Problem:
The Closest Circle

You are given N non-overlapping circles in xy-plane. The radius of each circle varies, but the radius of
the largest circle is not double longer than that of the smallest.

Figure 1: The Sample Input

The distance between two circles C1 and C2 is given by the usual formula

where (xi, yi ) is the coordinates of the center of the circle Ci, and ri is the radius of Ci, for i = 1, 2.

Your task is to write a program that finds the closest pair of circles and print their distance.

Input

The input consists of a series of test cases, followed by a single line only containing a single zero, which
indicates the end of input.

Each test case begins with a line containing an integer N (2 ≤ N ≤ 100000), which indicates the number
of circles in the test case. N lines describing the circles follow. Each of the N lines has three decimal
numbers R, X, and Y. R represents the radius of the circle. X and Y represent the x- and y-coordinates of
the center of the circle, respectively.

Output

For each test case, print the distance between the closest circles. You may print any number of digits
after the decimal point, but the error must not exceed 0.00001.

Sample Input

4
1.0 0.0 0.0
1.5 0.0 3.0
2.0 4.0 0.0
1.0 3.0 4.0
0

Output for the Sample Input

0.5

Solution in JAVA (judge verdict: Memory Limit Exceeded)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
	Scanner sc = new Scanner(System.in);

	void run() {
		for (;;) {
			int N = sc.nextInt();
			if (N == 0) {
				return;
			}
			Circle[] info = new Circle[N];
			for (int i = 0; i < N; i++) {
				info[i] = new Circle(sc.nextDouble(), sc.nextDouble(),
						sc.nextDouble());
			}
			double min = Integer.MAX_VALUE;
			double dist = 0;
			for (int i = 0; i < N; i++) {
				for (int j = i + 1; j < N; j++) {
					dist = Math.hypot(info[i].x - info[j].x, info[i].y
							- info[j].y);
					min = Math.min(min, dist - info[i].r - info[j].r);
				}
			}
			System.out.println(min);
		}
	}

	public static void main(String[] args) {
		new Main().run();
	}

	void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	class Circle {
		double r;
		double x;
		double y;

		Circle(double r, double x, double y) {
			this.r = r;
			this.x = x;
			this.y = y;
		}
	}
}