Permutation Separation

题意翻译

给定一个序列$p$(为1~n的排列)，和这个序列每一个数所对应的花费a以及序列的长度n。 取一数$1\leq k<n$，将$p$序列分成两个序列，分别是$p_1,p_2,...,p_k$和$p_{k+1},p_{k+2},...,p_n$ 将两个序列的某些数移到另一个序列使得第一个序列的所有数小于第二个序列的所有数，注意如果其中一组为空，则满足此条件，移动$p_i$的花费是$a_i$

题目描述

You are given a permutation $ p_1, p_2, \dots , p_n $ (an array where each integer from $ 1 $ to $ n $ appears exactly once). The weight of the $ i $ -th element of this permutation is $ a_i $ . At first, you separate your permutation into two non-empty sets — prefix and suffix. More formally, the first set contains elements $ p_1, p_2, \dots , p_k $ , the second — $ p_{k+1}, p_{k+2}, \dots , p_n $ , where $ 1 \le k < n $ . After that, you may move elements between sets. The operation you are allowed to do is to choose some element of the first set and move it to the second set, or vice versa (move from the second set to the first). You have to pay $ a_i $ dollars to move the element $ p_i $ . Your goal is to make it so that each element of the first set is less than each element of the second set. Note that if one of the sets is empty, this condition is met. For example, if $ p = [3, 1, 2] $ and $ a = [7, 1, 4] $ , then the optimal strategy is: separate $ p $ into two parts $ [3, 1] $ and $ [2] $ and then move the $ 2 $ -element into first set (it costs $ 4 $ ). And if $ p = [3, 5, 1, 6, 2, 4] $ , $ a = [9, 1, 9, 9, 1, 9] $ , then the optimal strategy is: separate $ p $ into two parts $ [3, 5, 1] $ and $ [6, 2, 4] $ , and then move the $ 2 $ -element into first set (it costs $ 1 $ ), and $ 5 $ -element into second set (it also costs $ 1 $ ). Calculate the minimum number of dollars you have to spend.

输入输出格式

输入格式

The first line contains one integer $ n $ ( $ 2 \le n \le 2 \cdot 10^5 $ ) — the length of permutation. The second line contains $ n $ integers $ p_1, p_2, \dots , p_n $ ( $ 1 \le p_i \le n $ ). It's guaranteed that this sequence contains each element from $ 1 $ to $ n $ exactly once. The third line contains $ n $ integers $ a_1, a_2, \dots , a_n $ ( $ 1 \le a_i \le 10^9 $ ).

输出格式

Print one integer — the minimum number of dollars you have to spend.

输入输出样例

输入样例 #1

3
3 1 2
7 1 4

输出样例 #1

4

输入样例 #2

4
2 4 1 3
5 9 8 3

输出样例 #2

3

输入样例 #3

6
3 5 1 6 2 4
9 1 9 9 1 9

输出样例 #3

2