Technogoblet of Fire

题意翻译

m 所学校参加比赛,每个学校只有一名学生参加。 这些学校总共有 n 名学生。在比赛开始前,所有的学生都把自己的名字和学校的名字提交了。之后,老师从每所学校中选出实力最强的学生参加。 Arkady 是一个黑客,他希望某些学校被选中。不幸的是,并不是所有的学校都是最强的,但阿卡迪可以编造一些新的学校名称,并用这些名称替换一些名称。每个化名不能重复使用一次。在这种情况下,也会选择那些组成学校的最强学生。 你知道每个学生和他们就读的学校的力量。计算 Arkady 必须补足的学校的最小数量,这样 k 所选择的学校将被选中。

题目描述

Everybody knows that the $ m $ -coder Tournament will happen soon. $ m $ schools participate in the tournament, and only one student from each school participates. There are a total of $ n $ students in those schools. Before the tournament, all students put their names and the names of their schools into the Technogoblet of Fire. After that, Technogoblet selects the strongest student from each school to participate. Arkady is a hacker who wants to have $ k $ Chosen Ones selected by the Technogoblet. Unfortunately, not all of them are the strongest in their schools, but Arkady can make up some new school names and replace some names from Technogoblet with those. You can't use each made-up name more than once. In that case, Technogoblet would select the strongest student in those made-up schools too. You know the power of each student and schools they study in. Calculate the minimal number of schools Arkady has to make up so that $ k $ Chosen Ones would be selected by the Technogoblet.

输入输出格式

输入格式


The first line contains three integers $ n $ , $ m $ and $ k $ ( $ 1 \le n \le 100 $ , $ 1 \le m, k \le n $ ) — the total number of students, the number of schools and the number of the Chosen Ones. The second line contains $ n $ different integers $ p_1, p_2, \ldots, p_n $ ( $ 1 \le p_i \le n $ ), where $ p_i $ denotes the power of $ i $ -th student. The bigger the power, the stronger the student. The third line contains $ n $ integers $ s_1, s_2, \ldots, s_n $ ( $ 1 \le s_i \le m $ ), where $ s_i $ denotes the school the $ i $ -th student goes to. At least one student studies in each of the schools. The fourth line contains $ k $ different integers $ c_1, c_2, \ldots, c_k $ ( $ 1 \le c_i \le n $ ) — the id's of the Chosen Ones.

输出格式


Output a single integer — the minimal number of schools to be made up by Arkady so that $ k $ Chosen Ones would be selected by the Technogoblet.

输入输出样例

输入样例 #1

7 3 1
1 5 3 4 6 7 2
1 3 1 2 1 2 3
3

输出样例 #1

1

输入样例 #2

8 4 4
1 2 3 4 5 6 7 8
4 3 2 1 4 3 2 1
3 4 5 6

输出样例 #2

2

说明

In the first example there's just a single Chosen One with id $ 3 $ . His power is equal to $ 3 $ , but in the same school $ 1 $ , there's a student with id $ 5 $ and power $ 6 $ , and that means inaction would not lead to the latter being chosen. If we, however, make up a new school (let its id be $ 4 $ ) for the Chosen One, Technogoblet would select students with ids $ 2 $ (strongest in $ 3 $ ), $ 5 $ (strongest in $ 1 $ ), $ 6 $ (strongest in $ 2 $ ) and $ 3 $ (strongest in $ 4 $ ). In the second example, you can change the school of student $ 3 $ to the made-up $ 5 $ and the school of student $ 4 $ to the made-up $ 6 $ . It will cause the Technogoblet to choose students $ 8 $ , $ 7 $ , $ 6 $ , $ 5 $ , $ 3 $ and $ 4 $ .