Little girls and boys on vessels deserve to have a spooky Christmas too! But delivering presents to moving targets can be a real hassle. The problem is that you have to fly your coffin-sleigh at where the vessel will be, instead of where it is now. The Pumpking King has asked you to write a program that helps him do that, and, given a set of vessels, plan a route that will take the minimum amount of time to complete.

You will be given the initial coordinates of the sleigh
and each vessel holding children. Each vessel is travelling
constantly at a heading and speed specified by the velocity
vector (`vx`, `vy`), meaning that after 1 hour
it would have travelled `vx` km in the `x`
direction and `vy` km in the `y`
direction (`vx` and `vy` may be negative).
The length of the
vector is the speed. Jack's Sleigh is capable of
travelling at a constant speed in any direction (assume
that acceleration and deceleration are instantaneous).
Jack must land on each vessel at least once, and it takes
5 minutes at each stop to unload the presents. The sleigh
can carry enough presents for all the children without having
to return to Pumpkin Town. All coordinates have km as units,
and all velocities and speeds have km/h as units.

Find the shortest time for Jack to deliver presents to each vessel and return to its starting location.

The input consists of a number of cases. Each case starts
with a line containing the integer `N` (`1 <= N <= 8`)
specifying the number of vessels. The next N lines contain
4 integers separated by a space: the initial (`x`,`y`) coordinates
of the `i-th` vessel and its velocity vector. The last line of
each case contains 3 integers specifying the initial (`x`,`y`)
coordinates of the sleigh and the speed of the sleigh. The
end of input is indicated by a case that starts with N = 0,
and this last case should not be processed. All input integers
have absolute value at most 1000. You may assume that the sleigh
travels at a greater speed than every vessel. Note that the paths
of the vessels may cross each other or even the sleigh's
initial location, but the captains will just make minor course
corrections to avoid collisions, so you don't have to take
this into account.

For each case, print its case number, a colon, followed by the minimum amount of time needed to complete the delivery in the format:

`Case a: b hour(s) c minute(s) d second(s)`

where `a`, `b`, `c`, `d` are
appropriate non-negative integers, and `c` and `d`
are at most 59. The time should be rounded up
to the next second.

Sample Input | Sample Output |
---|---|

5 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 0 0 1 3 1 2 3 4 2 2 40 23 7 8 22 10 0 0 50 0 |
Case 1: 15 hour(s) 0 minute(s) 0 second(s) Case 2: 5 hour(s) 59 minute(s) 50 second(s) |