CF1133D.Zero Quantity Maximization

普及/提高-

通过率：0%

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题目描述

You are given two arrays $a$ and $b$ , each contains $n$ integers.

You want to create a new array $c$ as follows: choose some real (i.e. not necessarily integer) number $d$ , and then for every $i \in [1, n]$ let $c_i := d \cdot a_i + b_i$ .

Your goal is to maximize the number of zeroes in array $c$ . What is the largest possible answer, if you choose $d$ optimally?

输入格式

The first line contains one integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the number of elements in both arrays.

The second line contains $n$ integers $a_1$ , $a_2$ , ..., $a_n$ ( $-10^9 \le a_i \le 10^9$ ).

The third line contains $n$ integers $b_1$ , $b_2$ , ..., $b_n$ ( $-10^9 \le b_i \le 10^9$ ).

输出格式

Print one integer — the maximum number of zeroes in array $c$ , if you choose $d$ optimally.

输入输出样例

输入#1
```
5
1 2 3 4 5
2 4 7 11 3
```
输出#1
```
2
```
输入#2
```
3
13 37 39
1 2 3
```
输出#2
```
2
```
输入#3
```
4
0 0 0 0
1 2 3 4
```
输出#3
```
0
```
输入#4
```
3
1 2 -1
-6 -12 6
```
输出#4
```
3
```

说明/提示

In the first example, we may choose $d = -2$ .

In the second example, we may choose $d = -\frac{1}{13}$ .

In the third example, we cannot obtain any zero in array $c$ , no matter which $d$ we choose.

In the fourth example, we may choose $d = 6$ .

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