The distance from a line segment to a circle

Determine the distance between a specified circle and a line segment.

Input

The first line of the input provides the coordinates of the circle's center and its radius. The second line gives the coordinates of one endpoint of the line segment, while the third line provides the coordinates of the other endpoint. The endpoints of the segment are distinct. All coordinates are integers, with absolute values not exceeding 10^4. The circle's radius is a positive integer.

Output

Output a single real number representing the distance from the line segment to the circle, accurate to at least 6 decimal places.

Examples