 10^9\)