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ZOJ Problem Set - 3267
Total Solar Eclipse

Time Limit: 1 Second      Memory Limit: 32768 KB

A total solar eclipse is a spectacular natural phenomenon which occurs when the moon passes between the Sun and the Earth so that the Sun is fully or partially covered. Total solar eclipses are rare events. Although they occur somewhere on Earth every 18 months on average, it has been estimated that they recur at any given place only once every 370 years, on average.

CM is a amateur astronomers. According to his calculation results, a total solar eclipse will occur near his home. The shadow of the moon is a circle, it moves in a straight line which pass the point (0,0), and with a velocity vector (Vx,Vy), and its radius is R. CM has N observatories in the area. He can fly from any one to the others by plane at the speed of V. When he is in a observatory in the shadow of moon, he can see this rare phenomenon, (It means he cannot do observation in the plane). Before the total solar eclipse begin, he can stay in any observatory to wait. Now he want to know how long he can see total solar eclipse at most.

Note that (0,0) is just a point on the way of center of the shadow, the shadow have appeared before it moved to (0,0).


There are multiple test cases. The first line of input contains an integer T (T <= 100), indicating the number of test cases. Then T test cases follow.

The first line of each test case contains 3 integers N, R and V, (0<N<=100, 0<V, R<=10000). The second line has 2 integers Vx and Vy, (0<=Vx, Vy<=200, and Vx+Vy>0). The following N lines will show the coordinate of each observatory by 2 integers, Xi and Yi, (0<=Xi, Yi<=10000). There is a blank line between different test cases.


For each test case, output the longest time CM can see total solar eclipse (accurate to two fractional digits, the unit of time is minute).

Sample Input

4 1 2
1 0
1 0
2 0
3 0
4 0

5 2 2
1 0
1 0
2 0
3 0
4 0
2 2

Sample Output



Case 1: Stay at (1,0) for 2 min -- fly to (3,0) -- stay at (3,0) for 1 min -- fly to (4,0) -- stay at (4,0) for 0.5 min

Case 2: Stay at (1,0) for 4 min -- fly to (4,0) -- stay at (4,0) for 1.5 min

Author: HUANG, Minzhi
Source: ZOJ Monthly, November 2009
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