count-covered-buildings

You are given a positive integer n, representing an n x n city. You are also given a 2D grid buildings, where buildings[i] = [x, y] denotes a unique building located at coordinates [x, y].

A building is covered if there is at least one building in all four directions: left, right, above, and below.

Return the number of covered buildings.

Example 1:

Input: n = 3, buildings = [[1,2],[2,2],[3,2],[2,1],[2,3]]

Output: 1

Explanation:

• Only building [2,2] is covered as it has at least one building:
  
  
  
  
  • above ([1,2])
  
  
  • below ([3,2])
  
  
  • left ([2,1])
  
  
  • right ([2,3])
  
  
  
  


• Thus, the count of covered buildings is 1.

Example 2:

Input: n = 3, buildings = [[1,1],[1,2],[2,1],[2,2]]

Output: 0

Explanation:

• No building has at least one building in all four directions.

Example 3:

Input: n = 5, buildings = [[1,3],[3,2],[3,3],[3,5],[5,3]]

Output: 1

Explanation:

• Only building [3,3] is covered as it has at least one building:
  
  
  
  
  • above ([1,3])
  
  
  • below ([5,3])
  
  
  • left ([3,2])
  
  
  • right ([3,5])
  
  
  
  


• Thus, the count of covered buildings is 1.

Constraints:

• 2 <= n <= 105


• 1 <= buildings.length <= 105


• buildings[i] = [x, y]


• 1 <= x, y <= n


• All coordinates of buildings are unique.