Lawn#459
Farmer Ivan has been taking care of his lawn since his youth. The lawn can be considered as an infinite plane where, at every point with integer coordinates, a single tuft of grass grows.
One Sunday, Ivan used his lawn mower to cut a certain rectangular area of the lawn. The sides of this rectangle are parallel to the coordinate axes, and its two opposite vertices have coordinates (X_1, Y_1) and (X_2, Y_2). Note that the tufts of grass located on the border of the rectangle are also considered mowed.
Satisfied with the result, Ivan bought and installed a sprinkler on the lawn. The sprinkler was placed at the point (X_3, Y_3) and has a radius . Thus, the sprinkler waters all tufts of grass whose distance to the point (X_3, Y_3) does not exceed .
Everything was fine, but Ivan became interested in the following question: how many tufts of grass were both mowed and watered this Sunday?
Write a program that will answer Ivan's question.
The first line contains four integers X_1, Y_1, X_2, Y_2 (-10^5 \le X_1 < X_2 \le 10^5; -10^5 \le Y_1 < Y_2 \le 10^5).
The second line contains three integers X_3, Y_3, (-10^5 \le X_3, Y_3 \le 10^5; 1 \le R \le 10^5).
Output the number of tufts of grass that were both mowed and watered.
Illustration for the example
Example 1