Maximizer

Maximizer has two permutations $A=\[a\_1,a\_2,\cdots,a\_N]$ and $B=\[b\_1,b\_2,\cdots,b\_N]$. Both $A, B$ have length $N$ and consists of distinct integers from $1$ to $N$. 

Maximizer wants to maximize the sum of differences of each element, $\sum\_{i=1}^{N} |a\_i - b\_i|$. But he can only swap two adjacent elements in $A$. Precisely, he can only swap $a\_i$ and $a\_{i+1}$ for some $i$ from $1$ to $N-1$. He can swap as many times as he wants.

What is the minimum number of swaps required for maximizing the difference sum?

The first line contains an integer $N$. ($1 \leq N \leq 250\\,000$)

The second line contains $N$ integers $a\_1,a\_2,\cdots,a\_N$ ($1 \leq a\_i \leq N$).

The third line contains $N$ integers $b\_1,b\_2,\cdots,b\_N$ ($1 \leq b\_i \leq N$).

Each of $\[a\_1,a\_2,\cdots,a\_N]$ and $\[b\_1,b\_2,\cdots,b\_N]$ is a permutation. In other words, it is consisted of distinct integers from $1$ to $N$.

Print an integer, the minimum number of swaps required for maximizing the difference sum.