An unusual painter is painting an unusual picture. We can imagine his canvas as a coordinate plane. It is white at the beginning of the creation of the picture, and the painter will create the picture by repeating the following procedure $N$ times:

• The painter chooses arbitrary integer coordinates $x$ and $y$.
• Then, he finds the largest square with sides parallel to the coordinate axes, centered at the point $(x, y)$, such that the entire square on the existing picture is of the same color. However, the side length of the square must not be greater than the given number $D$.
• The painter then repaints the entire square black if it was white, or white if it was black.

The images show the first example test case

Write a program that will calculate the total area of the picture painted black after the picture is finished. This area does not include black color that was later covered by white color.

Input

The first line contains two natural numbers, $N$ and $D$ ($1 \le N \le 1000$, $2 \le D \le 10^6$), the number of squares the painter will draw, and the maximum allowed side length of the square. The number $D$ will be even.

In each of the following $N$ lines, there are two integers $X$ and $Y$ ($-10^6 \le X, Y \le 10^6$), the coordinates of the center of each square.

Output

In the first and only line of output, print the total area of the picture painted black.

Examples

Input 1

4 10
8 12
8 9
8 19
8 14

Output 1

64

Input 2

2 1000000
0 0
0 0

Output 2

0

Input 3

6 200
0 0
-100 -100
-100 105
0 101
100 105
0 0

Output 3

204