CF1365C.Rotation Matching

After the mysterious disappearance of Ashish, his two favourite disciples Ishika and Hriday, were each left with one half of a secret message. These messages can each be represented by a permutation of size $n$. Let's call them $a$ and $b$.

Note that a permutation of $n$ elements is a sequence of numbers $a_1, a_2, \ldots, a_n$, in which every number from $1$ to $n$ appears exactly once.

The message can be decoded by an arrangement of sequence $a$ and $b$, such that the number of matching pairs of elements between them is maximum. A pair of elements $a_i$ and $b_j$ is said to match if:

• $i = j$, that is, they are at the same index.
• $a_i = b_j$

His two disciples are allowed to perform the following operation any number of times:

• choose a number $k$ and cyclically shift one of the permutations to the left or right $k$ times.

A single cyclic shift to the left on any permutation $c$ is an operation that sets $c_1:=c_2, c_2:=c_3, \ldots, c_n:=c_1$ simultaneously. Likewise, a single cyclic shift to the right on any permutation $c$ is an operation that sets $c_1:=c_n, c_2:=c_1, \ldots, c_n:=c_{n-1}$ simultaneously.

Help Ishika and Hriday find the maximum number of pairs of elements that match after performing the operation any (possibly zero) number of times.

在阿西什神秘失踪后，他两位最喜爱的弟子伊希卡（Ishika）和赫里亚德（Hriday）各自获得了一半秘密信息。这两段信息均可表示为一个长度为 $n$ 的排列。我们将其分别记作 $a$ 和 $b$。

注意：$n$ 个元素的一个排列是指一个序列 $a_1, a_2, \ldots, a_n$，其中 $1$ 到 $n$ 中的每个整数恰好出现一次。

该信息可通过调整序列 $a$ 和 $b$ 的相对位置来解码，使得二者之间匹配的元素对数量达到最大。元素对 $a_i$ 与 $b_j$ 被称为匹配，当且仅当满足以下两个条件：

• $i = j$，即它们位于相同下标位置；
• $a_i = b_j$。

两位弟子被允许执行以下操作任意多次（包括零次）：

• 选择一个整数 $k$，并对其中一个排列向左或向右进行 $k$ 次循环移位。

对任一排列 $c$ 执行一次向左循环移位，是指同时执行如下赋值操作：
$c_1 := c_2,\; c_2 := c_3,\; \ldots,\; c_n := c_1$。

类似地，对任一排列 $c$ 执行一次向右循环移位，是指同时执行如下赋值操作：
$c_1 := c_n,\; c_2 := c_1,\; \ldots,\; c_n := c_{n-1}$。

请帮助伊希卡和赫里亚德求出：在执行任意次数（可能为零）上述操作后，所能达到的最大匹配元素对数量。

The first line of the input contains a single integer $n$ $(1 \le n \le 2 \cdot 10^5)$ — the size of the arrays.

The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$ $(1 \le a_i \le n)$ — the elements of the first permutation.

The third line contains $n$ integers $b_1$, $b_2$, ..., $b_n$ $(1 \le b_i \le n)$ — the elements of the second permutation.

输入的第一行包含一个整数 $n$ $(1 \le n \le 2 \cdot 10^5)$ —— 数组的大小。

第二行包含 $n$ 个整数 $a_1$, $a_2$, ..., $a_n$ $(1 \le a_i \le n)$ —— 第一个排列的元素。

第三行包含 $n$ 个整数 $b_1$, $b_2$, ..., $b_n$ $(1 \le b_i \le n)$ —— 第二个排列的元素。

Print the maximum number of matching pairs of elements after performing the above operations some (possibly zero) times.

执行上述操作若干次（可能为零次）后，打印元素匹配对的最大数量。

For the first case: $b$ can be shifted to the right by $k = 1$. The resulting permutations will be ${1, 2, 3, 4, 5}$ and ${1, 2, 3, 4, 5}$.

For the second case: The operation is not required. For all possible rotations of $a$ and $b$, the number of matching pairs won't exceed $1$.

For the third case: $b$ can be shifted to the left by $k = 1$. The resulting permutations will be ${1, 3, 2, 4}$ and ${2, 3, 1, 4}$. Positions $2$ and $4$ have matching pairs of elements. For all possible rotations of $a$ and $b$, the number of matching pairs won't exceed $2$.

第一种情况：$b$ 可以向右平移 $k = 1$ 位。得到的排列分别为 ${1, 2, 3, 4, 5}$ 和 ${1, 2, 3, 4, 5}$。

第二种情况：无需执行该操作。对于 $a$ 和 $b$ 的所有可能旋转，匹配元素对的数量均不超过 $1$。

第三种情况：$b$ 可以向左平移 $k = 1$ 位。得到的排列分别为 ${1, 3, 2, 4}$ 和 ${2, 3, 1, 4}$。位置 $2$ 和 $4$ 处的元素构成匹配对。对于 $a$ 和 $b$ 的所有可能旋转，匹配元素对的数量均不超过 $2$。