Given you a circle and a rectangular in a plane.

You task is to find out how many intersecting points between the circle and the rectangular?

Multiple cases ended with EOF.

The first line contains three integers x, y, r, which indicates the coordinates of the center of the circle and the radius of the circle.

The second line contains four integers x1, y1, x2, y2, which indicates the left-upper and the right-bottom coordinates of the rectangular. You can assume the edges of the rectangular are parallel to x-axis and y-axis, and all the integers are not exceeding 1000 by the absolute value.

Only one integer, which is the intersecting points between the circle and the rectangular.

0 0 1
0 2 2 0

2