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:

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