QUESTION:
Alice is playing a board game. In this game, Alice has been given an array A of size N, containing integer coordinate points ( xiand yi) and in order to win this game, Alice has to cover all the given points on the board. In one step, Alice can move his player either up, down, right, or left by any distance (i.e if there are points on (1, 1) and (1, 4), Alice can move her player from (1, 1) to (1, 4) in one step). Alice noticed that using this way it is impossible for her to cover all the points, therefore he decided to add some extra points on the board.

Help Alice cover all points given by adding a minimum number of extra points.

Example:
Given,
N = 2
A = [ [1,2] , [2,1] ]
Approach

As Alice can not move from points (1, 2) to (2, 1) according to the given constraints.
Alice can add a point (1, 1)
So now, Alice will move from (1, 2) -> (1, 1) -> (2, 1) covering all the given points.
Thus the answer is 1.

Example:
Given,
N = 2
A = [ [2, 1] , [4, 1] ]
Approach

Alice can easily move from (2, 1 -> 4, 1) just by moving right, without adding any extra point.
Thus, the answer is 0.