Time limit : 1 s | Memory limit : 32 mb |
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Submitted : 1336 | Accepted : 408 |

Assume the coasting is an infinite straight line. Land is in one side of coasting, sea in the other. Each small island is a point locating in the sea side. And any radar installation, locating on the coasting, can only cover d distance, so an island in the sea can be covered by a radius installation, if the distance between them is at most d.

We use Cartesian coordinate system, defining the coasting is the x-axis. The
sea side is above x-axis, and the land side below. Given the position of each
island in the sea, and given the distance of the coverage of the radar installation,
your task is to write a program to find the minimal number of radar installations
to cover all the islands. Note that the position of an island is represented
by its x-y coordinates.

The input is terminated by a line containing pair of zeros.

For each test case output one line consisting of the test case number followed by the minimal number of radar installations needed. "-1" installation means no solution for that case.

3 2 1 2 -3 1 2 1 1 2 0 2 0 0

Case 1: 2 Case 2: 1