Optical Experiment

题意翻译

### 题目描述 如图所示，有 $n$ 条光线从矩形上边的 $n$ 个洞射入矩形区域后从下边的 $n$ 个洞射出。 已知从第 $i$ 个洞射入的光线编号为 $x_i$，从第 $i$ 个洞射出的光线编号为 $y_i$，要求从这 $n$ 条光线中选出最多数量的光线，使得这些光线中任意两条都会在矩形区域内相交。 ### 输入格式 第一行一整数 $n$ $(1 \leq n \leq 10^6)$ 表示光线数量，之后 $n$ 个整数 $x_i$ 表示从第 $i$ 个洞射入的光线编号，最后 $n$ 个整数 $y_i$ 表示从第 $i$ 个洞射出的光线编号。 ### 输出格式 输出所选光线数量最大值。

题目描述

Professor Phunsuk Wangdu has performed some experiments on rays. The setup for $ n $ rays is as follows. There is a rectangular box having exactly $ n $ holes on the opposite faces. All rays enter from the holes of the first side and exit from the holes of the other side of the box. Exactly one ray can enter or exit from each hole. The holes are in a straight line. Professor Wangdu is showing his experiment to his students. He shows that there are cases, when all the rays are intersected by every other ray. A curious student asked the professor: "Sir, there are some groups of rays such that all rays in that group intersect every other ray in that group. Can we determine the number of rays in the largest of such groups?". Professor Wangdu now is in trouble and knowing your intellect he asks you to help him.

输入输出格式

输入格式

The first line contains $ n $ ( $ 1<=n<=10^{6} $ ), the number of rays. The second line contains $ n $ distinct integers. The $ i $ -th integer $ x_{i} $ ( $ 1<=x_{i}<=n $ ) shows that the $ x_{i} $ -th ray enters from the $ i $ -th hole. Similarly, third line contains $ n $ distinct integers. The $ i $ -th integer $ y_{i} $ ( $ 1<=y_{i}<=n $ ) shows that the $ y_{i} $ -th ray exits from the $ i $ -th hole. All rays are numbered from $ 1 $ to $ n $ .

输出格式

Output contains the only integer which is the number of rays in the largest group of rays all of which intersect each other.

输入输出样例

输入样例 #1

5
1 4 5 2 3
3 4 2 1 5

输出样例 #1

3

输入样例 #2

3
3 1 2
2 3 1

输出样例 #2

2

说明

For the first test case, the figure is shown above. The output of the first test case is 3, since the rays number 1, 4 and 3 are the ones which are intersected by each other one i.e. 1 is intersected by 4 and 3, 3 is intersected by 4 and 1, and 4 is intersected by 1 and 3. Hence every ray in this group is intersected by each other one. There does not exist any group containing more than 3 rays satisfying the above-mentioned constraint.