gistfile1.cpp

#include <cstdio>
#define EPS (double)10e-2
#include <cmath>

using namespace std;

struct xy {
	int x, y;
};

int numHouses;
xy houses[1500];

int main() {
	scanf("%d", &numHouses);
	
	for (int n = 0; n < numHouses; n++) {
		scanf("%d %d", &houses[n].x, &houses[n].y);
	}
	
	int areas = 0;
	double runningTot = 0;
	
	for (int a = 0; a < numHouses - 2; a++) {
		for (int b = a + 1; b < numHouses - 1; b++) {
			for (int c = b + 1; c < numHouses; c++) {
				// Time for a F**K load of comp geom...
				
				double A1 = houses[b].y - houses[a].y;
				double B1 = houses[a].x - houses[b].x;
				
				double A1d = -B1;
				double B1d = A1;
				double C1d = A1d * ((houses[a].x + houses[b].x)/2) + B1d * ((houses[a].y + houses[b].y)/2);
				
				double A2 = houses[c].y - houses[b].y;
				double B2 = houses[b].x - houses[c].x;
				
				double A2d = -B2;
				double B2d = A2;
				double C2d = A2d * ((houses[b].x + houses[c].x)/2) + B2d * ((houses[b].y + houses[c].y)/2);
				
				double x = (B2d * C1d - B1d * C2d) / (A1d * B2d - A2d * B1d);
				double y = (A1d * C2d - A2d * C1d) / (A1d * B2d - A2d * B1d);
				
				double r = sqrt((x - houses[a].x) * (x - houses[a].x) + (y - houses[a].y) * (y - houses[a].y));
				
				int covered = 0;
				for (int n = 0; n < numHouses; n++) {
					if (r + EPS > sqrt((x - houses[n].x) * (x - houses[n].x) + (y - houses[n].y) * (y - houses[n].y))) {
						covered++;
					}
				}
				
				runningTot = (areas * runningTot + covered) / (areas + 1);
				areas++;
			}
		}
	}
	
	printf("%lf", runningTot);
	
	return 0;
}