And then the King said: You fought bravely, Knight, and your deed will not be forgotten for centuries. For your valor I grant you this castle and the lands around it. Things rush me, and I can not take you to the castle. Therefore, I will give you the way from this place to the castle. Now go and come back after the deadline. - as it is written in the Green Book of Years.
In addition, it is known from the Green Book of Years that the lands with which the castle was granted were in the shape of a circle. The king was very wise and, in order to avoid unnecessary proceedings regarding the right to land, always granted only areas of land on the map that have a convex shape.
Recently, historians have had information about where the castle was located and where this historical conversation took place. They want to know how much land did the Knight get on the assumption that the road to the castle was perfectly straight.
The following figure shows in light gray the territory originally granted to the knight, and in dark gray, the one that came to him as a result of the king giving him the way.
The first line of the input contains two floating-point numbers: xk and yk - the coordinates of the place where the dialogue took place. The second line contains three floating-point numbers: xc, yc and rc - the coordinates of the castle and the radius of the circle that bounds the land granted with it.
Print one floating-point number - the area of the land obtained by the Knight, with an accuracy of at least three characters after the decimal point.
2 1 1
2 3 5
1 2 1
Note: A triangle may not include the entire semicircle if it is too close to the center, as in the test I have given.