Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Permutation Separation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

Input

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 $$$a_1, a_2, \dots , a_n$$$ ($$$1 \le a_i \le 10^9$$$).

Output

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

Examples

Input

3 3 1 2 7 1 4

Output

4

Input

4 2 4 1 3 5 9 8 3

Output

3

Input

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

Output

2

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/09/2020 21:44:06 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|