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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 consists of several test cases. The first line of each case contains two integers n (1 ≤ n ≤ 1000) and d, where n is the number of islands in the sea and d is the distance of coverage of the radar installation. This is followed by n lines each containing two integers representing the coordinate of the position of each island. Then a blank line follows to separate the cases.
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