In this problem we will discuss the problems of a modern Romeo and a
modern Juliet. You are asked to solve their problems so that they don’t have to
be a tragic pair like that of Shakespeare’s. As usual the family of Romeo and
Juliet have hostile relationships and so they are locked up in two different
places M and N. Two cannons are placed in location A and
two cannons are placed in location B. One cannon of location A is
aimed towards M and the other aimed towards N. The same thing
applies to the two cannons of location B. The M and N are
always on the opposite side of AB.
The movements of
the cannons, which are aimed at M, are interrelated; the angle between their directions is constant. So
angle CMD ((5 degree)
<= (angle CMD) < (80 degree)) is constant. Same rule applies to the other two
cannons. That’s angle ENF ((5 degree) <= (angle ENF) < (80 degree)) is also constant. All these things are shown in the
picture above. But another important thing is missing in the figure above is
that the locations N, A, M are always kept in a straight line. The reason behind this is very
strange. A robot has been hired to guard Romeo and Juliet. It has two eyes at
the opposite sides of its head and this robot is positioned in point A. To be precise, A, B and angle CMD and angle ENF are constants in one scenario and all other positions or values are
variable. Also remember that point M must always remain pointed by the two cannons. Same thing applies to
point N.
The problem is
that in starry nights Mr. Romeo sings the song “Blue Nights” of “Michael Learns to Rock” in a loud voice and both parents don’t want
Ms. Juliet to hear this song. So they want to place the houses (M and N) as far as possible preserving all the
constraints explained before. Your job is to measure this maximum distance
between M and N and inform it to Romeo, so that he can
decide whether he should sing or not or what should be his voice level.
Input
The input file contains several lines of
input. Each line contains six floating-point numbers, x1, y1, x2, and y2 (0<= x1, y1, x2, y2 <=10000) CMD,
ENF.
Here (x1, y1) is the coordinate of A, (x2, y2) is the coordinate of B, CMD is the angle
between the directions of cannons pointed towards M and ENF is the similar
value for point N. Input is terminated by end-of-file.
Output
For each line of input you should produce one line of output, which
contains a floating-point number F. F is the maximum possible distance between
Romeo’s house and Juliet’s house and it has three digits after the decimal
point.
Sample Input:
Sample Output
Shahriar Manzoor