CF1850F.We Were Both Children

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?

米海和斯拉维克正在观察一群 $n$ 只青蛙，编号从 $1$ 到 $n$，所有青蛙初始时均位于坐标点 $0$。青蛙 $i$ 的单次跳跃长度为 $a_i$。

每一秒，青蛙 $i$ 向前跳跃 $a_i$ 个单位长度。在任何青蛙开始跳跃之前，斯拉维克和米海可以在某个坐标位置恰好放置一个陷阱，以捕获所有曾经经过该坐标的青蛙。

然而，孩子们不能离家太远，因此他们只能将陷阱放置在前 $n$ 个坐标点上（即坐标值在 $1$ 到 $n$ 之间的整数点），且他们不能将陷阱放在坐标点 $0$ 处（因为他们害怕青蛙）。

你能帮斯拉维克和米海找出：使用一个陷阱最多能捕获多少只青蛙？

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 $2 \cdot 10^5$.

输入的第一行包含一个整数 $t$（$1 \le t \le 100$）—— 表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \leq n \leq 2 \cdot 10^5$）—— 表示青蛙的数量，该数值也等于 Slavic 和 Mihai 可以移动以放置陷阱的距离。

每个测试用例的第二行包含 $n$ 个整数 $a_1, \ldots, a_n$（$1 \leq a_i \leq 10^9$）—— 表示对应青蛙的跳跃长度。

保证所有测试用例中 $n$ 的总和不超过 $2 \cdot 10^5$。

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

对于每个测试用例，输出一个整数——Slavic 和 Mihai 使用陷阱最多能捕获的青蛙数量。

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.

在第一个测试用例中，青蛙的跳跃路径如下：

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

因此，若斯拉维克和米海将陷阱设置在坐标 $4$ 处，他们可以捕获三只青蛙：青蛙 1、青蛙 2 和青蛙 4。可以证明，他们无法捕获更多青蛙。

在第二个测试用例中，斯拉维克和米海可将陷阱设置在坐标 $2$ 处，从而立即捕获全部三只青蛙。