Global Roaming

A great deal of today's mobile communication relies on having a direct line of sight to a satellite. For communication providers it is therefore crucial to know where their services are available.

You must identify the locations that have a direct line of sight to a given satellite; that is, the satellite must be above the horizon. To simplify the computation, assume that the earth is a perfect sphere with a radius of $6378$ km (mountains will be added next year...). The satellite is treated as a point-like object above the earth's surface.

The input consists of several test cases. The first line of each test case contains the number of locations $n$ to be checked, followed by the position of the satellite: its latitude, its longitude (both in degrees), and its height (in km) above the earth's surface.

Each of the following $n$ lines describes one location on the earth's surface: the location's label (a string of fewer than $60$ printable ASCII characters containing no whitespace) followed by its latitude and longitude (both in degrees).

The input is terminated by a line with $n=0$.

For each test case, first print a line of the form Test case k:, where $k$ is the test-case number starting from $1$. Then print the labels of the locations from which the satellite is visible, one per line, in the same order as they appear in the input.

Separate two consecutive test cases with a single blank line.