[ICPC2024 Xi'an I] Make Them Straight

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'.

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 $b_1,...,b_n(0\leq b_i\leq 10^6)$.

One integer, the answer.

5
1 4 3 2 5
1 1 1 1 1

2

5
1 4 3 2 5
1 9 1 1 1

3