Treasure Chests

Problem Description

On the $X$-axis there are $N$ keys and $N$ treasure chests. The player starts at position $x = 0$ and may move one step to $x + 1$ or $x - 1$ each turn.

When the player reaches a position that has a key, they may pick it up. When the player reaches a position that has a treasure chest, they may choose to use a key to open it.

Find the minimum number of steps the player needs to open all the treasure chests.

Note: a position may simultaneously contain both a chest and a key, but no position contains more than one chest or more than one key.

Input Format

The first line contains a positive integer $N$, the number of chests and keys.

The next line contains $N$ positive integers $b_1, b_2, \dots, b_n$, where $b_i$ is the position of chest $i$.

The third line contains $N$ positive integers $c_1, c_2, \dots, c_n$, where $c_i$ is the position of key $i$.

Output Format

One line containing a positive integer: the answer.

Sample Input 1

4
1 6 7 12
3 5 10 11

Sample Output 1

21

Sample Input 2

2
1 2
1 1000000000

Sample Output 2

1999999998

Constraints

For all data, $1 \le N \le 10^5$, $1 \le b_i, c_i \le 10^9$, with $b_1 < b_2 < \dots < b_n$ and $c_1 < c_2 < \dots < c_n$.