Stall Shuffle

# Stall Shuffle ## Problem Bessie is organizing a barn dance, and she needs to assign each cow to a stall. There are N cows and N stalls, each at a specific position on the barn floor. Each cow must be assigned to exactly one stall, and each stall can hold exactly one cow. The cost of assigning a cow to a stall is the absolute distance between their positions. Your goal is to find an assignment that minimizes the total distance traveled by all cows. ## Input The first line contains a single integer N (1 ≤ N ≤ 100,000), the number of cows and stalls. The second line contains N integers representing the positions of the cows. The third line contains N integers representing the positions of the stalls. ## Output Print a single integer: the minimum total distance required to assign all cows to stalls. ## Constraints - 1 ≤ N ≤ 100,000 - 0 ≤ position ≤ 1,000,000 ## Sample **Input:** ``` 3 1 5 9 2 6 8 ``` **Output:** ``` 3 ``` **Explanation:** Sort both arrays: cows = [1, 5, 9], stalls = [2, 6, 8]. Assign in sorted order: - Cow at position 1 → Stall at position 2: distance = |1 - 2| = 1 - Cow at position 5 → Stall at position 6: distance = |5 - 6| = 1 - Cow at position 9 → Stall at position 8: distance = |9 - 8| = 1 Total distance = 1 + 1 + 1 = 3