Spreading Black on an Infinite Grid

In an infinite square grid (with vertices at integer coordinates), there are initially n black vertices and all the other vertices are white. Every second, all internal white points turn black simultaneously, and this process continues until no internal white point remains. A white vertex P(x,y) is called an internal white point if and only if both of the following conditions hold:

• There exist two black vertices on the same horizontal line as P, one strictly to its left and one strictly to its right. In other words, there exist x₁ and x₂ with x₁ < x < x₂ such that \(P(x₁,y)\) and \(P(x₂,y)\) are black.
• There exist two black vertices on the same vertical line as P, one strictly below and one strictly above. That is, there exist y₁ and y₂ with y₁ < y < y₂ such that \(P(x,y₁)\) and \(P(x,y₂)\) are black.

Your task is to compute the total number of black vertices in the final configuration after the process stops. Note that once a vertex becomes black, it remains black forever.

Note: Any formulas are written in LaTeX format. For example, the horizontal condition is: $$\exists\; x_1,x_2 \text{ such that } x_1 < x < x_2 \text{ and } P(x_1,y),\; P(x_2,y) \text{ are black.}$$

inputFormat

The first line contains an integer n representing the number of initially black vertices. Each of the following n lines contains two space‐separated integers x and y representing the coordinates of a black vertex.

outputFormat

Output a single integer which is the total number of black vertices in the grid after the process stops.

sample

4
0 0
2 0
0 2
2 2

4