We Were Both Children

Description:

Input:

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$) — the number of frogs, which equals the distance Slavic and Mihai can travel to place a trap.

The second line of each test case contains $$$n$$$ integers $$$a_1, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10^9$$$) — the lengths of the hops of the corresponding frogs.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case output a single integer — the maximum number of frogs Slavic and Mihai can catch using a trap.

Sample Input:

7
5
1 2 3 4 5
3
2 2 2
6
3 1 3 4 9 10
9
1 3 2 4 2 3 7 8 5
1
10
8
7 11 6 8 12 4 4 8
10
9 11 9 12 1 7 2 5 8 10

Sample Output:

3
3
3
5
0
4
4

Note:

In the first test case, the frogs will hop as follows:

• Frog 1: $$$0 \to 1 \to 2 \to 3 \to \mathbf{\color{red}{4}} \to \cdots$$$
• Frog 2: $$$0 \to 2 \to \mathbf{\color{red}{4}} \to 6 \to 8 \to \cdots$$$
• Frog 3: $$$0 \to 3 \to 6 \to 9 \to 12 \to \cdots$$$
• Frog 4: $$$0 \to \mathbf{\color{red}{4}} \to 8 \to 12 \to 16 \to \cdots$$$
• Frog 5: $$$0 \to 5 \to 10 \to 15 \to 20 \to \cdots$$$

Therefore, if Slavic and Mihai put a trap at coordinate $$$4$$$, they can catch three frogs: frogs 1, 2, and 4. It can be proven that they can't catch any more frogs.

In the second test case, Slavic and Mihai can put a trap at coordinate $$$2$$$ and catch all three frogs instantly.