Time Limit : 1 Second
Memory Limit : 128 MB
Submission: 161
Solved: 38
Description


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?


Input


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.


Output


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


sample input
0 0 1
0 2 2 0
sample output
2
hint
source
ACman
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