CF1133D Zero Quantity Maximization

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?

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 $ ).

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

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 $ .