Problem 102: Find the Germans

(U.M. ACM Runoffs 2001, problem 2)

Description

German spies are on the loose in Flatland, radioing vital secrets back to the fatherland. The flatlanders have built a radio direction finding system to catch them. The system consists of two tracking stations, called A and B, with A exactly 10 miles due North of B. When the german spies transmit, each of the tracking stations can quickly find out the direction that the transmission is coming from. Using this information, the Flatland Army can calculate the exact position of the spies by triangulation, catch them, and give them a good telling off.

Unfortunately, the radio direction finding equipment isn't very accurate. In fact there is a 5 degree error in the directions it reports, so if one of the stations reports the bearing to the spies as 90 degrees, the real direction could be anything from 85 to 95 degrees. The diagram shows the situation when station A reports a direction of 100 degrees and B reports 45 degrees. The angle from A between N and Y is 100 degrees, between N and Y0 is 95 degrees, and between N and Y1 is 105 degrees. The angle from B between N and X is 45 degrees, between N and X0 is 40 degrees, and between N and X1 is 50 degrees. The Germans could be anywhere in the shaded area delimited by the four lines A-Y0, A-Y1, B-X0, B-X1.

The Flatland Army needs to know the area of that shaded patch in square miles, so that it can decide how many soldiers to send on the search party.

Input Format

The input will consist of a sequence of lines, each containing two floating point numbers separated by spaces. The first number is the direction reported by station A, the second is the direction reported by station B. Directions are in degrees, with 0 being North, 90 East, 180 South, etc. The end of the input is represented by a line containing the two numbers "0.0 180.0", which should not be processed as a test case.

Output Format

For each test case, your program should print a single line reporting the area to be searched, in square miles, rounded to the nearest integer. Print the answer as an integer, with no decimal point.

If the area is greater than 100 square miles, print the string "Too Big" instead of the correct answer.

Limits

The equipment is always correct; there will be no inconsistent cases in which there is nowhere the spies could possibly be. For example, the inputs 90.0 270.0 which would mean that the Germans are East of A but West of B can not appear.

The two stations are at the Western edge of Flatland, so the directions they report will always be greater than 10 degrees and less than 170 degrees.

Sample Input

100.0 45.0
90.0 90.0
0.0 180.0

Sample Output

4
Too Big