# Problem C

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 |