Estate
And then the King said: "You have fought bravely, Knight, and your deeds will be remembered through the ages. For your valor, I grant you this castle and the lands surrounding it. However, you have violated the strictest of prohibitions—fighting without a Hat on your head like savages, which could have allowed evil spirits to possess you. According to the law of our ancestors, those like you must send their souls to the heavens until any evil that might have taken root is expelled. Yet, I have the power to spare you, for I believe you are strong enough to resist this evil. You must promise not to leave your land for three months and three days, and every day for three hours after sunset, pray to the good spirits for protection. Urgent matters call me away, and I cannot accompany you to the castle, so I also grant you the road from here to the castle. Now go, and return at the end of the term."
- as recorded in the Green Book of Years.
Additionally, the Green Book of Years reveals that the lands granted with the castle were circular. The King, being very wise, always granted lands that were convex on the map to avoid disputes over land rights. Recently, historians have discovered the location of the castle and where this historic conversation took place. They are interested in determining the area of the land plot received by the Knight, assuming the road to the castle was perfectly straight.
Input
The first line of the input file contains two real numbers x_k and y_k—the coordinates of the place where the dialogue occurred. The second line contains three real numbers x_c, y_c, and r_c—the coordinates of the castle and the radius of the circle enclosing the granted land. All numbers in the input file do not exceed 10000 in absolute value.
Output
In the output file, print one real number—the area of the land plot received by the Knight, with an accuracy of at least three decimal places.
In the illustration, the territory initially granted to the Knight is shown in light gray, and the additional land granted with the road is shown in dark gray.