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2021-09-12 08:15 AKDT

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2021-09-12 09:00 AKDT
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Problem E
Hotter Colder

The children’s game Hotter Colder is played as follows. Player A leaves the room while player B hides an object somewhere in the room. Player A re-enters at position $(0,0)$ and then visits various other positions about the room. When player A visits a new position, player B announces “Hotter” if this position is closer to the object than the previous position; player B announces “Colder” if it is farther and “Same” if it is the same distance.

Input

Input consists of up to $50$ lines, each containing an $x,y$ coordinate pair followed by “Hotter”, “Colder”, or “Same”. Each pair represents a position within or at the boundary of the room, which may be assumed to be a square with opposite corners at $(0,0)$ and $(10,10)$. The coordinates are given with at most $2$ decimals after the decimal point.

Output

For each line of input print a line giving the total area of the region in which the object may have been placed, accurate to an absolute or relative error of at most $10^{-6}$. If there is no such region, we consider the answer to be $0$.

Sample Input 1 Sample Output 1
10.0 10.0 Colder
10.0 0.0 Hotter
0.0 0.0 Colder
10.0 10.0 Hotter
50
37.500000
12.50
0.0