The Hunting#890
Barrister was interested in one of the methods for catching a Snark, which he read about in the manual 3/4Snark Hunting for Dummies in 21 days?. The Snark can be caught as follows: hunters land on the island at night from different directions, approaching a specific point. Then, some participants throw ropes to each other, forming a closed polygon with the Snark, presumably sleeping, inside. After that, the capture becomes a matter of technique, assuming everyone remains quiet.
Blagozvon wants to use this method with the minimum total length of rope. After all, the rope stock on the ship is limited, and after catching the Snark, it might be necessary to tie it up. Additionally, the maximum length to which a rope can be thrown is limited and equals . Calculate the minimum total length of rope needed, given the final coordinates of all participants and the coordinates of the Snark.
The first line contains the number of expedition members — an integer from to , and — the maximum length of a rope segment, a real number greater than and not exceeding . The next line contains a pair of coordinates for the Snark. Next, pairs of coordinates X_i, Y_i are given for the final positions of each expedition member, one pair per line.
Coordinates are given with decimal digits and do not exceed in absolute value.
Output the minimum length of rope required, accurate to decimal places.
Example 1