Mihai and Slavic were looking at a group of $$$n$$$ frogs, numbered from $$$1$$$ to $$$n$$$, all initially located at point $$$0$$$. Frog $$$i$$$ has a hop length of $$$a_i$$$.

Each second, frog $$$i$$$ hops $$$a_i$$$ units forward. Before any frogs start hopping, Slavic and Mihai can place exactly one trap in a coordinate in order to catch all frogs that will ever pass through the corresponding coordinate.

However, the children can't go far away from their home so they can only place a trap in the first $$$n$$$ points (that is, in a point with a coordinate between $$$1$$$ and $$$n$$$) and the children can't place a trap in point $$$0$$$ since they are scared of frogs.

Can you help Slavic and Mihai find out what is the maximum number of frogs they can catch using a trap?

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.

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.

We Were Both Children

Examples