CF1513F Swapping Problem

You are given 2 arrays $ a $ and $ b $ , both of size $ n $ . You can swap two elements in $ b $ at most once (or leave it as it is), and you are required to minimize the value $ $$$\sum_{i}|a_{i}-b_{i}|. $ $$$ Find the minimum possible value of this sum.

The first line contains a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ). The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le {10^9} $ ). The third line contains $ n $ integers $ b_1, b_2, \ldots, b_n $ ( $ 1 \le b_i \le {10^9} $ ).

Output the minimum value of $ \sum_{i}|a_{i}-b_{i}| $ .

In the first example, we can swap the first and fifth element in array $ b $ , so that it becomes $ [ 5, 2, 3, 4, 1 ] $ . Therefore, the minimum possible value of this sum would be $ |5-5| + |4-2| + |3-3| + |2-4| + |1-1| = 4 $ . In the second example, we can swap the first and second elements. So, our answer would be $ 2 $ .