A16161. We Were Both Children
编程题
普及/提高-
知识点
题目描述
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?
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?
输入格式
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 $2 \cdot 10^5$ .
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 $2 \cdot 10^5$ .
输出格式
For each test case output a single integer — the maximum number of frogs Slavic and Mihai can catch using a trap.
输入输出样例
输入 #1
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
输出 #1
3 3 3 5 0 4 4
说明/提示
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.
- 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.