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:

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