# [ICPC2024 Xi'an I] Make Them Straight

## 题目描述

There is a sequence $a$ of non-negative integers of length $n$, the $i$-th element of it is $a_i(1\leq i\leq n)$.
A sequence is defined as 'good' if and only if there exists a non negative integer $k(0\leq k\leq 10^6)$ that satisfies the following condition:
$a_{i}=a_{1}+(i-1)k$ for all $1\leq i\leq n$.
To make this sequence 'good', for each $i(1\leq i\leq n)$, you can do nothing, or pay $b_i$ coin to replace $a_i$ with any non-negative integer.
The question is, what is the minimum cost to make this sequence 'good'.

## 输入输出格式

### 输入格式

The first line contains an integer $n(1\leq n\leq 2\times 10^5)$, described in the statement.
The second line contains $n$ integers $a_1,...,a_n(0\leq a_i\leq 10^6)$.
The third line contains $n$ integers $b_1,...,b_n(0\leq b_i\leq 10^6)$.

### 输出格式

One integer, the answer.

## 输入输出样例

### 输入样例 #1

```
5
1 4 3 2 5
1 1 1 1 1
```

### 输出样例 #1

`2`

### 输入样例 #2

```
5
1 4 3 2 5
1 9 1 1 1
```

### 输出样例 #2

`3`