A11639 | Game with Tokens

The first line contains a single integer $n$ ( $1<=n<=10^{5}$ ) — the number of black points.

The ( $i+1$ )-th line contains two integers $x_{i}$ , $y_{i}$ ( $-10^{5}<=x_{i},y_{i},<=10^{5}$ ) — the coordinates of the point where the $i$ -th black token is initially located.

It is guaranteed that initial positions of black tokens are distinct.

Print the number of points where the white token can be located initially, such that if both players play optimally, the black player wins.

In the first and second examples initial positions of black tokens are shown with black points, possible positions of the white token (such that the black player wins) are shown with white points.

The first example: 

The second example: 

In the third example the white tokens should be located in the inner square $2×2$ , to make the black player win.