Given a set of N integer points on the Cartesian plane. Your task is to find an integer point satisfying its sum of distances to N given points (S) is minimum.

------ Input ------ 

There are several test cases (fifteen at most), each formed as follows:
The first line contains a positive integer N (N ≤ 2,000).
N lines follow, each containing a pair of integers (each having an absolute value of 10^{9} at most) describing coordinates of a given point.

The input is ended with N = 0.

------ Output ------ 

For each test case, output on a line a real number (with exactly 6 decimal places) which is the respective minimum sum S found.

----- Sample Input 1 ------ 
3
1 1
2 2
3 3
5
1 4
2 3
5 2
3 5
4 1
0

----- Sample Output 1 ------ 
2.828427
9.640986

Difficulty: MEDIUM_HARD

Solutions:
from math import sqrt, floor, ceil
N = int(input())
while N > 0:
	x = []
	y = []
	for i in range(N):
		s = input().split()
		x.append(float(s[0]))
		y.append(float(s[1]))
	xn = 42.0
	yn = 42.0
	xo = 0.0
	yo = 0.0
	disto = 42.0
	distn = 41.0
	for it in range(25):
		xn = 0.0
		yn = 0.0
		for i in range(N):
			di = sqrt((x[i] - xo) ** 2 + (y[i] - yo) ** 2)
			if di < 1e-12:
				di = 1e-12
			xn += x[i] / di
			yn += y[i] / di
		d = 0.0
		for i in range(N):
			di = sqrt((x[i] - xo) ** 2 + (y[i] - yo) ** 2)
			if di < 1e-12:
				di = 1e-12
			d += 1.0 / di
		xn /= d
		yn /= d
		xo = xn
		yo = yn
		disto = distn
		distn = 0.0
		for i in range(N):
			distn += sqrt((x[i] - xo) ** 2 + (y[i] - yo) ** 2)
	dist = [0.0, 0.0, 0.0, 0.0]
	for i in range(N):
		dist[0] += sqrt((x[i] - floor(xo)) ** 2 + (y[i] - floor(yo)) ** 2)
	for i in range(N):
		dist[1] += sqrt((x[i] - floor(xo)) ** 2 + (y[i] - ceil(yo)) ** 2)
	for i in range(N):
		dist[2] += sqrt((x[i] - ceil(xo)) ** 2 + (y[i] - floor(yo)) ** 2)
	for i in range(N):
		dist[3] += sqrt((x[i] - ceil(xo)) ** 2 + (y[i] - ceil(yo)) ** 2)
	print('{0:.6f}'.format(min(dist)))
	N = int(input())