You are given an array of size N, denoting capacity of N boxes, and an integer K, denoting extended capacity factor. You are also given the weights of M balls. Each $i^{th}$ box can accommodate exactly one ball having weight in range $[capacity_i, capacity_i+K]$ (both inclusive). Find the maximum number of boxes that can be filled.

Constraints:

• $1 ≤ T ≤ 50$
• $1 ≤ N,M ≤ 10000$
• $1 ≤ K ≤ 1000$
• $1 ≤ Capacity_i ≤ 1000$
• $1 ≤ Weight_i ≤ 2000$

Input format:
First line: T i.e. Number of test cases.
For each test case:
First line: Three space-separated integers N, M and K.
Second line: N space-separated integers denoting the capacity of boxes.
Third line: M space-separated integers denoting the weight of balls.

Output format:
For each test case, print the answer in a separate line.