input: Write a Python function that, given three positive integers n, x, and y, returns an array where each element represents the count of pairs of houses such that the shortest path between the two houses is exactly k streets. Houses are numbered from 1 to n, connected sequentially, with an extra street between houses numbered x and y. Note that x and y can be identical.
  
  Examples:
  >>> n = 3, x = 1, y = 3
  [6,0,0]
  >>> n = 5, x = 2, y = 4
  [10,8,2,0,0]
  >>> n = 4, x = 1, y = 1
  [6,4,2,0]
  
  Constraints:
  2 <= n <= 100
  1 <= x, y <= n
output: def count_pairs(n, x, y):
      counts = [0] * (n - 1)
      for i in range(1, n+1):
          for j in range(i+1, n+1):
              normal_dist = j - i
              extra_dist = min(abs(i - x) + 1 + abs(j - y), abs(i - y) + 1 + abs(j - x))
              distance = min(normal_dist, extra_dist)
              counts[distance - 1] += 1
      return counts