gadfadar3

When you can guess the solution, it's a shame to think at it.

After helping Don identify the intruders, he has put his trust in you. Therefore, to prevent the appearance of other intruders, Don has given you the number $N$ and two sequences $a_1, a_2, \cdots a_N$ and $b_1, b_2, \cdots b_N$ of natural numbers.

We denote the absolute value of $x$ by $|x|$.

For a sequence $x_1, x_2, \cdots x_k$ of integers, we define $f(x) =$ the minimum value of the sum $|x_1 - v| + |x_2 - v| + ... + |x_k - v|$ for an integer $v$.

You can form any sequence $c_1, c_2, \cdots c_N$ of natural numbers with the property that $c_i = a_i$ or $c_i = b_i$ for each $i$ from $1$ to $N$.

Task

To keep your job as an advisor to the organization, you need to find the minimum value of $f(c)$ for all the sequences $c$ that you can form.

Input data

The first line of the input file gadfadar3.in contains a non-zero natural number $N$. The second line contains $N$ natural numbers, separated by spaces, representing the sequence $a_1, a_2 \cdots a_N$. The third line contains $N$ natural numbers, separated by spaces, representing the sequence $b_1, b_2, \cdots b_N$.

Output data

The first line of the output file gadfadar3.out will contain a single integer, representing the minimum value of $f(c)$ among all the sequences $c$ that you can form.

Constraints and clarifications

• $1 \leq N \leq 300\ 000$
• $0 \leq a_i, b_i \leq 10^9$

Example 1

gadfadar3.in

5
2 6 10 2 5
3 9 3 1 2 

gadfadar3.out

5

Explanation

We can form the sequence $c = [2, 6, 3, 2, 2]$, and $f(c) = 5$ if we choose $v = 2$.

Example 2

gadfadar3.in

7
1 2 5 0 9 30 7
11 30 30 5 8 0 7

gadfadar3.out

17

Explanation

We can form the sequence $c = [1, 2, 5, 5, 8, 0, 7]$, and $f(c) = 17$ if we choose $v = 5$.