Saurv4u and Daenerys were a loving couple. But due to 'Irreconcilable Differences', the couple is thinking of 'breaking' up.

To measure the depth of the differences $D$, Saurv4u has shaded the inner region of the rectangles (The sides of the rectangle are parallel to the Cartesian axes and the center of rectangle is origin) such that the perimeter of rectangle is less than $4*a$ , while Daenerys has shaded (on the same plane) the inner region of all the rectangles (The sides of the rectangle are parallel to the Cartesian axes and the center of rectangle is origin) such that the area of rectangle is less than $\frac{3*a*a}{4}$.

The measure of the depth of differences $D$ is the common area bounded by the two.

Given the value of $a = 1000$, find the value of $\lfloor\frac{D}{100}\rfloor$

$\lfloor x \rfloor$ means the greatest integer $<= x$