Description

Little A has $n$ objects arranged in a row, each with volume $V$ and mass $M$. The volumes of the $n$ objects are within $1 \sim n$ and are all distinct, but the masses may be the same.

Now Little A needs to reorder the $n$ objects in increasing order of volume. His sorting method is: each operation swaps two objects. Each swap costs the sum of the masses of the two objects.

Little A wants to know the minimum total energy he must spend to sort the objects.

Input Format

The first line contains a positive integer $n$, the number of objects.

The second line contains $n$ positive integers; the $i$-th number is the volume of the $i$-th object from left to right.

The third line contains $n$ positive integers; the $i$-th number is the mass of the $i$-th object from left to right.

Output Format

Output a single integer, the minimum total energy Little A will spend.

3
1 3 2
2 2 3

5

Hint

Translated by ChatGPT 5