Competitions

# Titanic

It is a historical fact that during the legendary voyage of "Titanic" the wireless telegraph machine had delivered 6 warnings about the danger of icebergs. Each of the telegraph messages described the point where an iceberg had been noticed. The first five warnings were transferred to the captain of the ship. The sixth one came late at night and a telegraph operator did not notice that the coordinates mentioned were very close to the current ship's position.

Write a program that will warn the operator about the danger of icebergs!

Input

The input messages are of the following format:

Here <n> is a positive integer, <HH>:<MM>:<SS> is the time of the message reception, <X1>^<X2>'<X3>" <NL/SL> and <Y1>^<Y2>'<Y3>" <EL/WL> means "X1 degrees X2 minutes X3 seconds of North (South) latitude and Y1 degrees Y2 minutes Y3 seconds of East (West) longitude."

Output

Your program should print to the output message in the following format:

The distance to the iceberg: <s> miles.

Where <s> should be the distance between the ship and the iceberg, (that is the length of the shortest path on the sphere between the ship and the iceberg). This distance should be printed up to (and correct to) two decimal digits. If this distance is less than (but not equal to!) 100 miles the program should print one more line with the text:

DANGER!

Time limit 1 second
Memory limit 16 MiB
Input example #1
Message #513.
Current ship�s coordinates are
41^46'00" NL
and 50^14'00" WL.
An iceberg was noticed at
41^14'11" NL
and 51^09'00" WL.
===

Output example #1
The distance to the iceberg: 52.04 miles.
DANGER!

Author Evgeny Shtykov
Source 1999 III Ural Collegiate Programming Contest, Ekaterinburg, March 19 - 20, Problem C